Abstract

We consider the non-horizontal distributions of orbital angular momentum biphotons through free-space atmospheric channels, in which case the non-Kolmogorov turbulent effects shall be considered. By considering the case of initial non-perfect resource, i.e., the orbital angular momentum biphotons are initially prepared in an extended Werner-like state, we investigate the non-Kolmogorov effects on the propagations of nonclassical correlations, including quantum entanglement and quantum discord. It is found that universal decay laws of entanglement and discord also exist for non-Kolmogorov turbulence but with their decay curves different from that of entanglement for Kolmogorov turbulence reported by Leonhard et al. [Phys. Rev. A 91, 012345 (2015) [CrossRef]  ]. We show that the universal decay laws are dependent on the power-law exponent of the non-Kolmogorov spectrum and compare the differences of decay properties between entanglement and discord caused by non-Kolmogorov turbulence.

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

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References

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    [Crossref]
  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, 227902 (2003).
    [Crossref]
  3. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [Crossref]
  4. E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
    [Crossref]
  5. B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
    [Crossref]
  6. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
    [Crossref]
  7. S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
    [Crossref]
  8. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
    [Crossref]
  9. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
    [Crossref]
  10. C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94–101 (2007).
    [Crossref]
  11. F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A 83, 053822 (2011).
    [Crossref]
  12. X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37, 2607–2609 (2012).
    [Crossref]
  13. T. Brünner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
    [Crossref]
  14. J. R. Gonzalez Alonso and T. A. Brun, “Protecting orbitalangular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
    [Crossref]
  15. N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
    [Crossref]
  16. B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
    [Crossref]
  17. M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
    [Crossref]
  18. M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
    [Crossref]
  19. B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
    [Crossref]
  20. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [Crossref]
  21. L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
    [Crossref]
  22. H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
    [Crossref]
  23. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
    [Crossref]
  24. D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
    [Crossref]
  25. A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
    [Crossref]
  26. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
    [Crossref]
  27. X. Yan, P. F. Zhang, J. H. Zhang, H. Q. Chun, and C. Y. Fan, “Decoherence of orbital angular momentum tangled photons in non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 33, 1831–1835 (2016).
    [Crossref]
  28. 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]
  29. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [Crossref]
  30. J. I. Davis, “Consideration of atmospheric turbulence in laser system design,” Appl. Opt. 5, 139–147 (1966).
    [Crossref]
  31. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).
  32. C. Paterson, “Atmospheric turbulence and free-space optical communication using orbital angular momentum of single photons,” Proc. SPIE 5572, 187–198 (2004).
    [Crossref]
  33. R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277–4281 (1989).
    [Crossref]
  34. B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
    [Crossref]
  35. J. Lee and M. S. Kim, “Entanglement teleportation via Werner states,” Phys. Rev. Lett. 84, 4236–4239 (2000).
    [Crossref]
  36. M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
    [Crossref]
  37. A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
    [Crossref]
  38. T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
    [Crossref]
  39. T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
    [Crossref]
  40. E. P. Wigner and M. M. Yanase, “Information contents of distributions,” Proc. Natl. Acad. Sci. USA 49, 910–918 (1963).
    [Crossref]
  41. F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
    [Crossref]

2017 (1)

S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
[Crossref]

2016 (1)

2015 (2)

F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
[Crossref]

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

2014 (1)

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

2013 (4)

M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

T. Brünner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

J. R. Gonzalez Alonso and T. A. Brun, “Protecting orbitalangular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

2012 (4)

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

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

M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37, 2607–2609 (2012).
[Crossref]

2011 (3)

B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A 83, 053822 (2011).
[Crossref]

2009 (3)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
[Crossref]

2008 (2)

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[Crossref]

2007 (3)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
[Crossref]

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

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94–101 (2007).
[Crossref]

2006 (2)

A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
[Crossref]

T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
[Crossref]

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

2004 (1)

C. Paterson, “Atmospheric turbulence and free-space optical communication using orbital angular momentum of single photons,” Proc. SPIE 5572, 187–198 (2004).
[Crossref]

2003 (1)

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, 227902 (2003).
[Crossref]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

2001 (2)

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[Crossref]

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

2000 (1)

J. Lee and M. S. Kim, “Entanglement teleportation via Werner states,” Phys. Rev. Lett. 84, 4236–4239 (2000).
[Crossref]

1999 (1)

M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

1995 (1)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

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]

1989 (1)

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277–4281 (1989).
[Crossref]

1966 (1)

1963 (1)

E. P. Wigner and M. M. Yanase, “Information contents of distributions,” Proc. Natl. Acad. Sci. USA 49, 910–918 (1963).
[Crossref]

’t Hooft, G. W.

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

Acín, A.

A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
[Crossref]

Adesso, G.

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

Allen, L.

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]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Andrews, R.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94–101 (2007).
[Crossref]

Babiker, M.

S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
[Crossref]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

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]

Bellomo, B.

B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[Crossref]

Boyd, R. W.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

Brodutch, A.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

Brun, T. A.

J. R. Gonzalez Alonso and T. A. Brun, “Protecting orbitalangular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

Brünner, T.

T. Brünner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

Buchleitner, A.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

Cable, H.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

Chun, H. Q.

Compagno, G.

B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[Crossref]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

da Cunha Pereira, M. V.

M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

Davis, J. I.

De Martini, F.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Eberly, J. H.

T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
[Crossref]

T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
[Crossref]

Eliel, E. R.

B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

Fan, C. Y.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
[Crossref]

Fickler, R.

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

Filpi, L. A. P.

M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

Franco, R. L.

B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[Crossref]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Girolami, D.

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

Gisin, N.

A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
[Crossref]

Golbraikh, E.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

Gonzalez Alonso, J. R.

J. R. Gonzalez Alonso and T. A. Brun, “Protecting orbitalangular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

Gopaul, C.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94–101 (2007).
[Crossref]

Henderson, L.

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[Crossref]

Horodecki, K.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

Horodecki, M.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
[Crossref]

Horodecki, P.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
[Crossref]

Horodecki, R.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
[Crossref]

Jennewein, T.

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, 227902 (2003).
[Crossref]

Karimi, E.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Kim, M. S.

J. Lee and M. S. Kim, “Entanglement teleportation via Werner states,” Phys. Rev. Lett. 84, 4236–4239 (2000).
[Crossref]

Kopeika, N. S.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

Krenn, M.

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

Kupershmidt, I.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

Lapkiewicz, R.

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

Lavery, M. P. J.

Leach, J.

Lee, J.

J. Lee and M. S. Kim, “Entanglement teleportation via Werner states,” Phys. Rev. Lett. 84, 4236–4239 (2000).
[Crossref]

Leonhard, N. D.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

Lloyd, S. M.

S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
[Crossref]

Magaña-Loaiza, O. S.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Maher, L.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Malik, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

Marrucci, L.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Masanes, L.

A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
[Crossref]

Miatto, F.

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

Mirhosseini, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

Modi, K.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

Molina-Terriza, G.

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

Monken, C. H.

M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

Nagali, E.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

O’sullivan, M.

Ollivier, H.

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

Padgett, M. J.

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, 227902 (2003).
[Crossref]

Paterek, T.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
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Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

C. Paterson, “Atmospheric turbulence and free-space optical communication using orbital angular momentum of single photons,” Proc. SPIE 5572, 187–198 (2004).
[Crossref]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Piccirillo, B.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[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, 640–643 (2012).
[Crossref]

Pors, B.-J.

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

Ramelow, S.

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

Rodenburg, B.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

M. Malik, M. O’sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Roux, F. S.

F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
[Crossref]

T. Brünner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A 83, 053822 (2011).
[Crossref]

Sansoni, L.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Santamato, E.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Schaeff, C.

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

Sciarrino, F.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Shatokhin, V. N.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
[Crossref]

Sheng, X.

Shtemler, Y.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

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]

Steinhoff, N. K.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Thirunavukkarasu, G.

S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
[Crossref]

Torner, L.

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

Torres, J. P.

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

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence for uplink and downlink paths,” Proc. SPIE 6708, 670803 (2007).
[Crossref]

Tufarelli, T.

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

Tyler, G. A.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

Vaziri, A.

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, 227902 (2003).
[Crossref]

Vedral, V.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[Crossref]

Virtser, A.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

Weihs, G.

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, 227902 (2003).
[Crossref]

Wellens, T.

F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
[Crossref]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
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Werner, R. F.

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277–4281 (1989).
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Wigner, E. P.

E. P. Wigner and M. M. Yanase, “Information contents of distributions,” Proc. Natl. Acad. Sci. USA 49, 910–918 (1963).
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Woerdman, J. P.

B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[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]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

Yan, X.

Yanakas, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
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Yanase, M. M.

E. P. Wigner and M. M. Yanase, “Information contents of distributions,” Proc. Natl. Acad. Sci. USA 49, 910–918 (1963).
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Yu, T.

T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
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T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
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Yuan, J.

S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, “Electron vortices: beams with orbital angular momentum,” Rev. Mod. Phys. 89, 035004 (2017).
[Crossref]

Zeilinger, A.

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

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, 227902 (2003).
[Crossref]

Zhang, J. H.

Zhang, L.

Zhang, P. F.

Zhang, Y.

Zhao, F.

Zhu, Y.

Ziberman, A.

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

Zurek, W. H.

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

Appl. Opt. (1)

Atmos. Res. (1)

A. Ziberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[Crossref]

J. Opt. (1)

B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt. 13, 064008 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. A (1)

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[Crossref]

Nat. Photonics (1)

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720–723 (2009).
[Crossref]

Nat. Phys. (1)

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

New J. Phys. (3)

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94–101 (2007).
[Crossref]

B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the laboratory with application to orbital angular momentum communication,” New J. Phys. 16, 033020 (2014).
[Crossref]

T. Brünner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (9)

J. R. Gonzalez Alonso and T. A. Brun, “Protecting orbitalangular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[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]

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277–4281 (1989).
[Crossref]

B. Bellomo, R. L. Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888–1898 (1999).
[Crossref]

F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A 83, 053822 (2011).
[Crossref]

M. V. da Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled twophoton beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

F. S. Roux, T. Wellens, and V. N. Shatokhin, “Entanglement evolution of twisted photons in strong atmospheric turbulence,” Phys. Rev. A 92, 012326 (2015).
[Crossref]

Phys. Rev. Lett. (9)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[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, 227902 (2003).
[Crossref]

A. Acín, N. Gisin, and L. Masanes, “From Bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97, 120405 (2006).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Source at the ground produces pairs of OAM-entangled photons propagating through turbulent atmosphere along the z direction and received by two detectors.
Fig. 2.
Fig. 2. C n 2 as a function of z with C 0 = 10 14 and θ = π / 3 .
Fig. 3.
Fig. 3. Concurrence as a function of (a)  z and ϑ and of (b)  z and γ . The parameters are chosen as l 0 = 1 , C 0 = 10 14 , α = 3.8 , θ = π / 3 for (a)  γ = 1 and (b)  ϑ = π / 2 .
Fig. 4.
Fig. 4. Vanishing distance as functions of (a)  ϑ and of (b)  γ . The parameters are chosen the same as Fig. 3.
Fig. 5.
Fig. 5. LQU as a function of (a)  z and ϑ and of (b)  z and γ . The parameters are chosen the same as Fig. 3.
Fig. 6.
Fig. 6. (a) Concurrence and (b) LQU as functions of z for different l 0 . The parameters are chosen as C 0 = 10 14 , α = 3.8 , θ = π / 3 , γ = 1 , and ϑ = π / 2 .
Fig. 7.
Fig. 7. (a) Concurrence and (b) LQU as functions of z for different α . The parameters are chosen as l 0 = 1 , C 0 = 10 14 , θ = π / 3 , γ = 1 , and ϑ = π / 2 .
Fig. 8.
Fig. 8. Concurrence as a function of the ratio ξ ( l 0 ) / r 0 for different l 0 . The parameters are chosen as C 0 = 10 14 , θ = π / 3 , γ = 1 ϑ = π / 2 , (a)  α = 3.1 and (b)  α = 3.8 .
Fig. 9.
Fig. 9. LQU as a function of the ratio ξ ( l 0 ) / r 0 for different l 0 . The parameters are chosen the same as Fig. 8.
Fig. 10.
Fig. 10. (a) Concurrence and (b) LQU as functions of ξ ( l 0 ) / r 0 and α . The parameters are chosen as l 0 = 100 , C 0 = 10 14 , θ = π / 3 , γ = 1 , and ϑ = π / 2 .

Equations (23)

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U p | l | ( r , z , ϕ ) = 2 p ! π ( p + | l | ) ! 1 ω ( z ) [ 2 r ω ( z ) ] | l | exp [ r 2 ω 2 ( z ) ] × L p | l | [ 2 r 2 ω 2 ( z ) ] exp ( i l ϕ ) exp [ i k r 2 z 2 ( z 2 + z R 2 ) ] × exp [ i ( 2 p + | l | + 1 ) tan 1 ( z z R ) ] = R p | l | ( r , z ) exp ( i l ϕ ) 2 π .
R p | l | ( r , z ) = 2 p ! ( p + | l | ) ! 1 ω ( z ) [ 2 r ω ( z ) ] | l | exp [ r 2 ω 2 ( z ) ] × L p | l | [ 2 r 2 ω 2 ( z ) ] exp [ i k r 2 2 R ( z ) ] × exp [ i ( 2 p + | l | + 1 ) tan 1 ( z z R ) ] ,
L p | l | ( x ) = m = 0 p ( 1 ) m ( p + | l | ) ! ( p m ) ! ( m + | l | ) ! m ! x m ,
ϕ n ( α , κ ) = A ( α ) C n 2 ( z , α ) κ α , 0 κ , 3 < α < 4 ,
A ( α ) = Γ ( α 1 ) cos ( α π / 2 ) / ( 4 π 2 ) ,
C n 2 ( z , α ) = 0.033 ( k z ) α 11 / 3 [ 0.00594 ( v / 27 ) 2 × ( z cos θ × 10 5 ) 10 × exp ( z cos θ / 1000 ) + 2.7 × 10 16 exp ( z cos θ / 1500 ) + C 0 exp ( z cos θ / 1000 ) ] / A ( α ) ,
ρ ( 0 ) = 1 γ 4 I + γ | Ψ 0 Ψ 0 | ,
| Ψ 0 = cos ( ϑ 2 ) | l 0 , l 0 + e i ϕ sin ( ϑ 2 ) | l 0 , l 0 ,
ρ = ( M 1 M 2 ) ρ ( 0 ) ,
M l ˜ , l ˜ l , l = δ l l , l ˜ l ˜ 2 π 0 d r R 0 l 0 ( r ) R 0 l 0 * ( r ) r × 0 2 π d Δ φ e i Δ φ [ ( l ˜ + l ˜ ) ( l + l ) ] / 2 e D S ( 2 r | sin ( Δ φ / 2 ) | ) / 2 ,
ϱ 0 ( α ) = [ 2 Γ ( 3 α 2 ) π 1 2 k 2 Γ ( 2 α 2 ) z 0 1 C n 2 ( ξ z , α ) ( 1 ξ ) α 2 d ξ ] 1 / ( α 2 ) .
ρ ( 0 ) = ( ρ 11 ( 0 ) ρ 14 ( 0 ) ρ 22 ( 0 ) ρ 23 ( 0 ) ρ 32 ( 0 ) ρ 33 ( 0 ) ρ 41 ( 0 ) ρ 44 ( 0 ) ) ,
ρ 11 ( 0 ) = 1 γ 4 , ρ 22 ( 0 ) = 1 γ 4 + γ cos 2 ( ϑ 2 ) , ρ 33 ( 0 ) = 1 γ 4 + γ sin 2 ( ϑ 2 ) , ρ 44 ( 0 ) = 1 γ 4 , ρ 14 ( 0 ) = 0 , ρ 23 ( 0 ) = γ 2 e i ϕ sin ϑ , ρ 41 ( 0 ) = ρ 14 ( 0 ) * , ρ 32 ( 0 ) = ρ 23 ( 0 ) * .
ρ i i , j j l l , m m M i i l l M j j m m ρ | l m l m | ( 0 ) | i j i j | ,
ρ 11 = ( a 2 ρ 11 ( 0 ) + a b ρ 22 ( 0 ) + a b ρ 33 ( 0 ) + b 2 ρ 44 ( 0 ) ) / ( a + b ) 2 , ρ 22 = ( a b ρ 11 ( 0 ) + a 2 ρ 22 ( 0 ) + b 2 ρ 33 ( 0 ) + a b ρ 44 ( 0 ) ) / ( a + b ) 2 , ρ 33 = ( a b ρ 11 ( 0 ) + b 2 ρ 22 ( 0 ) + a 2 ρ 33 ( 0 ) + a b ρ 44 ( 0 ) ) / ( a + b ) 2 , ρ 44 = ( b 2 ρ 11 ( 0 ) + a b ρ 22 ( 0 ) + a b ρ 33 ( 0 ) + a 2 ρ 44 ( 0 ) ) / ( a + b ) 2 , ρ 14 = a 2 ρ 14 ( 0 ) / ( a + b ) 2 , ρ 41 = a 2 ρ 41 ( 0 ) / ( a + b ) 2 , ρ 23 = a 2 ρ 23 ( 0 ) / ( a + b ) 2 , ρ 32 = a 2 ρ 32 ( 0 ) / ( a + b ) 2 ,
a = M l 0 , l 0 l 0 , l 0 = M l 0 , l 0 l 0 , l 0 = M l 0 , l 0 l 0 , l 0 = M l 0 , l 0 l 0 , l 0 , b = M l 0 , l 0 l 0 , l 0 = M l 0 , l 0 l 0 , l 0 .
C ( ρ ) = max { λ 1 λ 2 λ 3 λ 4 , 0 } ,
R = ρ ( σ y σ y ) ρ * ( σ y σ y ) ,
U A ( ρ A B ) = min { K A } { I ( ρ A B , K A I B ) } = 1 2 min { K A } { Tr ( [ ρ A B , K A I B ] 2 ) } ,
U A ( ρ A B ) = 1 λ max { W A B } ,
( W A B ) i j = Tr [ ρ A B ( σ i A I B ) ρ A B ( σ j A I B ) ] ,
ξ ( l 0 ) = sin ( π 2 | l 0 | ) ω 0 2 Γ ( | l 0 | + 3 / 2 ) Γ ( | l 0 | + 1 ) ,
r 0 ( α ) = [ 2 Γ ( 3 α 2 ) ( 8 α 2 Γ ( 2 α 2 ) ) ( α 2 ) / 2 π 1 2 k 2 Γ ( 2 α 2 ) z 0 1 C n 2 ( ξ z , α ) ( 1 ξ ) α 2 d ξ ] 1 / ( α 2 ) .