Abstract

We observe entanglement between photons in controlled superposition states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality. We demonstrate this violation in a number of two-dimensional subspaces of the higher dimensional OAM Hilbert space.

© 2009 Optical Society of America

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  1. M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
  2. M. B. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007).
  3. A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
    [Crossref]
  4. A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
    [Crossref]
  5. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
    [Crossref] [PubMed]
  6. J. G. Rarity and P. R. Tapster, “Experimental violation of Bells inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495–2498 (1990).
    [Crossref] [PubMed]
  7. J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
    [Crossref] [PubMed]
  8. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [Crossref] [PubMed]
  9. S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)
  10. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
    [Crossref] [PubMed]
  11. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
    [Crossref] [PubMed]
  12. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  13. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
    [Crossref] [PubMed]
  14. M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
    [Crossref]
  15. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
    [Crossref] [PubMed]
  16. A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
    [Crossref]
  17. J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
    [Crossref] [PubMed]
  18. J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
    [Crossref]
  19. 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]
  20. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
    [Crossref]
  21. L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
    [Crossref]
  22. M. J. Padgett and J. Courtial, “Poincare-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
    [Crossref]
  23. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
    [Crossref]
  24. A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
    [Crossref]
  25. B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
    [Crossref]
  26. S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
    [Crossref]
  27. J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
    [Crossref]
  28. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
    [Crossref]
  29. J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1965).
  30. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
    [Crossref]
  31. S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
    [Crossref]
  32. J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D 10, 526–535 (1974).
    [Crossref]
  33. D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
    [Crossref] [PubMed]
  34. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47, 4, A32–A42, (2008).
    [Crossref] [PubMed]

2008 (5)

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
[Crossref]

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[Crossref]

M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47, 4, A32–A42, (2008).
[Crossref] [PubMed]

2007 (2)

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

2005 (3)

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[Crossref]

2004 (3)

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]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

2003 (1)

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
[Crossref]

2002 (3)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

1999 (2)

L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
[Crossref]

M. J. Padgett and J. Courtial, “Poincare-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[Crossref]

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

1993 (1)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

1990 (1)

J. G. Rarity and P. R. Tapster, “Experimental violation of Bells inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495–2498 (1990).
[Crossref] [PubMed]

1982 (1)

A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

1981 (1)

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

1974 (1)

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D 10, 526–535 (1974).
[Crossref]

1972 (1)

S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Abouraddy, A. F.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

Aiello, A.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

Alexandrescu, A.

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
[Crossref]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
[Crossref]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

Almeida, M. P.

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Aspect, A.

A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Barnett, S. M.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

Barreiro, J. T.

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[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]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

Bell, J. S.

J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1965).

Bennink, R. S.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Bentley, S. J.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Boyd, R. W.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Buller, G. S.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
[Crossref] [PubMed]

Chuang, I. L.

M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

Clauser, J. F.

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D 10, 526–535 (1974).
[Crossref]

S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Courtial, J.

M. J. Padgett and J. Courtial, “Poincare-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[Crossref]

L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
[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]

de Oliveira, A. N.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

Dymale, R. C.

Eliel, E. R.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Franke-Arnold, S.

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[Crossref]

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
[Crossref]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

Freedman, S. J.

S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

Gilchrist, A.

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]

Gisin, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Grangier, P.

A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Groblacher, S.

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

Gruneisen, M. T.

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]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Hooft, G. W. t

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Horne, M. A.

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D 10, 526–535 (1974).
[Crossref]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Howell, J. C.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Jack, B.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[Crossref]

Jennewein, T.

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

Jha, A. K.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Kwiat, P. G.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
[Crossref] [PubMed]

Kwiat, Paul G.

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[Crossref]

Langford, N. K.

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[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]

Leach, J.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

Linden, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Ma, X.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Massar, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Miller, W. A.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

Monken, C. H.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Nielsen, M.

M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

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]

Oemrawsingh, S. S. R.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
[Crossref]

Padgett, M. J.

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[Crossref]

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
[Crossref]

M. J. Padgett and J. Courtial, “Poincare-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[Crossref]

Pellat-Finet, P.

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[Crossref]

Plenio, M. B.

M. B. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007).

Popescu, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

Pors, J. B.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

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]

Rarity, J. G.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bells inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495–2498 (1990).
[Crossref] [PubMed]

Roger, G.

A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Saleh, B. E. A.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Souto Ribeiro, P. H.

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
[Crossref] [PubMed]

Stotz, M.

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Sweiti, A. M.

Tapster, P. R.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bells inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495–2498 (1990).
[Crossref] [PubMed]

Tasca, D. S.

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Teich, M. C.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

Thebaldi, R. S.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

Torner, L.

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

Torres, J. P.

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

van Exter, M. P.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Virmani, S.

M. B. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007).

Voigt, D.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Walborn, S. P.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

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]

Woerdman, J. P.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

Yao, E.

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

Yarnall, T.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

Zeilinger, A.

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Stotz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007).
[Crossref]

Laser & Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser & Photon. Rev. 2, 299–313 (2008).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of Orbital Angular Momentum States of Photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

New J. Phys. (1)

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (3)

A. K. Jha, B. Jack, E. Yao, J. Leach, R. W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Fourier relationship between the angle and angular momentum of entangled photons,” Phys. Rev. A 78, 043810 (2008).
[Crossref]

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[Crossref]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993)
[Crossref] [PubMed]

Phys. Rev. A. (4)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A. 45, 8185–8189 (1992).
[Crossref] [PubMed]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A. 5, 052114, (2005)
[Crossref]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A. 68, 050301 (2003).
[Crossref]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A. 65, 033823 (2002).
[Crossref]

Phys. Rev. D (1)

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D 10, 526–535 (1974).
[Crossref]

Phys. Rev. E (1)

L. Allen, J. Courtial, and M. J. Padgett, “Matrix formulation for the propagation of light beams with orbital and spin angular momenta,” Phys. Rev. E 60, 7497–7503 (1999).
[Crossref]

Phys. Rev. Lett. (15)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref] [PubMed]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and Paul G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[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]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental Violation of Bell’s Inequality in Spatial-Parity Space,” Phys. Rev. Lett. 99, 170408, (2007)
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental Two-Photon, Three-Dimensional Entanglement for Quantum Communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

J. G. Rarity and P. R. Tapster, “Experimental violation of Bells inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495–2498 (1990).
[Crossref] [PubMed]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

Other (4)

M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

M. B. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007).

S. P. Walborn, D. S. Tasca, M. P. Almeida, P. Pellat-Finet, C. H. Monken, and P. H. Souto Ribeiro, “Violation of Bell’s Inequality with Continuous Variables and Fractional Fourier Transforms,” arXiv:quant-ph/061214 (2006)

J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1965).

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Figures (3)

Fig. 1.
Fig. 1.

Bloch spheres for (a) polarization and (b) OAM (∣±2〉) states. The sphere for OAM states shows the phase structure (grayscale) of the relevant modes. The states on the sphere are expressed solely in terms of their azimuthal phase (i.e. -value) without any reference to their radial dependence.

Fig. 2.
Fig. 2.

Schematic of experimental apparatus for using spatial light modulators to measure the correlations in orbital states of down-converted photons

Fig. 3.
Fig. 3.

The relative coincidence count as a function of relative orientation of the sector apertures. The measured count rates were normalized by D, the denominator in equ 6. It is the coincidence counts at orientations θA = 0, θB = π8 , θ'A = π4 and θ'B = 3π8 which show the largest violation of the Bell inequality.

Tables (1)

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Table 1. Different entangled states |ψ〉 l and the associated measured value of S. A value of |S| > 2 violates the CHSH inequality.

Equations (6)

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θ=12(eiθ++eiθ)
ψ=n=n=+cn|nsni .
C(θA,θB)=θAθBψ2cos2[(θAθB)].
ψ=12[si+si]
S=E(θA,θB)E(θA,θ'B)+E(θ'A,θB)+E(θ'A,θ'B)
E(θA,θB)=C(θA,θB)+C(θA+π2,θB+π2)C(θA+π2,θB)C(θA,θB+π2)C(θA,θB)+C(θA+π2,θB+π2)+C(θA+π2,θB)+C(θA,θB+π2) .

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