Abstract

In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of the protocol. Here, we demonstrate a quantum communication scheme where the information on the bases is shared “non-classically,” by encoding this information in the same photons used for carrying the data. This enhanced capability is achieved by exploiting the localization of the photonic wave function, observed when the photons are prepared and measured in the same quantum basis. We experimentally implement our scheme by using a multi-mode optical fiber coupled to an adaptive optics setup. We observe a decrease in the error rate for higher dimensionality, indicating an improved resilience against noise.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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  1. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
    [Crossref]
  2. M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
    [Crossref]
  3. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
    [Crossref]
  4. S. J. Jones and H. M. Wiseman, “Nonlocality of a single photon: Paths to an Einstein-Podolsky-Rosen-steering experiment,” Phys. Rev. A 84, 012110 (2011).
    [Crossref]
  5. A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
    [Crossref]
  6. J. A. Wheeler and W. H. Zurek, Quantum theory and measurement (Princeton University, 2014).
  7. M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
    [Crossref] [PubMed]
  8. G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
    [Crossref]
  9. 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]
  10. F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
    [Crossref] [PubMed]
  11. T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
    [Crossref]
  12. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
    [Crossref] [PubMed]
  13. S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
    [Crossref] [PubMed]
  14. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [Crossref]
  15. P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
    [Crossref]
  16. V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
    [Crossref]
  17. 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]
  18. J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
    [Crossref] [PubMed]
  19. Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
    [Crossref]
  20. Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
    [Crossref]
  21. 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]
  22. T. B. H. Tentrup, T. Hummel, T. A. W. Wolterink, R. Uppu, A. P. Mosk, and P. W. H. Pinkse, “Transmitting more than 10 bit with a single photon,” Opt. Express 25, 2826–2833 (2017).
    [Crossref]
  23. P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
    [Crossref] [PubMed]
  24. A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
    [Crossref]
  25. F. Grazioso and F. Grosshans, “Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks,” Phys. Rev. A 88, 052302 (2013).
    [Crossref]
  26. A. B. Price, J. G. Rarity, and C. Erven, “A quantum key distribution protocol for rapid denial of service detection,” arXiv:1707.03331 [quant-ph] (2017).
  27. 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]
  28. M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).
  29. P. W. Anderson, “The question of classical localization a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
    [Crossref]
  30. T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).
  31. D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
    [Crossref]
  32. S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635–639 (2012).
    [Crossref]
  33. R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19, 247–254 (2011).
    [Crossref] [PubMed]
  34. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (John Wiley & Sons, Inc., 1991).
    [Crossref]
  35. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [Crossref] [PubMed]
  36. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [Crossref] [PubMed]
  37. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
    [Crossref]
  38. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320 (2010).
    [Crossref]
  39. D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19, 4017–4029 (2011).
    [Crossref] [PubMed]
  40. J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
    [Crossref]
  41. R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
    [Crossref]
  42. A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
    [Crossref]
  43. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
    [Crossref] [PubMed]

2018 (1)

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

2017 (6)

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
[Crossref]

F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
[Crossref] [PubMed]

T. B. H. Tentrup, T. Hummel, T. A. W. Wolterink, R. Uppu, A. P. Mosk, and P. W. H. Pinkse, “Transmitting more than 10 bit with a single photon,” Opt. Express 25, 2826–2833 (2017).
[Crossref]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

2016 (2)

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

2015 (1)

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

2014 (1)

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]

2013 (3)

F. Grazioso and F. Grosshans, “Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks,” Phys. Rev. A 88, 052302 (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]

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

2012 (2)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635–639 (2012).
[Crossref]

2011 (5)

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19, 247–254 (2011).
[Crossref] [PubMed]

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19, 4017–4029 (2011).
[Crossref] [PubMed]

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

S. J. Jones and H. M. Wiseman, “Nonlocality of a single photon: Paths to an Einstein-Podolsky-Rosen-steering experiment,” Phys. Rev. A 84, 012110 (2011).
[Crossref]

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

2010 (2)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

2009 (1)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

2007 (5)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

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]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[Crossref] [PubMed]

2006 (2)

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[Crossref] [PubMed]

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[Crossref]

2004 (1)

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

2002 (2)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[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]

2000 (1)

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

1997 (1)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

1985 (1)

P. W. Anderson, “The question of classical localization a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

Acín, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Akbulut, D.

Alber, G.

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[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]

Allman, M. S.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Almeida, M. P.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[Crossref] [PubMed]

Anderson, P. W.

P. W. Anderson, “The question of classical localization a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

Bassi, A.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

Beetz, J.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635–639 (2012).
[Crossref]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19, 247–254 (2011).
[Crossref] [PubMed]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Bonneau, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bouchard, F.

F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
[Crossref] [PubMed]

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]

Bouzid, A.

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Boyd, R. W.

F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
[Crossref] [PubMed]

Brassard, G.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

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, J.

Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
[Crossref]

Cai, X.

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[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]

Chen, J.-L.

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

Conti, C.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

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]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Dalgaard, K.

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

DelRe, E.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

Deng, F.-G.

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635–639 (2012).
[Crossref]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19, 247–254 (2011).
[Crossref] [PubMed]

Ding, Y.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Dudley, A.

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]

Durt, T.

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Erven, C.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

A. B. Price, J. G. Rarity, and C. Erven, “A quantum key distribution protocol for rapid denial of service detection,” arXiv:1707.03331 [quant-ph] (2017).

Fickler, R.

F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
[Crossref] [PubMed]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Fiore, A.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Forbes, A.

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]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

Frucci, G.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Fujiwara, M.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

Furusawa, A.

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

Fuwa, M.

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

Gaggero, A.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Gerrits, T.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

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.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[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]

Godfrey, M.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

Gong, Q.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

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]

Grazioso, F.

F. Grazioso and F. Grosshans, “Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks,” Phys. Rev. A 88, 052302 (2013).
[Crossref]

Grosshans, F.

F. Grazioso and F. Grosshans, “Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks,” Phys. Rev. A 88, 052302 (2013).
[Crossref]

Hadfield, R. H.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Höfling, S.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Hooijschuur, P.

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

Howell, J. C.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

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]

Huisman, T. J.

Hummel, T.

Jahanmirinejad, S.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Jones, S. J.

S. J. Jones and H. M. Wiseman, “Nonlocality of a single photon: Paths to an Einstein-Podolsky-Rosen-steering experiment,” Phys. Rev. A 84, 012110 (2011).
[Crossref]

Kamp, M.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Karbasi, S.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

Karlsson, A.

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]

Kaszlikowski, D.

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

Kim, S. M.

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Konrad, T.

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, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[Crossref]

Kwak, S.

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Kwek, L. C.

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

Lagendijk, A.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320 (2010).
[Crossref]

Laing, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

Lemelle, D. S.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[Crossref] [PubMed]

Leonetti, M.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

Leoni, R.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Lermer, M.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Li, X.-H.

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

Lloyd, S.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Lochan, K.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Luiten, W. M.

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

Lum, D. J.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Lupo, C.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

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]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Mafi, A.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

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]

Malik, M.

M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[Crossref]

Mancinska, L.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Marrucci, L.

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]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Mattioli, F.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

McLaren, 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]

Miki, S.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

Moon, S.

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Mor, T.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Mosk, A. P.

Nagali, E.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Nam, S. W.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Natarajan, C. M.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

Nikolopoulos, G. M.

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[Crossref]

O’Brien, J. L.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Oxenløwe, L. K.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Padgett, M. J.

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]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

Paesani, S.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Pan, Z.

Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
[Crossref]

Park, J.-B.

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[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]

Pinkse, P. W. H.

T. B. H. Tentrup, T. Hummel, T. A. W. Wolterink, R. Uppu, A. P. Mosk, and P. W. H. Pinkse, “Transmitting more than 10 bit with a single photon,” Opt. Express 25, 2826–2833 (2017).
[Crossref]

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Price, A. B.

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

A. B. Price, J. G. Rarity, and C. Erven, “A quantum key distribution protocol for rapid denial of service detection,” arXiv:1707.03331 [quant-ph] (2017).

Ranade, K. S.

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[Crossref]

Rarity, J. G.

A. B. Price, J. G. Rarity, and C. Erven, “A quantum key distribution protocol for rapid denial of service detection,” arXiv:1707.03331 [quant-ph] (2017).

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

Ribeiro, P. H. S.

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[Crossref] [PubMed]

Rottwitt, K.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Sahin, D.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Salavrakos, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (John Wiley & Sons, Inc., 1991).
[Crossref]

Sanders, B. C.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Sanjines, R.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Santagati, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Sasaki, M.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

Satin, S.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Scheidl, T.

M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[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]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Sibson, P.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

Silverstone, J. W.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Singh, T. P.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Skrzypczyk, P.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

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]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Sorel, M.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[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]

Sprengers, J. P.

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Strain, M. J.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Takeda, S.

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

Tanner, M. G.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (John Wiley & Sons, Inc., 1991).
[Crossref]

Tentrup, T. B. H.

T. B. H. Tentrup, T. Hummel, T. A. W. Wolterink, R. Uppu, A. P. Mosk, and P. W. H. Pinkse, “Transmitting more than 10 bit with a single photon,” Opt. Express 25, 2826–2833 (2017).
[Crossref]

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

Terai, H.

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

Thompson, M. G.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

Tura, J.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Ulbricht, H.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Uppu, R.

Ursin, R.

M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[Crossref]

Vallone, G.

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]

van der Meer, R.

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

van Putten, E. G.

Vellekoop, I. M.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320 (2010).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[Crossref] [PubMed]

Verma, V. B.

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Villoresi, P.

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]

Vos, W. L.

Walborn, S. P.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[Crossref] [PubMed]

Wang, C.

Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
[Crossref]

Wang, J.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Wheeler, J. A.

J. A. Wheeler and W. H. Zurek, Quantum theory and measurement (Princeton University, 2014).

Wiseman, H. M.

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

S. J. Jones and H. M. Wiseman, “Nonlocality of a single photon: Paths to an Einstein-Podolsky-Rosen-steering experiment,” Phys. Rev. A 84, 012110 (2011).
[Crossref]

Wolterink, T. A. W.

Yamashita, T.

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

Zeilinger, A.

M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[Crossref]

Zhou, H.-Y.

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

Zhou, P.

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

Zhou, X.

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Zurek, W. H.

J. A. Wheeler and W. H. Zurek, Quantum theory and measurement (Princeton University, 2014).

Zwierz, M.

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

Curr. Appl. Phys. (1)

A. Bouzid, J.-B. Park, S. M. Kim, S. Kwak, and S. Moon, “Characterization of a single-photon detector at 1.55μm operated with an active hold-off technique for quantum key distribution,” Curr. Appl. Phys. 11, 903–908 (2011).
[Crossref]

Int. J. Theor. Phys. (1)

Z. Pan, J. Cai, and C. Wang, “Quantum key distribution with high order fibonacci-like orbital angular momentum states,” Int. J. Theor. Phys. 56, 2622–2634 (2017).
[Crossref]

J. Opt. (1)

R. Santagati, J. W. Silverstone, M. J. Strain, M. Sorel, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Silicon photonic processor of two-qubit entangling quantum logic,” J. Opt. 19, 114006 (2017).
[Crossref]

J. Phys. A: Math. Theor. (1)

P. Zhou, X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel,” J. Phys. A: Math. Theor. 40, 13121–13130 (2007).
[Crossref]

Lab on a Chip (1)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635–639 (2012).
[Crossref]

Nat. Commun. (3)

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, “Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements,” Nat. Commun. 6, 6665 (2015).
[Crossref] [PubMed]

Nat. Photonics (2)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320 (2010).
[Crossref]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

npj Quantum Inf. (1)

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Philos. Mag. B (1)

P. W. Anderson, “The question of classical localization a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

Phys. Rev. A (6)

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]

F. Grazioso and F. Grosshans, “Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks,” Phys. Rev. A 88, 052302 (2013).
[Crossref]

T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, “Security of quantum key distributions with entangled qudits,” Phys. Rev. A 69, 032313 (2004).
[Crossref]

S. J. Jones and H. M. Wiseman, “Nonlocality of a single photon: Paths to an Einstein-Podolsky-Rosen-steering experiment,” Phys. Rev. A 84, 012110 (2011).
[Crossref]

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[Crossref]

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: Experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

Phys. Rev. Lett. (7)

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[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]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref] [PubMed]

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
[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]

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]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Rev. Mod. Phys. (3)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Sci. Adv. (1)

F. Bouchard, R. Fickler, and R. W. Boyd, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
[Crossref] [PubMed]

Sci. Rep. (1)

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6, 29918 (2016).

Science (1)

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Other (6)

J. A. Wheeler and W. H. Zurek, Quantum theory and measurement (Princeton University, 2014).

M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum Communication with Photons in Optics in Our Time (Springer International Publishing, 2016), pp. 455–482.
[Crossref]

T. B. H. Tentrup, W. M. Luiten, R. van der Meer, P. Hooijschuur, and P. W. H. Pinkse, “Large-alphabet quantum key distribution using spatially encoded light,” arXiv:1808.02823 [quant-ph] (2018).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (John Wiley & Sons, Inc., 1991).
[Crossref]

A. B. Price, J. G. Rarity, and C. Erven, “A quantum key distribution protocol for rapid denial of service detection,” arXiv:1707.03331 [quant-ph] (2017).

A. B. Price, P. Sibson, C. Erven, J. G. Rarity, and M. G. Thompson, “High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, (Optical Society of America, 2018), p. JTh2A.24.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Alice sends an attenuated laser into a reflective spatial light modulator (SLM), which focuses the light on the far side of a multi-mode fiber in two mutually unbiased bases. Bob may choose whether to measure in the computational or the Fourier basis by exploiting a flip mirror (not shown). If he measures correctly, the probability density is localized, allowing him to retrieve the bit sent by Alice and confirming his basis choice. If he measures incorrectly, Bob can be expected to obtain inconsistent results as the probability density is delocalized.
Fig. 2
Fig. 2 (a) Probability of detecting only one photon on each pixel of the detector (PD) for a localized state. (b) Probability of detecting two successive single photons on the same pixel (PD2) for a localized state. (c) and (d) respectively PD and PD2 for a delocalized state, which corresponds to a measurement in the wrong basis. All results are for a 17 × 17 detector configuration.
Fig. 3
Fig. 3 (a) Theoretical and experimental results for the error probability over the probability of successful communication (PErr/PCorr) vs the dimensionality (D). The inset graph is a magnified view of the region with experimental points. (b) Error probability over the probability of successful communication vs dark counts (γ) and the dimensionality. While individual-photon bit encoding (red) is more effective for low dimensions, data basis shuffling (blue) quickly becomes less prone to error when the dimensionality is greater than 20. The number of dark counts does not significantly affect this performance metric.
Fig. 4
Fig. 4 PErr/PCorr as a function of loss (1 − η) for four different dimensionality (D) values. γ and λ are fixed at 500 dark counts per second and 0.2 respectively. (a) At D = 4, IPBE always outperforms DBS, regardless of the loss. (b) At D = 16, DBS starts to become preferable when the loss exceeds 45%. (c) and (d) At higher values of D, DBS always outperforms IPBE, regardless of the loss.
Fig. 5
Fig. 5 Experimental data points and theoretical curves showing the potential resilience of a DBS-based quantum key distribution protocol to photon number splitting attacks (a) when D = 16 and (b) when D = 36.

Tables (1)

Tables Icon

Table 1 Experimental conditions. η is the Efficiency of the quantum communication channel, γ is the Dark count rate and λ is the Mean photon number.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

Bit Basis State sent 0 { | 0 , | 1 } | 00 1 { | 0 , | 1 } | 11 0 { | + , | } | + + 1 { | + , | } |
| 00 00 | | 11 11 | | + + + + | | |
{ | k } k = 0 , , D 1 = { | 0 , | 1 , | 2 , , | D 1 } ,
| f l = 1 D k = 0 D 1 e i 2 π k l D | k
C = j = 2 , 4 , 6 N j ! 2 ! ( j 2 ) !
E n = A n e i ϕ n ,
E m = n = 1 N | t n m | σ n A n e i arg ( t n m )
P ( x , y ) = E m * E m = n = 1 N k = 1 N | t n m | | t k m | A n e i arg ( t n m ) A k e i arg ( t k m ) σ n σ k .
P Err P Corr = P BE + P EE P Corr ,
P Corr = η 2 4 ( 1 e λ ) 2 exp 2 γ τ ( D 1 ) ,
P BE = η 2 4 D ( 1 e λ ) 2 ,
P EE = e 2 λ P γ 2 / D + ( 1 e λ ) 2 ( 1 η ) 2 P γ 2 / D ,
P Err P Corr exp 2 γ τ ( D 1 ) / D .
P EE IPBE = e λ P γ + ( 1 e λ ) ( 1 η ) P γ .
P BE = P bothE + P bSinglE ,
P BE = P bothE = η 2 4 D ( 1 e λ ) 2 .
P γ = 1 e γ τ ( D 1 ) .
P EE = e 2 λ P γ 2 / D + ( 1 e λ ) 2 ( 1 η ) 2 P γ 2 / D .
P EE IPBE = e λ P γ + ( 1 e λ ) ( 1 η ) P γ .
P Corr = η 2 ( 1 e λ ) 2 ( 1 P γ ) 2 4 .
P Correct IPBE = η ( 1 e λ ) ( 1 P γ ) 2 .
P Err P Corr = P BE + P EE P Corr .
P γ = 1 e γ τ ( D 1 ) .
P B = ( η 2 ( 1 P γ ) ) 2 = η 2 4 exp 2 γ τ ( D 1 ) ,
P O = 1 2 ( P mult / P phot ) 2 ,
P B P O = ( η 2 e γ τ ( D 1 ) ) 2 1 2 ( P mult / P phot ) 2 .
P B IPBE P O IPBE = η 2 e γ τ ( D 1 ) ( P mult / P phot ) .