Abstract

Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon’s spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. H. Bennett Ch and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.
  2. P. W. Shor and J. Preskill, “Simple proof of security of the bb84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
    [Crossref] [PubMed]
  3. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
    [Crossref]
  4. T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
    [Crossref] [PubMed]
  5. C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
    [Crossref]
  6. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
    [Crossref] [PubMed]
  7. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref] [PubMed]
  8. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
    [Crossref]
  9. M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
    [Crossref]
  10. H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
    [Crossref]
  11. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
    [Crossref] [PubMed]
  12. I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
    [Crossref] [PubMed]
  13. F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).
  14. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
    [Crossref]
  15. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
    [Crossref]
  16. G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40, 4887 (2015).
    [Crossref] [PubMed]
  17. P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24, 15143 (2016).
    [Crossref] [PubMed]
  18. G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
    [Crossref] [PubMed]
  19. J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
    [Crossref]
  20. C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
    [Crossref]
  21. G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
    [Crossref] [PubMed]
  22. B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
    [Crossref]
  23. B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
    [Crossref]
  24. B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
    [Crossref]
  25. A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
    [Crossref]
  26. M. Huber and M. Pawłowski, “Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement,” Phys. Rev. A 88, 032309 (2013).
    [Crossref]
  27. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
    [Crossref]
  28. Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
    [Crossref]
  29. M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
    [Crossref] [PubMed]
  30. C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
    [Crossref]
  31. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref] [PubMed]
  32. F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
    [Crossref]
  33. D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
    [Crossref] [PubMed]
  34. I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
    [Crossref]
  35. G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
    [Crossref]
  36. G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
    [Crossref]
  37. P. Li, Y. Zhang, S. Liu, H. Cheng, L. Han, D. Wu, and J. Zhao, “Generation and self-healing of vector bessel-gauss beams with variant state of polarizations upon propagation,” Opt. Express 25, 5821–5831 (2017).
    [Crossref] [PubMed]
  38. E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).
  39. C. Rosales-Guzmán, N. Bhebhe, and A. Forbes, “Simultaneous generation of multiple vector beams on a single slm,” Opt. Express 25, 25697–25706 (2017).
    [Crossref] [PubMed]
  40. E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
    [Crossref]
  41. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
    [Crossref]
  42. B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
    [Crossref] [PubMed]
  43. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
    [Crossref]
  44. A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
    [Crossref] [PubMed]
  45. M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
    [Crossref]
  46. Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
    [Crossref] [PubMed]
  47. Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
    [Crossref] [PubMed]
  48. C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE Press, 2017).
    [Crossref]
  49. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
    [Crossref]
  50. J. Turunen, A. Vasara, and A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [Crossref] [PubMed]
  51. D. M. Cottrell, J. M. Craven, and J. A. Davis, “Nondiffracting random intensity patterns,” Opt. Lett. 32, 298–300 (2007).
    [Crossref] [PubMed]
  52. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [Crossref]
  53. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
    [Crossref] [PubMed]
  54. B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
    [Crossref]
  55. M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
    [Crossref]
  56. D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.
  57. M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
    [Crossref]
  58. J. Mendoza-Hernández, M. L. Arroyo-Carrasco, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Laguerre–gauss beams versus bessel beams showdown: peer comparison,” Opt. Lett. 40, 3739–3742 (2015).
    [Crossref]
  59. N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
    [Crossref]
  60. N. Mphuthi, R. Botha, and A. Forbes, “Are bessel beams resilient to aberrations and turbulence?” J. Opt. Soc. Am. A 35, 1021–1027 (2018).
    [Crossref]
  61. M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24, 18105 (2016).
    [Crossref] [PubMed]
  62. Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
    [Crossref]
  63. V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
    [Crossref]
  64. H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).
  65. F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).
  66. S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
    [Crossref]
  67. G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
    [Crossref]
  68. E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
    [Crossref]

2018 (4)

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

N. Mphuthi, R. Botha, and A. Forbes, “Are bessel beams resilient to aberrations and turbulence?” J. Opt. Soc. Am. A 35, 1021–1027 (2018).
[Crossref]

2017 (8)

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

P. Li, Y. Zhang, S. Liu, H. Cheng, L. Han, D. Wu, and J. Zhao, “Generation and self-healing of vector bessel-gauss beams with variant state of polarizations upon propagation,” Opt. Express 25, 5821–5831 (2017).
[Crossref] [PubMed]

C. Rosales-Guzmán, N. Bhebhe, and A. Forbes, “Simultaneous generation of multiple vector beams on a single slm,” Opt. Express 25, 25697–25706 (2017).
[Crossref] [PubMed]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

2016 (8)

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24, 15143 (2016).
[Crossref] [PubMed]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
[Crossref] [PubMed]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24, 18105 (2016).
[Crossref] [PubMed]

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

2015 (5)

2014 (6)

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).

Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
[Crossref] [PubMed]

2013 (5)

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

M. Huber and M. Pawłowski, “Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement,” Phys. Rev. A 88, 032309 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

2012 (2)

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

2011 (3)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref] [PubMed]

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

2010 (1)

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

2009 (1)

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
[Crossref]

2008 (2)

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

2007 (4)

D. M. Cottrell, J. M. Craven, and J. A. Davis, “Nondiffracting random intensity patterns,” Opt. Lett. 32, 298–300 (2007).
[Crossref] [PubMed]

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[Crossref]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

2006 (2)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

2004 (2)

C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

2003 (1)

2002 (1)

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

2000 (2)

P. W. Shor and J. Preskill, “Simple proof of security of the bb84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

1999 (1)

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
[Crossref]

1988 (1)

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
[Crossref]

1982 (1)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Abbas, A.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Acin, A.

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

Ahmed, N.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Aiello, A.

Alfano, R. R.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40, 4887 (2015).
[Crossref] [PubMed]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Ali-Khan, I.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

Almaiman, A.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Aolita, L.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Arroyo-Carrasco, M. L.

Ashrafi, S.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

Bennett Ch, H.

H. Bennett Ch and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

Bhebhe, N.

Borges, C.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Botha, R.

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
[Crossref]

Bouchard, F.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Bourgoin, J.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

Boyd, R. W.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Brassard, G.

H. Bennett Ch and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

Broadbent, C. J.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

Cai, W.-Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Cai, X.-L.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Cai, Y.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

Campos, J.

Cañas, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Cao, Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Cardano, F.

Cardenas, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Cariñe, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Cerf, N. J.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Chakraborty, O.

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

Chávez-Cerda, S.

Chen, S.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Chen, W.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Chen, X.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Chen, Y.-A.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Cheng, H.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
[Crossref]

Connolly, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Cottrell, D. M.

Cox, M. A.

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24, 18105 (2016).
[Crossref] [PubMed]

Craven, J. M.

D’Ambrosio, V.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Davis, J. A.

de Lisio, C.

Deng, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Denz, C.

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

Dholakia, K.

Diamanti, E.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

Du, C.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
[Crossref] [PubMed]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Eisaman, M.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

Elser, D.

Erven, C.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

Etcheverry, S.

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Fan, J.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

Fickler, R.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Figueroa, M.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Fink, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Forbes, A.

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

N. Mphuthi, R. Botha, and A. Forbes, “Are bessel beams resilient to aberrations and turbulence?” J. Opt. Soc. Am. A 35, 1021–1027 (2018).
[Crossref]

C. Rosales-Guzmán, N. Bhebhe, and A. Forbes, “Simultaneous generation of multiple vector beams on a single slm,” Opt. Express 25, 25697–25706 (2017).
[Crossref] [PubMed]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
[Crossref] [PubMed]

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24, 18105 (2016).
[Crossref] [PubMed]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
[Crossref] [PubMed]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
[Crossref]

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE Press, 2017).
[Crossref]

Friberg, A. T.

Fürst, M.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Gabriel, C.

Gagnon-Bischoff, J.

Gao, S.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Garcés-Chávez, V.

Gauthier, D. J.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Giovannini, D.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Gisin, N.

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Gobby, C.

C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

Gómez, E.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

González, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
[Crossref]

Gottesman, D.

D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.

Goyal, S.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
[Crossref]

Günthner, K.

Guo, G.-C.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Gupta, D.

H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).

Han, L.

Han, Z.-F.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Handsteiner, J.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Heim, B.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

Hernandez-Aranda, R. I.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

Heshami, K.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Holleczek, A.

Howell, J. C.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

Hu, T.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Huang, H.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Huang, Y.-M.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Huber, M.

M. Huber and M. Pawłowski, “Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement,” Phys. Rev. A 88, 032309 (2013).
[Crossref]

Hufnagel, F.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Huguenin, J.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Ibrahim, A. H.

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

Iturbe-Castillo, M. D.

Jennewein, T.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Jia, J.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Jiang, X.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Karimi, E.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Karlsson, A.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Khoury, A.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Klitis, C.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Konrad, T.

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Krenn, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Kurt-siefer, C.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Laflamme, R.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

Larocque, H.

Lavery, M. P.

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Lavery, M. P. J.

Leach, J.

Lei, T.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Leuchs, G.

Li, F.-Z.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Li, L.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Li, P.

Li, S.-M.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Li, Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Li, Z.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Li, Z.-P.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Liao, P.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Liao, S.-K.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Lima, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Litvin, I. A.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
[Crossref]

Liu, J.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Liu, N.-L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Liu, S.

Liu, W.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Lo, H.-K.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.

Lu, C.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Lutkenhaus, N.

D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.

Lütkenhaus, N.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Ma, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Mafu, M.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Magaña-Loaiza, O. S.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Malik, M.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Marquardt, C.

Marrucci, L.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

McGloin, D.

McLaren, M.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
[Crossref] [PubMed]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

McLaren, M. G.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
[Crossref]

Mendoza-Hernández, J.

Meyer-Scott, E.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

Mhlanga, T.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Migdall, A.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

Milione, G.

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40, 4887 (2015).
[Crossref] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Mirhosseini, M.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Mo, Q.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[Crossref]

Molisch, A. F.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Moreno, I.

Mouane, O.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Mphuthi, N.

Nape, I.

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

Ndagano, B.

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Nguyen, T. A.

Nogueira, W.

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Nolan, D. A.

O’Sullivan, M. N.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Otte, E.

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

Padgett, M. J.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
[Crossref]

Pan, J.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Pawlowski, M.

M. Huber and M. Pawłowski, “Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement,” Phys. Rev. A 88, 032309 (2013).
[Crossref]

Peng, C.-Z.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Perdigues, J.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Perez-Garcia, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

Petruccione, F.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Peuntinger, C.

Piccirillo, B.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Polyakov, S. V.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

Prabhakar, S.

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

Preskill, J.

P. W. Shor and J. Preskill, “Simple proof of security of the bb84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.

Przysiezna, A.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Qi, B.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Rarity, J. G.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Ren, J.-G.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Ren, Y.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Ribordy, G.

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

Rodenburg, B.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Romero, J.

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

Rosales-Guzman, C.

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Rosales-Guzmán, C.

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

C. Rosales-Guzmán, N. Bhebhe, and A. Forbes, “Simultaneous generation of multiple vector beams on a single slm,” Opt. Express 25, 25697–25706 (2017).
[Crossref] [PubMed]

M. A. Cox, C. Rosales-Guzmán, M. P. J. Lavery, D. J. Versfeld, and A. Forbes, “On the resilience of scalar and vector vortex modes in turbulence,” Opt. Express 24, 18105 (2016).
[Crossref] [PubMed]

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE Press, 2017).
[Crossref]

Roux, F. S.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
[Crossref] [PubMed]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

Saavedra, C.

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Santamato, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Sauge, S.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Scarani, V.

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

Scheidl, T.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Schiavon, M.

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

Schmitt-Manderbach, T.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Scholes, S.

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

Sciarrino, F.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Sephton, B.

Shen, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Shields, A.

C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

Shor, P. W.

P. W. Shor and J. Preskill, “Simple proof of security of the bb84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

Shu, R.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Silva, T. Ferreira da

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Singh, A.

H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).

Singh, H.

H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).

Sit, A.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Slussarenko, S.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref] [PubMed]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Sodnik, Z.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Sorel, M.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Souza, C.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Sun, L.-H.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Swillo, M.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Tengner, M.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Ticozzi, F.

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

Tiefenbacher, F.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Tittel, W.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[Crossref]

Tur, M.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Turunen, J.

Ursin, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Vallés, A.

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

Vallone, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Vasara, A.

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Vera, N.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Versfeld, D. J.

Villoresi, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
[Crossref]

Walborn, S.

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

Wang, A.-D.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Wang, B.

Wang, F.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

Wang, J.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Wang, J.-F.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Wang, J.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Wang, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Wang, X.-B.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Wang, Z.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Weier, H.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Weihs, G.

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Weinfurter, H.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

Willner, A. E.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Willner, A. J.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Wootters, W. K.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Wu, D.

Wu, G.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

Wu, J.-C.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Xavier, G.

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Xavier, G. B.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Xi, T.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Xie, G.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 x 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

Xie, Z.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Yan, Y.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Yin, J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Yu, S.-Y.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Yuan, X.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Yuan, Y.

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

Yuan, Z.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Yzuel, M. J.

Zeilinger, A.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Zhang, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Zhang, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Zhang, T.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Zhang, X.

Zhang, Y.

P. Li, Y. Zhang, S. Liu, H. Cheng, L. Han, D. Wu, and J. Zhao, “Generation and self-healing of vector bessel-gauss beams with variant state of polarizations upon propagation,” Opt. Express 25, 5821–5831 (2017).
[Crossref] [PubMed]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

Y. Zhang, M. Mclaren, F. S. Roux, and A. Forbes, “Simulating quantum state engineering in spontaneous parametric down-conversion using classical light,” Opt. express 22, 17039–17049 (2014).
[Crossref] [PubMed]

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

Zhao, J.

Zhao, Z.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Zhou, Y.-L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Zhu, L.

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Zhu, Z.-C.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

Zurek, W. H.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Adv. Opt. Photonics (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

C. Gobby, Z. Yuan, and A. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

IOSR J. Comput. Eng. (IOSR-JCE) (1)

H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols: a review,” IOSR J. Comput. Eng. (IOSR-JCE) 1616 (2014).

J. Light. Technol. (1)

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
[Crossref]

J. Opt. (1)

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Light. Sci. Appl. (2)

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin-orbit coupling,” Light. Sci. Appl. 7, 18009 (2018).
[Crossref]

J. Liu, S.-M. Li, L. Zhu, A.-D. Wang, S. Chen, C. Klitis, C. Du, Q. Mo, M. Sorel, S.-Y. Yu, X.-L. Cai, and J. Wang, “Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters,” Light. Sci. Appl. 7, 17148 (2018).
[Crossref]

Nat. Commun. (1)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Nat. Phys. (2)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397 (2017).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[Crossref]

Nature (2)

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

New J. Phys. (4)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

C. Erven, B. Heim, E. Meyer-Scott, J. Bourgoin, R. Laflamme, G. Weihs, and T. Jennewein, “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys. 14, 123018 (2012).
[Crossref]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

NPJ Quantum Inf. (1)

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” NPJ Quantum Inf. 2, 16025 (2016).
[Crossref]

Opt. Commun. (3)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207 – 211 (1998).
[Crossref]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating bessel–gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078 – 1082 (2009).
[Crossref]

F. Gori, G. Guattari, and C. Padovani, “Bessel-gauss beams,” Opt. Commun. 64, 491 – 495 (1987).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (9)

M. Huber and M. Pawłowski, “Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement,” Phys. Rev. A 88, 032309 (2013).
[Crossref]

Y. Zhang, S. Prabhakar, A. H. Ibrahim, F. S. Roux, A. Forbes, and T. Konrad, “Experimentally observed decay of high-dimensional entanglement through turbulence,” Phys. Rev. A 94, 032310 (2016).
[Crossref]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized bessel-gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 1–4 (2008).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of bessel-gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

M. Schiavon, G. Vallone, F. Ticozzi, and P. Villoresi, “Heralded single-photon sources for quantum-key-distribution applications,” Phys. Rev. A 93, 012331 (2016).
[Crossref]

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Phys. Rev. Lett. (8)

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurt-siefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

P. W. Shor and J. Preskill, “Simple proof of security of the bb84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Phys. review letters (1)

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. review letters 92, 057901 (2004).
[Crossref]

Rev. Sci. Instruments (1)

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instruments 82, 071101 (2011).
[Crossref]

Sci. Reports (4)

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple bessel-gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Reports 6, 22082 (2016).
[Crossref]

Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, “Beam wander relieved orbital angular momentum communication in turbulent atmosphere using bessel beams,” Sci. Reports 7, 42276 (2017).
[Crossref]

S. Etcheverry, G. Cañas, E. Gómez, W. Nogueira, C. Saavedra, G. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Reports 3, 2316 (2013).
[Crossref]

B. Ndagano, I. Nape, B. Perez-Garcia, S. Scholes, R. I. Hernandez-Aranda, T. Konrad, M. P. Lavery, and A. Forbes, “A deterministic detector for vector vortex states,” Sci. Reports 7, 13882 (2017).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Other (6)

H. Bennett Ch and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv preprint ar”Xiv:1801.10299 (2018).

E. Otte, I. Nape, C. Rosales-Guzmán, A. Vallés, C. Denz, and A. Forbes, “Recovery of local entanglement in self-healing vector vortex bessel beams,” arXiv preprint ar”Xiv:1805.08179 (2018).

F. Bouchard, A. Sit, K. Heshami, R. Fickler, and E. Karimi, “Round-robin differential phase-shift quantum key distribution with twisted photons,” arXiv preprint ar”Xiv:1803.00166 (2018).

D. Gottesman, H.-K. Lo, N. Lutkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” in International Symposium on Information Theory, 2004 (IEEE, 2004), p. 136.

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE Press, 2017).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Intensity and polarization mappings of vector (first row) and scalar (second row) MUB modes with (a) BG and (b) LG radial profiles for = ±1. The polarization projections on the (c) vector |Ψ〉 and (d) scalar |Φ〉 basis BG modes. The vector modes have spatially varying polarizations which consequently render the polarization and spatial DoF as non-separable. This is easily seen in the variation of the transverse spatial profile when polarization projections are performed (orientation indicated by white arrow) on the |Ψ〉 modes. In contrast, the scalar modes have separable polarization and spatial DoF hence polarization projections only cause fluctuations in the intensity of the transverse profile for the |Φ〉 modes.
Fig. 2
Fig. 2 (a) Conceptual drawing of the QKD with self-healing BG modes. The SLMs post-select the self-healing BG radial profile from the SPDC source. The prepare (P) and measure (M) optics modulate and demodulate the OAM and polarization DoF of the heralded photon. The physical obstruction (O) is placed at a distance L from the rightmost SLM, which decodes the radial information of Bob’s photon. The optics are within zmax = 54 cm distance of the BG modes depicted as the rhombus shape. The propagation of the post-selected BG mode can be determined via back-projection. (b) Numerical scattering probability matrix for the vector and scalar modes sets in free-space. The channels correspond to the probabilities |Cij|2 calculated from Eq. (22). (c) Optical elements required by Alice and Bob to prepare and measure the spin-coupled states of the heralded photons (cf. Table 1).
Fig. 3
Fig. 3 Experimental setup for the self-healing QKD. Pump: λ = 405 nm (Cobalt, MLD laser diode); f: Fourier lenses of focal length f1,2,3&4 = 100 mm, 750 mm, 500 mm, 2 mm, respectively; PPKTP: periodically poled potassium titanyl phosphate (nonlinear crystal); BS: 50:50 beam splitter; s and i: signal and idler photon paths; P: preparation of the state (Alice); O: variable sized obstacle; M: measurement of the state (Bob); SLM: spatial light modulator (Pluto, Holoeye); BPF: band-pass filter; SMF: single mode fiber; D1&2: single photon detectors (Perkin Elmer); C.C.: coincidence electronics.
Fig. 4
Fig. 4 (a) Measured photon count rates and (b) average photon number (µ) per-gating window of 25 ns in free-space (FS) and the two obstructions (R1 = 600 µm and R2 = 800 µm) for the radially polarized mode |ψ00. (c) and (d) show coincidence rates with the same obstructions for the BG and LG radial profiles, respectively. The BG count rate is lower for smaller obstructions due to the high kr hologram on the SLM [55].
Fig. 5
Fig. 5 Crosstalk (scattering) matrix for vector and scalar modes in (a) (I) free-space having post-selected in a BG radial profile. The vector and scalar measured probabilities with the first obstruction (II) having a radius R1 = 600µm (L > zmin) when taking into account (b) BG and (c) LG radial profiles. Measured probabilities with (III) an obstruction of R2 = 800µm (L < zmin) when taking into account (d) BG and (e) LG radially profiled single photons.
Fig. 6
Fig. 6 (a) Experimental normalized coincidence (NC) count-rate for the BG and LG MUB for free-space (FS) and the two obstructions (R1 = 600 µm and R2 = 800 µm) on the radially polarized mode |ψ00. (b) The QBER, mutual information (IAB) and key rate (RΔ/Qµ) for the BG and LG modes with no perturbation and under the two tested obstructions are shown.

Tables (2)

Tables Icon

Table 1 Generation of vector and scalar modes from a horizontally polarized BG mode ( = 0) at the input. The angles α1,2 and β1,2 are defined with respect to the horizontal polarization. For each V ^ i and S ^ i we present the angles needed to perform the mapping of 1 { | Ψ i } and 2 { | Φ i } with a one-to-one correspondence.

Tables Icon

Table 2 Measured security parameters for the self-healing BG (LG) modes. NC represents the normalized coincidence counts. The normalization was performed with respect to the counts obtained from the free-space measurements.

Equations (26)

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J , k r ( r , φ , z ) = 2 π J ( z R k r r z R i z ) exp ( i φ i k z z ) exp ( i k r 2 z w 0 2 k r 2 4 ( z R i z ) ) ,
| Ψ i | Φ j | 2 = 1 d ,
| Ψ 00 = 1 2 J , k r ( r ) ( | R | + | L | ) ,
| Ψ 01 = 1 2 J , k r ( r ) ( | R | | L | ) ,
| Ψ 10 = 1 2 J , k r ( r ) ( | L | + | R | ) ,
| Ψ 11 = 1 2 J , k r ( r ) ( | L | | R | ) ,
| Φ 00 = J , k r ( r ) | D | ,
| Φ 01 = J , k r ( r ) | D | ,
| Φ 10 = J , k r ( r ) | A | ,
| Φ 11 = J , k r ( r ) | A | ,
c s , i = m s * ( x ) m i * ( x ) m p ( x ) d 2 x ,
m s , i ( r , φ ) = J s , i , k r ( r ) exp ( i s , i φ ) ,
| Ψ A B = c , k r , 1 , k r , 2 | , k r , 1 s | , k r , 2 i | H s | H i ,
T ( r , φ ) = sign { J ( k r r ) } exp ( i φ ) ,
Q ^ = ( cos ( 2 q φ ) sin ( 2 q φ ) sin ( 2 q φ ) cos ( 2 q φ ) , )
J ^ λ 2 ( θ ) = ( cos ( 2 θ ) sin ( 2 θ ) sin ( 2 θ ) cos ( 2 θ ) ) ,
J ^ λ 4 ( θ ) = ( cos 2 ( θ ) + isin 2 ( θ ) ( 1 i ) sin ( θ ) cos ( θ ) ( 1 i ) sin ( θ ) cos ( θ ) sin 2 ( θ ) + icos 2 ( θ ) ) .
V ^ ( α 1 , α 2 ) = J ^ λ 2 ( α 2 ) Q ^ J ^ λ 2 ( α 1 ) P ^ H ,
S ^ ( β 1 , β 2 ) = J ^ λ 4 ( β 2 ) Q ^ J ^ λ 4 ( β 1 ) P ^ H ,
| a i = A ^ i J 0 , k r ( r ) | H ,
| b j = B ^ j J 0 , k r ( r ) | H .
C i j = b j | a i = 0 2 π 0 H | J 0 , k r * ( r ) B ^ j A ^ i J 0 , k r ( r ) | H r d r d ϕ ,
I A B = log 2 ( d ) + ( 1 e ) log 2 ( 1 e ) + ( e ) log 2 ( e d 1 ) .
R Δ = Q μ ( ( 1 Δ ) ( 1 H d ( e 1 Δ ) ) f EC H d ( e ) ) ,
Y n = η n + p D ( 1 η n ) ,
η n = 1 ( 1 η ) n .

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