Abstract

High-dimensional entanglement is a valuable resource for secure and efficient quantum information processing. A major challenge for practical use of multidimensional quantum systems is the establishment of controls over arbitrary superposition states in realistic conditions. This work demonstrates spatially entangled photon pairs propagating through two separate four-core optical fibers with the amplitudes and phases of the superposition being independently controllable. Using quantum state analyzers that can detect arbitrary multicore superposition states, Bell-type CGLMP inequalities in two, three, and four dimensions are directly tested. Enhanced violation of the inequality by slight nonmaximality of entanglement is also demonstrated.

© 2018 Chinese Laser Press

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  1. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
    [Crossref]
  2. S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
    [Crossref]
  3. S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
    [Crossref]
  4. F. Bouchard, R. Fickler, R. W. Boyd, and E. Karimi, “High-dimensional quantum cloning and applications to quantum hacking,” Sci. Adv. 3, e1601915 (2017).
    [Crossref]
  5. N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
    [Crossref]
  6. D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequality for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
    [Crossref]
  7. X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
    [Crossref]
  8. L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
    [Crossref]
  9. M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
    [Crossref]
  10. A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
    [Crossref]
  11. H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (2017).
    [Crossref]
  12. J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
    [Crossref]
  13. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref]
  14. 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]
  15. M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
    [Crossref]
  16. F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).
  17. A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
    [Crossref]
  18. T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
    [Crossref]
  19. S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
    [Crossref]
  20. M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
    [Crossref]
  21. G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
    [Crossref]
  22. Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
    [Crossref]
  23. M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
    [Crossref]
  24. Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Inf. 3, 25 (2017).
    [Crossref]
  25. G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
    [Crossref]
  26. J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
    [Crossref]
  27. E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
    [Crossref]
  28. H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
    [Crossref]
  29. D. Barrera, I. Gasulla, and S. Sales, “Multipoint two-dimensional curvature optical fiber sensor based on a nontwisted homogeneous four-core fiber,” J. Lightwave Technol. 33, 2445–2450 (2015).
    [Crossref]
  30. A. Acín, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Phys. Rev. A 65, 052325 (2002).
    [Crossref]
  31. A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
    [Crossref]
  32. J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
    [Crossref]
  33. C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
    [Crossref]
  34. T. Ikuta and H. Takesue, “Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A 93, 022307 (2016).
    [Crossref]
  35. G. M. Fernandes, N. J. Muga, A. M. Rocha, and A. N. Pinto, “Switching in multicore fibers using flexural acoustic waves,” Opt. Express 23, 26313–26325 (2015).
    [Crossref]
  36. Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
    [Crossref]

2018 (4)

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

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

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
[Crossref]

2017 (11)

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (2017).
[Crossref]

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

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

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

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

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

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
[Crossref]

2016 (2)

T. Ikuta and H. Takesue, “Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A 93, 022307 (2016).
[Crossref]

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

2015 (2)

2013 (2)

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

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

2012 (1)

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

2011 (1)

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]

2009 (3)

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
[Crossref]

2006 (2)

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

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

2005 (3)

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
[Crossref]

2002 (3)

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

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

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

2001 (1)

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

Acín, A.

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

A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
[Crossref]

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

Agnew, M.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

Aguirre Gómez, J. G.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Almeida, M. P.

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

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]

Augusiak, R.

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

Azaña, J.

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

Bacco, D.

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

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

Barrera, D.

Bernhard, C.

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

Bessire, B.

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

Bobrov, I. B.

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

Bonneau, D.

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

Bouchard, F.

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

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Bourennane, M.

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

Boyd, R. W.

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

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Brunner, N.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

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.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Cahall, C.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Cai, X.

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

Cañas, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

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

Cardenas, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Cariñe, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Caspani, L.

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

Cerf, N. J.

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

Chen, J.-L.

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

Chiuri, A.

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

Choi, S.-K.

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (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, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Cino, A.

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

Collins, D.

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

Connolly, P. W. R.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Cortés, L. R.

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

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]

Dalgaard, K.

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

Delgado, A.

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

Designolle, S.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Ding, Y.

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

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

Durt, T.

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

England, D.

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Englert, B.-G.

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Erhard, M.

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

Etcheverry, S.

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

Fedrizzi, A.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

Fernandes, G. M.

Fernandes, M. F.

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

Ferreira da Silva, T.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Feurer, T.

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

Fickler, R.

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

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

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Figueroa, F.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Forbes, A.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Fröwis, F.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Galvez, E. J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Gasulla, I.

Gauthier, D. J.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Ge, M.-L.

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

Gill, R.

A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
[Crossref]

Giovannini, D.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Gisin, N.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
[Crossref]

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

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

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

Gómez, E. S.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

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

Gong, Q.

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

González, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Guerreiro, T.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Guo, G.-C.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Guo, Y.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Guzmán, R.

Heshami, K.

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Howell, J. C.

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

Hu, X.-M.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Huang, Y.-F.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Huber, M.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Iemmi, C.

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

Ikuta, T.

T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
[Crossref]

T. Ikuta and H. Takesue, “Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A 93, 022307 (2016).
[Crossref]

Islam, N. T.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Jiménez, O.

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

Karimi, E.

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

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Karlsson, A.

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

Khan, I. A.

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

Kim, J.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Kleinmann, M.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Konrad, T.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

Kovlakov, E. V.

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

Krenn, M.

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

Kues, M.

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

Kulik, S. P.

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

Kwek, L. C.

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

Laing, A.

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

Langford, N. K.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

Latorre, J. I.

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

Leach, J.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[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]

Ledesma, S.

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

Lee, E.

H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
[Crossref]

Lee, H. J.

H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
[Crossref]

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (2017).
[Crossref]

Lemelle, D. S.

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

Li, C.-F.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Lim, C. C. W.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Lima, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

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

G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Linden, N.

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

Little, B. E.

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

Liu, B.-H.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[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]

Mancinska, L.

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

Martin, A.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Martini, F. D.

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

Massar, S.

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

Mataloni, P.

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

McLaren, M. G.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Monken, C. H.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Morandotti, R.

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

Moss, D. J.

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

Muga, N. J.

Neves, L.

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Nogueira, W. A. T.

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

O’Brien, J. L.

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

O’Sullivan-Hale, M. N.

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

Oh, C. H.

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

Oxenløwe, L. K.

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

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

Padgett, M. J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[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]

Pádua, S.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Paesani, S.

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

Park, H. S.

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (2017).
[Crossref]

H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
[Crossref]

Pinto, A. N.

Popescu, S.

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

Przysiezna, A.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Ramelow, S.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

Ratschbacher, L.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

Rebón, L.

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

Reimer, C.

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

Ribeiro, P. H. S.

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

Rocha, A. M.

Romero, J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Rossi, A.

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

Rottwitt, K.

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

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

Roux, F. S.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

Roztocki, P.

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

Saavedra, C.

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

G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

Salavrakos, A.

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

Sales, S.

Sánchez-Soto, L. L.

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

Santagati, R.

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

Sciara, S.

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

Silverstone, J. W.

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

Skrzypczyk, P.

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

Solís-Prosser, M. A.

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

Stefano, Q. P.

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

Stefanov, A.

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

Straupe, S. S.

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

Takesue, H.

T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
[Crossref]

T. Ikuta and H. Takesue, “Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A 93, 022307 (2016).
[Crossref]

Thompson, M. G.

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

Tiranov, A.

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

Tura, J.

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

Vallone, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

Vargas, A.

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]

Vera, N.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Vértesi, T.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Villoresi, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Walborn, S. P.

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

Wang, J.

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

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]

Wetzel, B.

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

Wu, C.

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

Xavier, G. B.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

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

Xiang, G.-Y.

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

Zeilinger, A.

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[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]

Zhang, Y.

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

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

Zhou, X.

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

IEEE Photon. Technol. Lett. (1)

H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photon. Technol. Lett. 29, 2250–2253 (2017).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. (1)

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[Crossref]

Light Sci. Appl. (1)

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photon: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

Nat. Phys. (1)

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]

Nature (2)

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

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

npj Quantum Inf. (1)

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

Opt. Express (2)

Phys. Rev. A (6)

Q. P. Stefano, L. Rebón, S. Ledesma, and C. Iemmi, “Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry,” Phys. Rev. A 96, 062328 (2017).
[Crossref]

J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh, and M.-L. Ge, “Violating bell inequalities maximally for two d-dimensional systems,” Phys. Rev. A 74, 032106 (2006).
[Crossref]

C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, “Shaping frequency-entangled qudits,” Phys. Rev. A 88, 032322 (2013).
[Crossref]

T. Ikuta and H. Takesue, “Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A 93, 022307 (2016).
[Crossref]

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, F. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over 0.3  km of multicore telecommunication optical fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

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

Phys. Rev. Lett. (12)

A. Acín, R. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Phys. Rev. Lett. 95, 210402 (2005).
[Crossref]

A. Martin, T. Guerreiro, A. Tiranov, S. Designolle, F. Fröwis, N. Brunner, M. Huber, and N. Gisin, “Quantifying photonic high-dimensional entanglement,” Phys. Rev. Lett. 118, 110501 (2017).
[Crossref]

E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, “Spatial bell-state generation without transverse mode subspace postselection,” Phys. Rev. Lett. 118, 030503 (2017).
[Crossref]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

M. A. Solís-Prosser, M. F. Fernandes, O. Jiménez, A. Delgado, and L. Neves, “Experimental minimum-error quantum-state discrimination in high dimensions,” Phys. Rev. Lett. 118, 100501 (2017).
[Crossref]

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

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

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

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref]

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. D. Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref]

Sci. Adv. (3)

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

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
[Crossref]

Sci. Rep. (3)

T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
[Crossref]

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

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multicore optical fibres,” Sci. Rep. 7, 4302 (2017).
[Crossref]

Science (1)

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

Other (1)

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” arxiv:1802.05773v2 (2018).

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Figures (5)

Fig. 1.
Fig. 1. Schematic of the experimental setup. (a) Arrangement of the optical components used to generate and measure the entangled photon pairs between two multicore fibers. (b) Imaging configuration for the pump beam and photons coupled to the fiber cores (L=250  mm, f1=50  mm, f2=75  mm, and f3=15  mm). Inset: phase patterns on SLM0. SLM, spatial light modulator; L, lens; MCF, multicore fiber; Q, quarter-wave plate; H, half-wave plate; PBS, polarizing beam splitter; IF, interference filter; FC, fiber coupler; SMF, single-mode fiber.
Fig. 2.
Fig. 2. Reconstructed density matrices by quantum state tomography: (a) d=2, (b) d=3, and (c) d=4.
Fig. 3.
Fig. 3. Quantum correlations between the two-core superposition states, while changing the relative phase of the pump beam spots. Photon 1 in MCF1 is projected onto the state (|j+|k)/2. Photon 2 in MCF2 is projected onto (|j+|k)/2 (red circles) or (|j+i|k)/2 (black squares). The phase ϕ of the two-photon state component |k|k is scanned from 0 to 2π by a relative phase of the relevant subsection pattern on SLM0. The coincidence counting period was 60 s. (a) j=0, k=1. (b) j=1, k=2. (c) j=2, k=3. (d) j=3, k=0.
Fig. 4.
Fig. 4. Measured Bell-type parameter Sd (squares), compared with the limit by the local variable theories (triangles) and the theoretical values for the maximally entangled states (circles).
Fig. 5.
Fig. 5. Relative amounts of the core-mode components and the Bell parameter S4 in entangled states (|0|0+γ|1|1+γ|2|2+|3|3)/2(1+γ2). Dashed lines denote the design values. (a) γ1.35. (b) γ1.00. (c) γ0.74. (d) γ0.32.

Tables (2)

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Table 1. Coincidence Counts for Quantum State Tomographya

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Table 2. Coincidence Counts for the Test of the CGLMP Inequalitiesa

Equations (4)

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|Ψ=k=03Ck|k1|k2,
Sd=k=0[d/2]1(12kd1){[P(A0=B0+k)+P(A1=B0k1)+P(A1=B1+k)+P(A0=B1k)][P(A0=B0k1)+P(A1=B0+k)+P(A1=B1k1)+P(A0=B1+k+1)]},
|vaA=1dk=0d1exp[i2πdk(v+αa)],|wbB=1dk=0d1exp[i2πdk(w+βb)],
|Ψ=12(1+γ2)(|0|0+γ|1|1+γ|2|2+|3|3),

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