Abstract

Orbital angular momentum entanglement (OAM) is one of the very intriguing topics in quantum physics. In addition to discovering and exploring its underlying mechanics, recent studies have also demonstrated a progress towards expanding degree of its entanglement. In this paper, we explore OAM entanglement by applying the Heisenberg uncertainty principle to the quantum position correlation within the azimuthal region. In particular, we decompose the pump light into a set of pump cone states characterized by their radii. The OAM entanglement can then be manipulated by controlling the radius of the pump cone state, the length of the nonlinear crystal and also the OAM carried by the pump field. That is followed by a detailed discussion and analysis. Such an exploration not only bring us a deeper understanding of OAM entanglement, but also help us to implement the high-dimensional quantum information tasks based on OAM entanglement.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. 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, (2)023811 (2004).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  21. C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92(12), 127903 (2004).
    [Crossref] [PubMed]
  22. F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
    [Crossref]
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    [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(4), 043810 (2008).
    [Crossref]
  25. W. Li and S. M. Zhao, “BellâĂŹs inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states,” Sci. Rep. 8, 4812 (2018).
    [Crossref]
  26. H. D. L. Pires, H. C. B. Florijn, and M. P. Van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104(2), 020505 (2010).
    [Crossref]
  27. A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields,” Phys. Rev. A 84(6), 063847 (2011).
    [Crossref]
  28. A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83(5), 053829 (2011).
    [Crossref]
  29. J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
    [Crossref]
  30. C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31(4), 2409 (1995).
    [Crossref]
  31. G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
    [Crossref]
  32. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control,” Phys. Rev. Lett. 84(23), 5304–5307 (2011).
    [Crossref]
  33. F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
    [Crossref]
  34. 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(21), 210403 (2004).
    [Crossref] [PubMed]
  35. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
    [Crossref]

2018 (1)

W. Li and S. M. Zhao, “BellâĂŹs inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states,” Sci. Rep. 8, 4812 (2018).
[Crossref]

2014 (1)

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

2012 (2)

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
[Crossref]

2011 (7)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control,” Phys. Rev. Lett. 84(23), 5304–5307 (2011).
[Crossref]

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
[Crossref]

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13(5), 053048 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields,” Phys. Rev. A 84(6), 063847 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83(5), 053829 (2011).
[Crossref]

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[Crossref]

2010 (3)

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

H. D. L. Pires, H. C. B. Florijn, and M. P. Van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104(2), 020505 (2010).
[Crossref]

2009 (1)

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

2008 (2)

C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77(1), 015810 (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(4), 043810 (2008).
[Crossref]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

2005 (1)

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

2004 (5)

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92(12), 127903 (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(21), 210403 (2004).
[Crossref] [PubMed]

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(5), 053601 (2004).
[Crossref] [PubMed]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
[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, (2)023811 (2004).
[Crossref]

2003 (2)

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68(5), 050301 (2003).
[Crossref]

2002 (2)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65(3), 033823 (2002).
[Crossref]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

2000 (1)

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85(2), 286–289 (2000).
[Crossref] [PubMed]

1997 (1)

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
[Crossref]

1995 (1)

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31(4), 2409 (1995).
[Crossref]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881 (1992).
[Crossref] [PubMed]

Agarwal, G. S.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields,” Phys. Rev. A 84(6), 063847 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83(5), 053829 (2011).
[Crossref]

Alexandrescu, A.

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68(5), 050301 (2003).
[Crossref]

Allen, L.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65(3), 033823 (2002).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[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(9), 677–680 (2011).
[Crossref]

Arnaut, H. H.

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85(2), 286–289 (2000).
[Crossref] [PubMed]

Barbosa, G. A.

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85(2), 286–289 (2000).
[Crossref] [PubMed]

Barnett, S. M.

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
[Crossref]

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

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(4), 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(3), 033823 (2002).
[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(5), 053601 (2004).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881 (1992).
[Crossref] [PubMed]

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(21), 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(21), 210403 (2004).
[Crossref] [PubMed]

Boyd, R. W.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83(5), 053829 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields,” Phys. Rev. A 84(6), 063847 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

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(4), 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(21), 210403 (2004).
[Crossref] [PubMed]

Brougham, T.

F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
[Crossref]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[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(4), 043810 (2008).
[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(9), 677–680 (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(5), 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, (2)023811 (2004).
[Crossref]

Deyanova, Y.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

Eberly, J. H.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control,” Phys. Rev. Lett. 84(23), 5304–5307 (2011).
[Crossref]

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92(12), 127903 (2004).
[Crossref] [PubMed]

Fickler, R.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Florijn, H. C. B.

H. D. L. Pires, H. C. B. Florijn, and M. P. Van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104(2), 020505 (2010).
[Crossref]

Franke-Arnold, S.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

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(4), 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(3), 033823 (2002).
[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(5), 053601 (2004).
[Crossref] [PubMed]

Giovannini, D.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
[Crossref]

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(5), 053601 (2004).
[Crossref] [PubMed]

Hendrych, M.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

Hong, C. K.

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31(4), 2409 (1995).
[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(21), 210403 (2004).
[Crossref] [PubMed]

Huber, M.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

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(4), 043810 (2008).
[Crossref]

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
[Crossref]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Jha, A. K.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83(5), 053829 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields,” Phys. Rev. A 84(6), 063847 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

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(4), 043810 (2008).
[Crossref]

Knight, P. L.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
[Crossref]

Krenn, M.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[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(5), 053601 (2004).
[Crossref] [PubMed]

Lapkiewicz, R.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Law, C. K.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control,” Phys. Rev. Lett. 84(23), 5304–5307 (2011).
[Crossref]

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92(12), 127903 (2004).
[Crossref] [PubMed]

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(9), 677–680 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

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(4), 043810 (2008).
[Crossref]

Li, W.

W. Li and S. M. Zhao, “BellâĂŹs inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states,” Sci. Rep. 8, 4812 (2018).
[Crossref]

Ma, P. C.

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
[Crossref]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Mandel, L.

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31(4), 2409 (1995).
[Crossref]

Miatto, F. M.

F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
[Crossref]

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
[Crossref]

Minardi, S.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

Molina-Terriza, G.

C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77(1), 015810 (2008).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[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, (2)023811 (2004).
[Crossref]

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(5), 053601 (2004).
[Crossref] [PubMed]

Osorio, C. I.

C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77(1), 015810 (2008).
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

Padgett, M. J.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

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(4), 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(3), 033823 (2002).
[Crossref]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Pires, H. D. L.

H. D. L. Pires, H. C. B. Florijn, and M. P. Van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104(2), 020505 (2010).
[Crossref]

Plenio, M. B.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
[Crossref]

Plick, W. N.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[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(5), 053601 (2004).
[Crossref] [PubMed]

Ramelow, S.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Rippin, M. A.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
[Crossref]

Ritsch-Marte, M.

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

Romero, J.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
[Crossref] [PubMed]

Schaeff, C.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[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, (2)023811 (2004).
[Crossref]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68(5), 050301 (2003).
[Crossref]

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (John Wiley & Sons, 2011).
[Crossref]

Torres, J. P.

C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77(1), 015810 (2008).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72(6), 065802 (2005).
[Crossref]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68(5), 050301 (2003).
[Crossref]

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (John Wiley & Sons, 2011).
[Crossref]

Van Exter, M. P.

H. D. L. Pires, H. C. B. Florijn, and M. P. Van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104(2), 020505 (2010).
[Crossref]

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
[Crossref]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Vedral, V.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78(12), 2275 (1997).
[Crossref]

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, (2)023811 (2004).
[Crossref]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control,” Phys. Rev. Lett. 84(23), 5304–5307 (2011).
[Crossref]

Wang, Y. W.

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
[Crossref]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
[Crossref]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 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(5), 053601 (2004).
[Crossref] [PubMed]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881 (1992).
[Crossref] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Yao, A. M.

F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
[Crossref]

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
[Crossref]

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13(5), 053048 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
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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(4), 043810 (2008).
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Zeilinger, A.

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
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S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
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A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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Zhan, Y. B.

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
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Zhang, Q. Y.

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
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Zhao, S. M.

W. Li and S. M. Zhao, “BellâĂŹs inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states,” Sci. Rep. 8, 4812 (2018).
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Chin. Phys. Lett. (1)

Y. B. Zhan, Q. Y. Zhang, Y. W. Wang, and P. C. Ma, “Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state,” Chin. Phys. Lett. 27(1), 010307 (2010).
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Eur. Phys. J. D (1)

F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons,” Eur. Phys. J. D 66(7), 183 (2012).
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Nat. Phys. (2)

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(9), 677–680 (2011).
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G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
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Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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New J. of Phys. (1)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. of Phys. 8(5), 75 (2004).
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New J. Phys. (1)

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13(5), 053048 (2011).
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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(4), 043810 (2008).
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F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83(3), 033816 (2011).
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C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77(1), 015810 (2008).
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S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65(3), 033823 (2002).
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J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86(1), 012334 (2011).
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A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
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B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a Bell inequality,” Phys. Rev. Lett. 103(85), 083602 (2009).
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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
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Proc. Natl. Acad. Sci. (1)

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100×100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014).
[Crossref] [PubMed]

Sci. Rep. (1)

W. Li and S. M. Zhao, “BellâĂŹs inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states,” Sci. Rep. 8, 4812 (2018).
[Crossref]

Science (2)

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
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R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Other (1)

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (John Wiley & Sons, 2011).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic illustration of the collinear SPDC in the representation of the cone states. (a) Illustration of the SPDC generated by a pump cone state. The incident rotationally symmetric pump light beam is focused into the nonlinear crystal(NL). During the SPDC, the output of the pump state with a spherical phase on its wavefront can be decomposed into a set of cone states characterized by pp, the transverse momentum projection within the plane perpendicular to the propagation principal axis. The pump cone state can be visualized as a ring within the transverse plane in the momentum representation, and it has a hollow cone structure in the position space. (b) Transformation of the transverse momentum correlation from cartesian coordinate to polar coordinates. The red and green dashed arrows labeled as qs and qi are the transverse momentum components of the signal and idler photons, respectively, and the corresponding solid arrows, labeled as qs and qi, represent how they depart from p p 2, which is half the transverse momentum component of the pump photon. Inset: schematic illustration of the down-converted two-photon transverse momentum correlation with respect to the pump momentum.
Fig. 2
Fig. 2 Evolution of the two-photon OAM quantum correlation spectrum A (ls, li) with respect to the radius of the pump cone state, |pp|, at L = 1 mm (a–c) and L = 6 mm (d–f).
Fig. 3
Fig. 3 Dependence of the two-photon OAM entanglement on the radius of the pump cone sate, |pp|. (a) Probability distribution P (l, −l) for two-photon OAM entanglement for different pump cone states. (b) The dependence of the entanglement entropy on |pp|. In this simulation, the OAM of the pump state lp is set to 0, and the length of the nonlinear crystal is fixed at 1mm.
Fig. 4
Fig. 4 Dependence of the two-photon OAM entanglement on the length of the nonlinear crystal. (a) Probability distribution P (l, −l) of the OAM entanglement for different crystal lengths. Here |pp| = 2π 0.004rad/mm is shown as an example. (b) Evolution of the entanglement entropy with respect to the length of the nonlinear crystal for different pump cone states.
Fig. 5
Fig. 5 Dependence of the two-photon OAM entanglement on the OAM of the pump cone state. (a) Probability distribution P (l, lpl) of the OAM entanglement for different lp, the OAM carried by the pump state. The parameters for this simulation are |pp| = 0.05 rad/mm, and Lz = 1 mm. (b) Dependence of the entanglement entropy on lp for four different pump cone states.

Equations (15)

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| Ψ = d k s d k i Φ ( k p , k s , k i ) | k s | k i ,
Φ ( k p , k s , k i ) = χ ( ω p , ω s , ω i ) E p ( ω s + ω i ) sin [ 1 2 ( k p k s k i ) L ] 1 2 | k p k s k i | × exp [ i 1 2 ( k p k s k i L ) ] ,
( k p k s k i ) L = ( k p k s k i ) L ,
k p = | k p | , k s ( i ) = | k s ( i ) | ( 1 1 2 | q s ( i ) k s ( i ) | 2 ) .
Φ ( k p , q s , q i ) = E p L sin c [ 1 2 ( | q s | 2 + | q i | 2 | k p | ) L ] exp [ i 1 2 ( | q s | 2 + | q i | 2 | k p | ) L ] .
Φ ( θ p , θ s , θ i ) = E p L × sin c [ 1 2 | p p | 2 + | j s | 2 + | j i | 2 | p p | | j s | cos ( θ s θ p ) | p p | | j i | cos ( θ i θ p ) 2 | k p | L ] × exp [ i 1 2 | p p | 2 + | j s | 2 + | j i | 2 | p p | | j s | cos ( θ s θ p ) | p p | | j i | cos ( θ i θ p ) 2 | k p | L ] ,
| Φ ( θ p ) = d θ s d θ i Φ ( θ p , θ s , θ i ) | θ s | θ i .
| θ = 1 2 π l = exp ( i l θ ) | l ,
| Φ p = 1 2 π d θ p exp ( i l p θ p ) | θ p .
| Ψ = 1 2 π d θ p exp ( i l p θ p ) | Ψ ( θ p ) = 1 2 π 2 π l = l = A ( l s , l i ) | l s | l i d θ p exp [ i ( l p l s l i ) θ p ] = 1 2 π l s = l i = A ( l s , l i ) δ l s , l p l i | l s | l i = 1 2 π l = A ( l , l p l ) | l | l p l .
A ( l s , l i ) = d θ s d θ i ϕ ( θ p , θ s , θ i ) exp [ i l s ( θ s θ p ) i l i ( θ i θ p ) ] ,
Φ ( θ p , θ s , θ i ) E p L sin c [ | p p | 2 ( ( θ s θ p ) 2 + ( θ i θ p ) 2 ) 8 | k p | L ] × exp [ i | p p | 2 ( ( θ s θ p ) 2 + ( θ i θ p ) 2 ) 8 | k p | L ] .
Δ ( θ s 2 + θ i 2 ) = 8 π | k p | | p p | 2 L .
P ( l , l ) = | A ( l , l ) | 2   l | A ( l , l ) | 2 .
E = l P ( l , l ) log 2 P ( l , l ) .

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