Abstract

Qudits, d-level quantum systems, have been shown to provide a better resource for quantum key distribution and other Quantum Information protocols. It is customary to generate photonic qudits using more than one degree of freedom of the same photon. In much the same way, multi-qubit states are generated using only a pair of photons and ingenious ways to manipulate more than one degree of freedom independently. In contrast to such costly implementations in terms of quantum resources, we present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. The degree of entanglement within each pair was inferred by exploiting the availability of two copies of the same state, without the need of a full tomographic reconstruction of the states, and both highly-entangled and separable states were generated. We show theoretically that the set of states obtainable using our setup is very diverse, ranging from maximally entangled states of qudits to separable states.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Control of quantum transverse correlations on a four-photon system

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua
Opt. Express 19(4) 3715-3729 (2011)

Hyperconcentration for entanglement in two degrees of freedom

Xi-Han Li, Xiao Chen, and Zhi Zeng
J. Opt. Soc. Am. B 30(11) 2774-2780 (2013)

References

  • View by:
  • |
  • |
  • |

  1. G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
    [Crossref]
  2. L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
    [Crossref] [PubMed]
  3. L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
    [Crossref]
  4. L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
    [Crossref]
  5. W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
    [Crossref]
  6. P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
    [Crossref] [PubMed]
  7. G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
    [Crossref]
  8. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
    [Crossref]
  9. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
    [Crossref] [PubMed]
  10. 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 (2011).
    [Crossref]
  11. V. D. Salakhutdinov, E. R. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
    [Crossref] [PubMed]
  12. M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
    [Crossref]
  13. E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
    [Crossref] [PubMed]
  14. E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
    [Crossref]
  15. E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
    [Crossref] [PubMed]
  16. G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
    [Crossref]
  17. A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
    [Crossref]
  18. J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
    [Crossref] [PubMed]
  19. H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
    [Crossref] [PubMed]
  20. L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
    [Crossref]
  21. H. J. Carmichael, R. J. Glauber, and M. O. Scully, Directions in Quantum Optics: A Collection of Papers Dedicated to Dan Walls (Springer, 2000).
  22. G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
    [Crossref] [PubMed]
  23. R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
    [Crossref]
  24. M. Genovese and P. Traina, “Review on qudits production and their application to quantum communication and studies on local realism,” Adv. Sci. Lett. 1, 153–160 (2008).
    [Crossref]
  25. B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
    [Crossref] [PubMed]
  26. M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
    [Crossref]
  27. L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A (R) 82, 030301 (2010).
    [Crossref]
  28. S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, “Quantum key distribution with higher-order alphabets using spatially encoded qudits,” Phys. Rev. Lett. 96, 090501 (2006).
    [Crossref] [PubMed]
  29. 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] [PubMed]
  30. M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
    [Crossref]
  31. M. H. Dehkordi and E. Fattahi, “Threshold quantum secret sharing between multiparty and multiparty using Greenberger-Horne-Zeilinger state,” Quant. Inf. Proc. 12, 1299–1306 (2013).
    [Crossref]
  32. E. Brainis, “Quantum imaging with N-photon states in position space,” Opt. Express 19, 24228–24240 (2011).
    [Crossref] [PubMed]
  33. S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
    [Crossref] [PubMed]
  34. J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
    [Crossref]
  35. S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
    [Crossref]
  36. T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
    [Crossref]
  37. M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
    [Crossref]
  38. C. Gneiting and K. Hornberger, “Detecting entanglement in spatial interference,” Phys. Rev. Lett. 106, 210501 (2011).
    [Crossref] [PubMed]
  39. C. Gneiting and K. Hornberger, “Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs,” Phys. Rev. A 88, 013610 (2013).
    [Crossref]
  40. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
    [Crossref]
  41. W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989).
    [Crossref]
  42. G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
    [Crossref] [PubMed]
  43. A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
    [Crossref]
  44. R.-B. Jin, R. Shimizu, K. Wakui, M. Fujiwara, T. Yamashita, S. Miki, H. Terai, Z. Wang, and M. Sasaki, “Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at telecom wavelength,” Opt. Express 22, 11498–11507 (2014).
    [Crossref] [PubMed]
  45. J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
    [Crossref]
  46. T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
    [Crossref]
  47. S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
    [Crossref]

2016 (2)

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
[Crossref] [PubMed]

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

2014 (4)

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

R.-B. Jin, R. Shimizu, K. Wakui, M. Fujiwara, T. Yamashita, S. Miki, H. Terai, Z. Wang, and M. Sasaki, “Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at telecom wavelength,” Opt. Express 22, 11498–11507 (2014).
[Crossref] [PubMed]

2013 (4)

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (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] [PubMed]

M. H. Dehkordi and E. Fattahi, “Threshold quantum secret sharing between multiparty and multiparty using Greenberger-Horne-Zeilinger state,” Quant. Inf. Proc. 12, 1299–1306 (2013).
[Crossref]

C. Gneiting and K. Hornberger, “Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs,” Phys. Rev. A 88, 013610 (2013).
[Crossref]

2012 (4)

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

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

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

2011 (5)

2010 (6)

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A (R) 82, 030301 (2010).
[Crossref]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

2009 (2)

W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[Crossref]

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

2008 (1)

M. Genovese and P. Traina, “Review on qudits production and their application to quantum communication and studies on local realism,” Adv. Sci. Lett. 1, 153–160 (2008).
[Crossref]

2007 (2)

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[Crossref]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

2006 (3)

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (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] [PubMed]

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

2005 (1)

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

2004 (4)

L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

2002 (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

2001 (1)

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

1998 (2)

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

1997 (2)

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
[Crossref]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

1995 (1)

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[Crossref]

1989 (1)

W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989).
[Crossref]

Acín, A.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

Almeida, M. P.

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

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 (2011).
[Crossref]

Bartlett, S. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Berruezo, L. P.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

Berthiaume, A.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
[Crossref]

Borges, G. F.

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

Bose, S.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

Boukama-Dzoussi, P. E.

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

Bouwmeester, D.

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

Brainis, E.

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 (2011).
[Crossref]

Buzek, V.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
[Crossref]

Cañas, G.

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] [PubMed]

Carmichael, H. J.

H. J. Carmichael, R. J. Glauber, and M. O. Scully, Directions in Quantum Optics: A Collection of Papers Dedicated to Dan Walls (Springer, 2000).

Carvalho, M. A. D.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

Ceccarelli, R.

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

Chen, Z.-B.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[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 (2011).
[Crossref]

Dalton, R. B.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Daniell, M.

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Davidovich, L.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

de Assis, P.-L

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

de Assis, P.-L.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

de Dood, M. J. A.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
[Crossref] [PubMed]

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Dehkordi, M. H.

M. H. Dehkordi and E. Fattahi, “Threshold quantum secret sharing between multiparty and multiparty using Greenberger-Horne-Zeilinger state,” Quant. Inf. Proc. 12, 1299–1306 (2013).
[Crossref]

Delgado, A.

Donati, G.

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

Dougakiuchi, T.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Eliel, E. R.

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

Erhard, M.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[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] [PubMed]

Fattahi, E.

M. H. Dehkordi and E. Fattahi, “Threshold quantum secret sharing between multiparty and multiparty using Greenberger-Horne-Zeilinger state,” Quant. Inf. Proc. 12, 1299–1306 (2013).
[Crossref]

Fedrizzi, A.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Ferraz, J.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

Fickler, R.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

Ficklera, R.

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

Fields, B. D.

W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989).
[Crossref]

Fonseca, E.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

Fujiwara, M.

Gasparoni, S.

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Genovese, M.

M. Genovese and P. Traina, “Review on qudits production and their application to quantum communication and studies on local realism,” Adv. Sci. Lett. 1, 153–160 (2008).
[Crossref]

Ghosh, S.

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

Gilchrist, A.

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[Crossref]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Giovannini, D.

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

Gisin, N.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

Glauber, R. J.

H. J. Carmichael, R. J. Glauber, and M. O. Scully, Directions in Quantum Optics: A Collection of Papers Dedicated to Dan Walls (Springer, 2000).

Gneiting, C.

C. Gneiting and K. Hornberger, “Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs,” Phys. Rev. A 88, 013610 (2013).
[Crossref]

C. Gneiting and K. Hornberger, “Detecting entanglement in spatial interference,” Phys. Rev. Lett. 106, 210501 (2011).
[Crossref] [PubMed]

Gómez, E. 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] [PubMed]

G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
[Crossref] [PubMed]

Gómez, J. A.

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

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

Goyal, S. K.

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

Guzmán, R.

Hamel, D. R.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Harvey, M. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Hiesmayr, B. C.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
[Crossref] [PubMed]

Hillery, M.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
[Crossref]

Hofmann, H. F.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Hornberger, K.

C. Gneiting and K. Hornberger, “Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs,” Phys. Rev. A 88, 013610 (2013).
[Crossref]

C. Gneiting and K. Hornberger, “Detecting entanglement in spatial interference,” Phys. Rev. Lett. 106, 210501 (2011).
[Crossref] [PubMed]

Horne, M. A.

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

Hradil, Z.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

Hübel, H.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Huber, M.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

Huberc, M.

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

Iinuma, M.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Jennewein, T.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Jin, R.-B.

Kadoya, Y.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Knight, P. L.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

Konrad, T.

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

Krenn, M.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

Krenna, M.

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

Kulik, S. P.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

Langford, N. K.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Lapkiewicza, R.

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[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 (2011).
[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] [PubMed]

Lima, G.

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] [PubMed]

G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
[Crossref] [PubMed]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

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

Löffler, W.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
[Crossref] [PubMed]

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

Lu, C.-Y.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Malik, M.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

Marrucci, L.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

Maslennikov, G. A.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

Mataloni, P.

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

Miki, S.

Molina-Terriza, G.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

Monken, C.

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

Monken, C. H.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Moreva, E. V.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

Nagali, E.

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

Neves, L.

G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
[Crossref] [PubMed]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

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

L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

Nishikawa, T.

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[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] [PubMed]

G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
[Crossref] [PubMed]

O’Brien, J. L.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Padgett, M. 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 (2011).
[Crossref]

Pádua, S.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

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

L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

Pan, J.-W.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

Peeters, W.

W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[Crossref]

Pryde, G. J.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Ralph, T. C.

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[Crossref]

Ramelow, S.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Ramelowa, S.

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

Rehácek, J.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

Renema, J.

W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[Crossref]

Renema, J. J.

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Resch, K. J.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[Crossref]

Ribeiro, P. H. S.

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

Ribeiro, P. H. Souto

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Roux, F. S.

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

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] [PubMed]

G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542–3552 (2011).
[Crossref] [PubMed]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

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

L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

Salakhutdinov, V. D.

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

Sansoni, L.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

Santamato, E.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

Santos, I.

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

Santos, I. F.

Sasaki, M.

Scarani, V.

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A (R) 82, 030301 (2010).
[Crossref]

Sciarrino, F.

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

P.-L. de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, F. Sciarrino, and S. Pádua, “Control of quantum transverse correlations on a four-photon system,” Opt. Express 19, 3715–3729 (2011).
[Crossref] [PubMed]

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

Scully, M. O.

H. J. Carmichael, R. J. Glauber, and M. O. Scully, Directions in Quantum Optics: A Collection of Papers Dedicated to Dan Walls (Springer, 2000).

Shalm, L. K.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

Sheridan, L.

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A (R) 82, 030301 (2010).
[Crossref]

Shimizu, R.

Simon, C.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

Slussarenko, S.

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

Straupe, S. S.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

Taguchi, G.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Terai, H.

Thew, R. T.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

Traina, P.

M. Genovese and P. Traina, “Review on qudits production and their application to quantum communication and studies on local realism,” Adv. Sci. Lett. 1, 153–160 (2008).
[Crossref]

Uesugi, N.

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[Crossref]

Vallone, G.

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

van der Torren, A. J. H.

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Van Exter, M.

W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[Crossref]

van Exter, M. P.

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Vargas, A.

Vaziri, A.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

Vedral, V.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

Wakui, K.

Walborn, S. P.

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

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

Wang, Z.

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Weinfurter, H.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

White, A. G.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

Wootters, W. K.

W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989).
[Crossref]

Xavier, G. B.

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] [PubMed]

Yamashita, T.

Yan, Z.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[Crossref]

Yorulmaz, S. C.

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Zbinden, H.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

Zeilinger, A.

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

Zukowski, M.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

Adv. Sci. Lett. (1)

M. Genovese and P. Traina, “Review on qudits production and their application to quantum communication and studies on local realism,” Adv. Sci. Lett. 1, 153–160 (2008).
[Crossref]

Ann. Phys. (1)

W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989).
[Crossref]

J. Appl. Phys. (1)

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

J. Ferraz, M. A. D. Carvalho, L. P. Berruezo, P.-L. de Assis, F. Sciarrino, and S. Pádua, “Diffraction of Einstein-Podolsky-Rosen states with one- and two-copies,” J. Phys. B: At. Mol. Opt. Phys. 47, 245504 (2014).
[Crossref]

Nat. Phys. (2)

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nat. Phys. 9, 19 (2013).
[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 (2011).
[Crossref]

Nature (1)

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Nature Photonics (1)

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nature Photonics 10, 248–252 (2016).
[Crossref]

Opt. Express (4)

Phys. Rep. (1)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Phys. Rev A (1)

G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev A 81, 052301 (2010).
[Crossref]

Phys. Rev. A (12)

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterizationof single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space”, Phys. Rev. A 73, 032340 (2006).
[Crossref]

L. Neves, S. Pádua, and C. Saavedra, “Controled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Charaterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[Crossref]

W. Peeters, J. Renema, and M. Van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[Crossref]

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1997).
[Crossref]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[Crossref]

M. A. D. Carvalho, J. Ferraz, G. F. Borges, P.-L de Assis, S. Pádua, and S. P. Walborn, “Experimental observation of quantum correlations in modular variables,” Phys. Rev. A 86, 032332 (2012).
[Crossref]

C. Gneiting and K. Hornberger, “Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs,” Phys. Rev. A 88, 013610 (2013).
[Crossref]

A. J. H. van der Torren, S. C. Yorulmaz, J. J. Renema, M. P. van Exter, and M. J. A. de Dood, “Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal,” Phys. Rev. A 85, 043837 (2012)
[Crossref]

Phys. Rev. A (R) (1)

L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A (R) 82, 030301 (2010).
[Crossref]

Phys. Rev. Lett. (14)

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

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref] [PubMed]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[Crossref]

C. Gneiting and K. Hornberger, “Detecting entanglement in spatial interference,” Phys. Rev. Lett. 106, 210501 (2011).
[Crossref] [PubMed]

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116, 073601 (2016).
[Crossref] [PubMed]

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

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-ohoton, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref] [PubMed]

E. Nagali, D. Giovannini, L. Marrucci, S. Slussarenko, E. Santamato, and F. Sciarrino, “Experimental optimal cloning of four-dimensional quantum states of photons,” Phys. Rev. Lett. 105, 073602 (2010).
[Crossref] [PubMed]

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

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, “Three-particle entanglement from two entangled pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglementand high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[Crossref] [PubMed]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

PNAS (1)

M. Krenna, M. Huberc, R. Ficklera, R. Lapkiewicza, S. Ramelowa, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” PNAS 111, 6243–6247 (2014).
[Crossref]

Quant. Inf. Proc. (1)

M. H. Dehkordi and E. Fattahi, “Threshold quantum secret sharing between multiparty and multiparty using Greenberger-Horne-Zeilinger state,” Quant. Inf. Proc. 12, 1299–1306 (2013).
[Crossref]

Rev. Mod. Phys. (1)

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Sci. Rep. (2)

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

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] [PubMed]

Other (1)

H. J. Carmichael, R. J. Glauber, and M. O. Scully, Directions in Quantum Optics: A Collection of Papers Dedicated to Dan Walls (Springer, 2000).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Complete setup for our experiment, comprised of a four-qudit state source and a detection apparatus. The source contains a 10 mm long periodically-poled KTP crystal that is pumped by a pulsed beam with λ = 413 nm, 200 fs pulse width and 76 MHz repetition rate, a dichroic mirror (DM) that reflects the pump light and allows the down-converted photons to pass, a cylindrical lens (CL) of focal length fCL = 5 cm that can be taken out of the optical path by a translation stage, a spherical lens (SL) of focal length fSL = 20 cm and a slide with either triple metallic slits or quadruple slits made of photographic film. The detection apparatus is composed of a lens with a focal distance of 30 cm in an f -f configuration between the apertures and the detection plane, so that the far field of the slits can be imaged. A polarizing beamsplitter (PBS) splits the photons coming from the slits into two branches, one with horizontally polarized photons and another with vertically polarized ones. This allows us to detect coincidences due exclusively to photons from different pairs. Each branch has a 50/50 beamsplitter (BS) that sends photons to the two avalanche photodiode detectors of each branch, D1 and D3 on the vertically polarized branch and D2 and D4 on the horizontally polarized one. The electrical pulses are then sent to custom electronics that process detections and registers as coincidences all pulses that arrive within a 5.6 ns window. Thus, we are able to detect two-, three- and fourfold coincidences between all possible combinations of detectors.
Fig. 2
Fig. 2 Optical setups used to control the qudit state generated after the slits. Figure (a) shows a telescope composed of a cylindrical lens with a focal distance 5 cm and a spherical lens with a focal distance 20 cm. Both share the same forward focal plane that coincides with the pump beam waist, positioned using the spherical lens SL1 that has a focal length of 30 cm, and the center of the PPKTP. The back focal plane of the spherical lens corresponds to the plane of the slits, so that a magnified astigmatic image of the crystal center is projected onto the apertures. Figure (b) shows the same spherical lens of Fig. (a) in an f -f configuration, that is obtained when the cylindrical lens is removed from the optical path. This configuration projects an Optical Fourier transform of the field at the center of the crystal onto the aperture plane.
Fig. 3
Fig. 3 Maps corresponding to a state of four qutrits, generated using a telescope with a cylindrical and a spherical lens between the PPKTP and a three-slit apperture, as shown on Fig. 2(a). The slits were 40 µm wide and had a 125 µm center-to-center spacing. Measurements were made with a 30 s integration time and a grid of 21 by 21 points separated by steps of 300 µm. The top row, maps (a) to (c) show data obtained with coincidence detection between photons with the same polarization. The bottom row (d) to (f) show data obtained with coincidence detection between photons with orthogonal polarizations. Maps (a), (b), (d), and (e) are obtained from experimental data, while maps (c) and (f) are simulations based on Eq. (19). Data in map (a) has been normalized to a maximum of 129 coincidence counts, while (d) has been normalized to a maximum of 448 coincidence counts.
Fig. 4
Fig. 4 Maps corresponding to a state of four qutrits, generated using a spherical lens between the PPKTP and a three-slit apperture, as shown on Fig. 2(b). The slits were 40 µm wide and had a 125 µm center-to-center spacing. Measurements were made with a 30 s integration time and a grid of 21 by 21 points separated by steps of 300 µm. The top row, maps (a) to (c) show data obtained with coincidence detection between photons with the same polarization. The bottom row (d) to (f) show data obtained with coincidence detection between photons with orthogonal polarizations. Maps (a), (b), (d), and (e) are obtained from experimental data, while maps (c) and (f) are simulations based on Eq. (18). Data in map (a) has been normalized to a maximum of 11 coincidence counts, while (d) has been normalized to a maximum of 33 coincidence counts.
Fig. 5
Fig. 5 Maps corresponding to a state of four ququarts, generated using a telescope with a cylindrical and a spherical lens between the PPKTP and a four-slit apperture, as shown on Fig. 2(a). The slits were 80 µm wide and had a 160 µm center-to-center spacing. Measurements were made with a 60 s integration time and a grid of 21 by 21 points separated by steps of 200 µm. The top row, maps (a) to (c) show data obtained with coincidence detection between photons with the same polarization. The bottom row (d) to (f) show data obtained with coincidence detection between photons with orthogonal polarizations. Maps (a), (b), (d), and (e) are obtained from experimental data, while maps (c) and (f) are simulations based on Eq. (21). Data in map (a) has been normalized to a maximum of 1204 coincidence counts, while (d) has been normalized to a maximum of 2932 coincidence counts.
Fig. 6
Fig. 6 Maps corresponding to a state of four ququarts, generated using a spherical lens between the PPKTP and a four-slit apperture, as shown on Fig. 2(b). The slits were 80 µm wide and had a 160 µm center-to-center spacing. Measurements were made with a 25 s integration time and a grid of 21 by 21 points separated by steps of 200 µm. The top row, maps (a) to (c) show data obtained with coincidence detection between photons with the same polarization. The bottom row (d) to (f) show data obtained with coincidence detection between photons with orthogonal polarizations. Maps (a), (b), (d), and (e) are obtained from experimental data, while maps (c) and (f) are simulations based on Eq. (20). Data in map (a) has been normalized to a maximum of 299 coincidence counts, while (d) has been normalized to a maximum of 459 coincidence counts.

Equations (23)

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

ζ ( x ) = exp [ i k f 2 M x 2 ] ,
| Ψ = + Φ ( x h , x v ) | 1 h , x h | 1 v , x v d x h d x v ,
ξ ( x h x v ) = s i n c ( ϕ + L ( q h q v ) 2 ( 8 n e f f ω ¯ / c ) ) exp [ i ( q h x h + q v x v ) ] d q h d q v
T j ( x ) = { 1 if | x d j | < 2 a 0 if | x d j | > 2 a ,
| Ψ = + Φ ( x h , x v ) T ( x h ) T ( x v ) | 1 h , x h | 1 v , x v d x h d x v ,
| Ψ = { l , m } c l m | l h | m v ,
| j π 1 2 a + T j ( x π ) | 1 π , x π d x π ,
Φ ( 2 d , 2 d ) Φ ( 0 , 2 d ) = 2 tan ( β ) ,
Φ ( 0 , 2 d ) Φ ( 2 d , 2 d ) = 3 tan ( α ) cos ( β ) 2 ,
Φ ( 2 d , 2 d ) Φ ( 0 , 2 d ) = 2 tan ( θ ) ,
Φ ( 0 , 2 d ) Φ ( 2 d , 2 d ) = 3 tan ( ϵ ) cos ( θ ) 2 .
Φ ( 3 d , 3 d ) Φ ( d , 3 d ) = 2 tan ( γ ) ,
Φ ( d , 3 d ) Φ ( d , 3 d ) = 6 tan ( β ) cos ( γ ) 2 ,
Φ ( d , 3 d ) Φ ( 3 d , 3 d ) = 2 tan ( α ) cos ( β ) 6 ,
Φ ( 3 d , 3 d ) Φ ( d , 3 d ) = 2 tan ( ν ) ,
Φ ( d , 3 d ) Φ ( d , 3 d ) = 6 tan ( θ ) cos ( ν ) 2 ,
Φ ( d , 3 d ) Φ ( 3 d , 3 d ) = 2 tan ( ϵ ) cos ( θ ) 6 ,
| Ψ + 3 = cos ( α ) [ | 02 + | 11 + | 20 3 ] + sin ( α ) cos ( β ) e i φ 1 [ | 01 + | 10 + | 12 + | 21 2 ] + sin ( α ) sin ( β ) e i φ 2 [ | 00 + | 22 2 ] ,
| Ψ 3 = cos ( ϵ ) [ e i ς ( 4 ) ( | 00 + | 22 ) + | 11 3 ] + sin ( ϵ ) cos ( θ ) e i ς ( 2 ) [ | 01 + | 10 + | 12 + | 21 2 ] + sin ( ϵ ) sin ( θ ) e i ς ( 4 ) [ | 02 + | 20 2 ] ,
| Ψ + 4 = cos ( α ) [ | 12 + | 21 + | 03 + | 30 2 ] + sin ( α ) cos ( β ) e i φ 1 [ | 11 + | 22 + | 02 + | 13 + | 20 + | 31 6 ] + sin ( α ) sin ( β ) cos ( γ ) e i φ 2 [ | 01 + | 10 + | 23 + | 32 2 ] + sin ( α ) sin ( β ) sin ( γ ) e i φ 3 [ | 00 + | 33 2 ] ,
| Ψ 4 = cos ( ϵ ) [ e i ς ( 1 ) ( | 11 + | 22 ) + e i ς ( 9 ) ( | 00 + | 33 ) 2 ] + sin ( ϵ ) cos ( θ ) [ e i ς ( 1 ) ( | 12 + | 21 ) + e i ς ( 5 ) ( | 01 + | 10 + | 23 + | 32 ) 6 ] + sin ( ϵ ) sin ( θ ) cos ( ν ) e i ς ( 5 ) [ | 02 + | 13 + | 20 + | 31 2 ] + sin ( ϵ ) sin ( θ ) sin ( ν ) e i ς ( 9 ) [ | 03 + | 30 2 ] ,
ς ( n ) = n k d 2 f 2 M .
S d ( ρ B ) = i λ i log d ( λ i ) ,

Metrics