Abstract

An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
    [Crossref]
  2. J. F. Clauser and A. Shimony, “Bell’s theorem. experimental tests and implications,” Rep. Prog. Phys. 41, 1881 (1978).
    [Crossref]
  3. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
    [Crossref]
  4. D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
    [Crossref] [PubMed]
  5. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
    [Crossref]
  6. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [Crossref]
  7. H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
    [Crossref] [PubMed]
  8. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [Crossref]
  9. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  10. R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
    [Crossref]
  11. F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
    [Crossref]
  12. E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
    [Crossref]
  13. T. Konrad and A. Forbes, “Quantum mechanics and classical light,” Contemp. Phys. 0, 1–22 (2019).
    [Crossref]
  14. A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
    [Crossref]
  15. C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
    [Crossref] [PubMed]
  16. K. Lee and J. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
    [Crossref] [PubMed]
  17. Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
    [Crossref] [PubMed]
  18. Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
    [Crossref]
  19. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
    [Crossref] [PubMed]
  20. E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
    [Crossref]
  21. C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
    [Crossref]
  22. S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
    [Crossref] [PubMed]
  23. F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
    [Crossref] [PubMed]
  24. B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).
  25. A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
    [Crossref]
  26. R. J. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
    [Crossref]
  27. K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
    [Crossref]
  28. M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
    [Crossref]
  29. D. Dragoman and M. Dragoman, Quantum-classical analogies (Springer Science & Business Media, 2013).
  30. 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, 397–402 (2017).
    [Crossref]
  31. E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
    [Crossref]
  32. S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
    [Crossref]
  33. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
    [Crossref]
  34. L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
    [Crossref]
  35. V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
    [Crossref] [PubMed]
  36. W. Löffler, V. D. Salakhutdinov, and E. R. Eliel, “Hybrid radial-angular quantum correlations of spatially entangled photons,” in Quantum Information and Measurement, (Optical Society of America, 2012), pp. QW3A–6.
    [Crossref]
  37. L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
    [Crossref] [PubMed]
  38. A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
    [Crossref]
  39. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  40. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161–204 (2011).
    [Crossref]
  41. E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
    [Crossref]
  42. M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
    [Crossref]
  43. A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
    [Crossref] [PubMed]
  44. Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
    [Crossref]
  45. E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
    [Crossref]
  46. D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
    [Crossref]
  47. M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).
  48. X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
    [Crossref] [PubMed]
  49. Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
    [Crossref]
  50. F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
    [Crossref]
  51. S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
    [Crossref]
  52. M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
    [Crossref] [PubMed]
  53. P. Li, S. Zhang, and X. Zhang, “Classically high-dimensional correlation: simulation of high-dimensional entanglement,” Opt. Express 26, 31413–31429 (2018).
    [Crossref]
  54. W. N. Plick and M. Krenn, “Physical meaning of the radial index of laguerre-gauss beams,” Phys. Rev. A 92, 063841 (2015).
    [Crossref]
  55. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
    [Crossref] [PubMed]
  56. B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
    [Crossref] [PubMed]
  57. G. Vallone, “Role of beam waist in laguerre–gauss expansion of vortex beams,” Opt. Lett. 42, 1097–1100 (2017).
    [Crossref] [PubMed]
  58. F. S. Roux and Y. Zhang, “Projective measurements in quantum and classical optical systems,” Phys. Rev. A 90, 033835 (2014).
    [Crossref]
  59. B. Ndagano and A. Forbes, “Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence,” Phys. Rev. A 98, 062330 (2018).
    [Crossref]
  60. S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).
  61. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [Crossref] [PubMed]
  62. B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
    [Crossref]
  63. T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
    [Crossref]
  64. M. D. Hannam and W. J. Thompson, “Estimating small signals by using maximum likelihood and poisson statistics,” Nucl. Instrum. Methods Phys. Res., Sect. A 431, 239–251 (1999).
    [Crossref]
  65. C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
    [Crossref]
  66. A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
    [Crossref]
  67. A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
    [Crossref]
  68. W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
    [Crossref] [PubMed]
  69. C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
    [Crossref]
  70. F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
    [Crossref]
  71. A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
    [Crossref] [PubMed]
  72. J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
    [Crossref]
  73. N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
    [Crossref]

2019 (2)

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

T. Konrad and A. Forbes, “Quantum mechanics and classical light,” Contemp. Phys. 0, 1–22 (2019).
[Crossref]

2018 (11)

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

P. Li, S. Zhang, and X. Zhang, “Classically high-dimensional correlation: simulation of high-dimensional entanglement,” Opt. Express 26, 31413–31429 (2018).
[Crossref]

B. Ndagano and A. Forbes, “Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence,” Phys. Rev. A 98, 062330 (2018).
[Crossref]

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

2017 (8)

C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
[Crossref]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

G. Vallone, “Role of beam waist in laguerre–gauss expansion of vortex beams,” Opt. Lett. 42, 1097–1100 (2017).
[Crossref] [PubMed]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (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, 397–402 (2017).
[Crossref]

2016 (3)

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

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

2015 (5)

W. N. Plick and M. Krenn, “Physical meaning of the radial index of laguerre-gauss beams,” Phys. Rev. A 92, 063841 (2015).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
[Crossref]

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

2014 (6)

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

F. S. Roux and Y. Zhang, “Projective measurements in quantum and classical optical systems,” Phys. Rev. A 90, 033835 (2014).
[Crossref]

2013 (3)

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

2012 (2)

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

2011 (4)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161–204 (2011).
[Crossref]

2010 (3)

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

2008 (2)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref] [PubMed]

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

2007 (2)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

2006 (2)

T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
[Crossref] [PubMed]

2005 (1)

A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
[Crossref]

2004 (1)

2003 (1)

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

2002 (4)

K. Lee and J. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

2001 (2)

R. J. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

1999 (1)

M. D. Hannam and W. J. Thompson, “Estimating small signals by using maximum likelihood and poisson statistics,” Nucl. Instrum. Methods Phys. Res., Sect. A 431, 239–251 (1999).
[Crossref]

1998 (2)

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1996 (1)

A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

1978 (1)

J. F. Clauser and A. Shimony, “Bell’s theorem. experimental tests and implications,” Rep. Prog. Phys. 41, 1881 (1978).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Abouraddy, A. F.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

Acin, A.

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

Agrawal, P.

C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
[Crossref]

Aiello, A.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Ambrosio, A.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Babazadeh, A.

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

Badurek, G.

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

Balthazar, W.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

Banzer, P.

Barnett, S.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Barnett, S. M.

Baron, M.

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Bavaresco, J.

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Bent, N.

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

Berg-Johansen, S.

Bolduc, E.

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

Borges, C.

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Bouchard, F.

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Boyd, R.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Boyd, R. W.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
[Crossref]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

Brandt, F.

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Cabello, A.

A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
[Crossref]

Capasso, F.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

Cardano, F.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Chen, L.

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Choudhary, S. K.

C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
[Crossref]

Chu, S. T.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Cino, A.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Clauser, J. F.

J. F. Clauser and A. Shimony, “Bell’s theorem. experimental tests and implications,” Rep. Prog. Phys. 41, 1881 (1978).
[Crossref]

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Cortés, L. R.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Courtial, J.

Dada, A. C.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Datta, C.

C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
[Crossref]

de Barros, J. A.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

De Guise, H.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

De La Hoz, P.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

de Lisio, C.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

De Oliveira, A.

A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
[Crossref]

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

Ding, D.

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Dragoman, D.

D. Dragoman and M. Dragoman, Quantum-classical analogies (Springer Science & Business Media, 2013).

Dragoman, M.

D. Dragoman and M. Dragoman, Quantum-classical analogies (Springer Science & Business Media, 2013).

Dudley, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

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

Durt, T.

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Eliel, E.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

Eliel, E. R.

W. Löffler, V. D. Salakhutdinov, and E. R. Eliel, “Hybrid radial-angular quantum correlations of spatially entangled photons,” in Quantum Information and Measurement, (Optical Society of America, 2012), pp. QW3A–6.
[Crossref]

Erhard, M.

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
[Crossref]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

Erker, P.

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Estebaranz, J.

A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
[Crossref]

Fickler, R.

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Fiorentino, M.

T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

Fischer, B.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

Forbes, A.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

T. Konrad and A. Forbes, “Quantum mechanics and classical light,” Contemp. Phys. 0, 1–22 (2019).
[Crossref]

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

B. Ndagano and A. Forbes, “Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence,” Phys. Rev. A 98, 062330 (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, 397–402 (2017).
[Crossref]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

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

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Franke-Arnold, S.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref] [PubMed]

Friis, N.

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

Fu, D.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

García-Alcaine, G.

A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
[Crossref]

Giacobino, E.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Gibson, G.

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

Giovannini, D.

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

Gisin, N.

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Goyal, S. K.

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Gu, X.

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

Guo, G.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Hannam, M. D.

M. D. Hannam and W. J. Thompson, “Estimating small signals by using maximum likelihood and poisson statistics,” Nucl. Instrum. Methods Phys. Res., Sect. A 431, 239–251 (1999).
[Crossref]

Hasegawa, Y.

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

Hernandez-Aranda, R. I.

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

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, 397–402 (2017).
[Crossref]

Hor-Meyll, M.

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Hradil, Z.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Huber, M.

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

Huguenin, J.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

Ireland, D.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Islam, M.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

Jack, B.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Jennewein, T.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Kagalwala, K. H.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

Karimi, E.

E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
[Crossref]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Kashyap, R.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

Khoury, A.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

Kim, M.

W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
[Crossref] [PubMed]

Kim, T.

T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref] [PubMed]

Klöckl, C.

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Konrad, T.

T. Konrad and A. Forbes, “Quantum mechanics and classical light,” Contemp. Phys. 0, 1–22 (2019).
[Crossref]

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

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, 397–402 (2017).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Krenn, M.

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

W. N. Plick and M. Krenn, “Physical meaning of the radial index of laguerre-gauss beams,” Phys. Rev. A 92, 063841 (2015).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Kues, M.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Kwiat, P. G.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Lapkiewicz, R.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Latorre, J. I.

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

Leach, J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Lee, J.

W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
[Crossref] [PubMed]

Lee, K.

K. Lee and J. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

Leuchs, G.

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Li, P.

Li, Y.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Linden, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Little, B. E.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Liu, S.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Liu, Z.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

Löffler, W.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

W. Löffler, V. D. Salakhutdinov, and E. R. Eliel, “Hybrid radial-angular quantum correlations of spatially entangled photons,” in Quantum Information and Measurement, (Optical Society of America, 2012), pp. QW3A–6.
[Crossref]

Loidl, R.

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

Loranger, S.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Malik, M.

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
[Crossref]

Marquardt, C.

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Marrucci, L.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Massa, F.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Massar, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

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, 397–402 (2017).
[Crossref]

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

Miatto, F. M.

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Milman, P.

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

Mirhosseini, M.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

Monken, C.

A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
[Crossref]

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, 397–402 (2017).
[Crossref]

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

Nape, I.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

Ndagano, B.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

B. Ndagano and A. Forbes, “Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence,” Phys. Rev. A 98, 062330 (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, 397–402 (2017).
[Crossref]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Nouroozi, R.

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

Ornigotti, M.

Padgett, M.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Padgett, M. J.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161–204 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref] [PubMed]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Paparo, D.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Pas’ko, V.

Passos, M.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

Perez-Garcia, B.

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

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, 397–402 (2017).
[Crossref]

Piccirillo, B.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Pivoluska, M.

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Plick, W. N.

W. N. Plick and M. Krenn, “Physical meaning of the radial index of laguerre-gauss beams,” Phys. Rev. A 92, 063841 (2015).
[Crossref]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Popescu, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Qassim, H.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Qiu, X.

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

Rafsanjani, S. M. H.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Ramelow, S.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Rauch, H.

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

Rehácek, J.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Reimer, C.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Romero, J.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Rosales-Guzman, C.

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, 397–402 (2017).
[Crossref]

Rosales-Guzmán, C.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[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, 397–402 (2017).
[Crossref]

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

F. S. Roux and Y. Zhang, “Projective measurements in quantum and classical optical systems,” Phys. Rev. A 90, 033835 (2014).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Roztocki, P.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Salakhutdinov, V.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

Salakhutdinov, V. D.

W. Löffler, V. D. Salakhutdinov, and E. R. Eliel, “Hybrid radial-angular quantum correlations of spatially entangled photons,” in Quantum Information and Measurement, (Optical Society of America, 2012), pp. QW3A–6.
[Crossref]

Saleh, B. E.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

Salem, A. B.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Sánchez-Soto, L. L.

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Santamato, E.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Schaeff, C.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

Sciara, S.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Sciarrino, F.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

Sephton, B.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

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

She, W.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Shi, B.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Shi, S.

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

Shimony, A.

J. F. Clauser and A. Shimony, “Bell’s theorem. experimental tests and implications,” Rep. Prog. Phys. 41, 1881 (1978).
[Crossref]

Simon, C.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Slussarenko, S.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Son, W.

W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
[Crossref] [PubMed]

Souza, C.

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

Spreeuw, R.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Spreeuw, R. J.

R. J. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

Stiller, B.

Thomas, J.

K. Lee and J. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

Thompson, W. J.

M. D. Hannam and W. J. Thompson, “Estimating small signals by using maximum likelihood and poisson statistics,” Nucl. Instrum. Methods Phys. Res., Sect. A 431, 239–251 (1999).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Toninelli, E.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

Töppel, F.

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Trichili, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Valencia, N. H.

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Vallés, A.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

Vallone, G.

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Vitagliano, G.

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

Walborn, S.

A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
[Crossref]

Wang, F.

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

Wei, T.-C.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Weinfurter, H.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Wetzel, B.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

Willner, A. E.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

Woerdman, J.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Wong, F. N.

T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

Xu, Z.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Yang, C.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Yao, A.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161–204 (2011).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zeilinger, A.

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
[Crossref]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Zghal, M.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Zhang, D.

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

Zhang, S.

Zhang, W.

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

Zhang, X.

Zhang, Y.

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (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, 397–402 (2017).
[Crossref]

F. S. Roux and Y. Zhang, “Projective measurements in quantum and classical optical systems,” Phys. Rev. A 90, 033835 (2014).
[Crossref]

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

Zhao, J.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

Zhou, Q.

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Zhou, Y.

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

Zhou, Z.

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

Adv. Opt. Photonics (2)

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11, 67–134 (2019).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161–204 (2011).
[Crossref]

Appl. Opt. (1)

Contemp. Phys. (1)

T. Konrad and A. Forbes, “Quantum mechanics and classical light,” Contemp. Phys. 0, 1–22 (2019).
[Crossref]

Found. Phys. (1)

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

J. Mod. Opt. (1)

B. Perez-Garcia, R. I. Hernandez-Aranda, A. Forbes, and T. Konrad, “The first iteration of grover’s algorithm using classical light with orbital angular momentum,” J. Mod. Opt. 65, 1942–1948 (2018).

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[Crossref]

J. Opt. B (1)

A. De Oliveira, S. Walborn, and C. Monken, “Implementing the deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B 7, 288–292 (2005).
[Crossref]

Light. Sci. Appl. (1)

Z. Zhou, Y. Li, D. Ding, W. Zhang, S. Shi, B. Shi, and G. Guo, “Orbital angular momentum photonic quantum interface,” Light. Sci. Appl. 5, e16019 (2016).
[Crossref]

Nat. Photonics (2)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

Nat. Phys. (5)

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, 397–402 (2017).
[Crossref]

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

C. Reimer, S. Sciara, P. Roztocki, M. Islam, L. R. Cortés, Y. Zhang, B. Fischer, S. Loranger, R. Kashyap, and A. Cino, “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys. 15, 148–153 (2018).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, “Measurements in two bases are sufficient for certifying high-dimensional entanglement,” Nat. Phys. 14, 1032–1037 (2018).
[Crossref]

Nat. Rev. Phys. (1)

N. Friis, G. Vitagliano, M. Malik, and M. Huber, “Entanglement certification from theory to experiment,” Nat. Rev. Phys. 1, 72–87 (2018).
[Crossref]

Nature (5)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, and B. E. Little, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref] [PubMed]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref] [PubMed]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, “Violation of a bell-like inequality in single-neutron interferometry,” Nature 425, 45–48 (2003).
[Crossref] [PubMed]

New J. Phys. (2)

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

Nucl. Instrum. Methods Phys. Res., Sect. A (1)

M. D. Hannam and W. J. Thompson, “Estimating small signals by using maximum likelihood and poisson statistics,” Nucl. Instrum. Methods Phys. Res., Sect. A 431, 239–251 (1999).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (2)

Philos. Trans. R. Soc. A (1)

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of laguerre-gaussian modes,” Philos. Trans. R. Soc. A 375, 20150442 (2017).
[Crossref]

Phys. Lett. A (1)

A. Cabello, J. Estebaranz, and G. García-Alcaine, “Bell-kochen-specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).
[Crossref]

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Phys. Rev. A (17)

M. Passos, W. Balthazar, J. A. de Barros, C. Souza, A. Khoury, and J. Huguenin, “Classical analog of quantum contextuality in spin-orbit laser modes,” Phys. Rev. A 98, 062116 (2018).
[Crossref]

R. J. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

C. Borges, M. Hor-Meyll, J. Huguenin, and A. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
[Crossref]

C. Datta, P. Agrawal, and S. K. Choudhary, “Measuring higher-dimensional entanglement,” Phys. Rev. A 95, 042323 (2017).
[Crossref]

F. S. Roux and Y. Zhang, “Projective measurements in quantum and classical optical systems,” Phys. Rev. A 90, 033835 (2014).
[Crossref]

B. Ndagano and A. Forbes, “Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence,” Phys. Rev. A 98, 062330 (2018).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

T. Kim, M. Fiorentino, and F. N. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

S. Liu, Z. Zhou, S. Liu, Y. Li, Y. Li, C. Yang, Z. Xu, Z. Liu, G. Guo, and B. Shi, “Coherent manipulation of a three-dimensional maximally entangled state,” Phys. Rev. A 98, 062316 (2018).
[Crossref]

W. N. Plick and M. Krenn, “Physical meaning of the radial index of laguerre-gauss beams,” Phys. Rev. A 92, 063841 (2015).
[Crossref]

E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via hong-ou-mandel interference,” Phys. Rev. A 89, 013829 (2014).
[Crossref]

Y. Zhang, F. S. Roux, M. McLaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[Crossref]

E. Karimi, R. Boyd, P. De La Hoz, H. De Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of laguerre-gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

D. Zhang, X. Qiu, W. Zhang, and L. Chen, “Violation of a bell inequality in two-dimensional state spaces for radial quantum number,” Phys. Rev. A 98, 042134 (2018).
[Crossref]

Phys. Rev. Lett. (10)

X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, “Gouy phase radial mode sorter for light: Concepts and experiments,” Phys. Rev. Lett. 120, 103601 (2018).
[Crossref] [PubMed]

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref] [PubMed]

W. Son, J. Lee, and M. Kim, “Generic bell inequalities for multipartite arbitrary dimensional systems,” Phys. Rev. Lett. 96, 060406 (2006).
[Crossref] [PubMed]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of bell’s inequality under strict einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

C. Souza, J. Huguenin, P. Milman, and A. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99, 160401 (2007).
[Crossref] [PubMed]

K. Lee and J. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U. S. A. (1)

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).

Rep. Prog. Phys. (1)

J. F. Clauser and A. Shimony, “Bell’s theorem. experimental tests and implications,” Rep. Prog. Phys. 41, 1881 (1978).
[Crossref]

Rev. Mod. Phys. (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Sci. Adv. (1)

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and R. W. Boyd, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Sci. Rep. (1)

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref] [PubMed]

Science (2)

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
[Crossref] [PubMed]

E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
[Crossref]

Other (3)

D. Dragoman and M. Dragoman, Quantum-classical analogies (Springer Science & Business Media, 2013).

W. Löffler, V. D. Salakhutdinov, and E. R. Eliel, “Hybrid radial-angular quantum correlations of spatially entangled photons,” in Quantum Information and Measurement, (Optical Society of America, 2012), pp. QW3A–6.
[Crossref]

S. Liu, Q. Zhou, S. Liu, Y. Li, Y. Li, Z. Zhou, G. Guo, and B. Shi, “Generation of a macroscopic schrödinger cat using vortex light,” arXiv preprint arXiv:1807.05498 (2018).

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Figures (5)

Fig. 1
Fig. 1 Setups for the generation of a HD-ARNS and measured modal decomposition density: (a) spatial vector distribution of the spatial vector, phase, and intensity for LG beam |1〉L |1〉P; (b) optical layout for generation and detection HD-ARNS. The input laser source is a semiconductor laser at the 780 nm. HWP: half wave plate. PBS: polarization beam splitter. F1–4: convex lens of two inches with f =300 mm. D: a power meter for detection. (c): a six-dimensional ARNS. (d) and (e) show the situation of a pure LG mode when radial L=0 and angular P=0, respectively; the range in each testing is from 0 to 10; the normalized distribution is calculated by the corresponding each row. The color scale represents the powers obtained by normalization of each row.
Fig. 2
Fig. 2 Results for Bell-CGLMP-type interference curves and the value of Bell-CGLMP-like inequality. (a) and (b) show the interference curves for the MHD-ARNS in d=2 and d=10, respectively. (c) shows the violations of the Bell-CGLMP-like inequality for nonlocal HD entangled states (blue) obtained in [38] and for local HD non-separable states (red) measured in our system.
Fig. 3
Fig. 3 Theoretical and experimental distributions of values of the Bell-CGLMP expression S and interference visibility V for a three-dimensional ARNS. (a) A three-dimensional surface shows the S and V plotted using two parameters ε0 and ε1; the purple dashed line marks the situation for ε1=1/3; the red boundary marks instance with Sd=3 = 2 and 71%. (b) Vertical distributions of visibility versus ε0 with ε0=1/3; (c) and (d) are instances of visibility changing with ε0n, where ε1 = 0 and ε1 = 1/3, respectively.
Fig. 4
Fig. 4 The orthogonality for angular and radial LG modes. (a) and (c): The orthogonality of LG 0 5 and LG 5 0 for standard LG modes. (c) and (d): The corresponding orthogonality for the revised LG modes. In the simulation, the beam waist w0 for input Gaussian beam is 1000 um, and the mode size W on the backward SLM is equal to 750 um.
Fig. 5
Fig. 5 The intensity- and phase-distribution of the LG modes. (a): The intensity distribution of the fundamental Gaussian beam. (b) and (c): The intensity distribution of the LG modes |6〉L|6〉P in standard and revised regimes, respectively. (d) The acquired phase for generation of six-dimensional maximally non-separable mode in SLM by the amplitude-phase and optical blazing encoding technology. In all the simulations, the wavelength and fundamental beam waist for a Gaussian beam are 780 nm and 2 mm.

Equations (9)

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| θ L a | θ P b = 1 d j = 0 j = d 1 exp ( i θ L a j ) | j L 1 d j = 0 j = d 1 exp ( i θ P b j ) | j P
I ( θ L a , θ P b ) = 1 d 3 / 2 | j = 0 j = d 1 exp ( i 2 π d j ( v w + a / 2 + ( 1 ) b / 4 ) ) | 2
| φ 3 = ε 0 | 0 L | 0 P + ε 1 | 1 L | 1 P + 1 ε 0 ε 1 | 2 L | 2 P
Cylin ( r , ϕ , z ) | L , P = 2 P ! π ( P + | L | ) ! 1 w ( z ) ( 2 r w ( z ) ) | L | L P | L | ( 2 r 2 w 2 ( z ) ) exp ( r 2 w ( z ) 2 ) × exp ( i ( L ϕ k r 2 z 2 ( z 2 + z r 2 ) + ( 2 P + | L | + 1 ) a tan ( z z r ) ) )
0 0 2 π LG L P ( r , ϕ ) * LG L P ( r , ϕ ) r d r d ϕ = δ L , L δ P , P
0 2 π exp ( i ( L L ) ϕ ) d ϕ = 2 π * δ L L , 0
0 L P | a | ( r ) * L P | a | ( r ) d r = Γ ( a + P + 1 ) P ! δ P , P
G ( u , w ) = 1 w 2 π exp ( | u | 2 w 2 )
LG L P | LG L P = 0 0 2 π LG L P ( r , ϕ ) * LG L P ( r , ϕ ) * G ( r , W ) r d r d ϕ

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