We consider the possibility of performing quantum key distribution (QKD) by encoding information onto individual photons using plane-wave basis states. We compare the results of this calculation to those obtained by earlier workers, who considered encoding using OAM-carrying vortex modes of the field. We find theoretically that plane-wave encoding is less strongly influenced by atmospheric turbulence than is OAM encoding, with potentially important implications for free-space quantum key distribution.

© 2011 OSA

1. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001). [CrossRef] [PubMed]
2. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics1, 165–171 (2007). [CrossRef]
3. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002). [CrossRef] [PubMed]
4. M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002). [CrossRef]
5. 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. A45, 8185–8189 (1992). [CrossRef] [PubMed]
6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88, 013601 (2002). [CrossRef] [PubMed]
7. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt.47, A33–A41 (2008). [CrossRef]
8. J. Leach, M. R. Denis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys.7, 55 (2005). [CrossRef]
9. 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,” Science329, 662–665 (2010). [CrossRef] [PubMed]
10. B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A74, 062104 (2006). [CrossRef]
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12. C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys.9, 94 (2007). [CrossRef]
13. G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A25, 225–260 (2008). [CrossRef]
14. G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett.34, 142–144 (2009). To allow straightforward comparison between the OAM and plane-wave cases, in the present article we use notation similar to that of this earlier paper. [CrossRef] [PubMed]
15. C. Bonato, A. Tomaello, V. Da Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2009). [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. Express19, 6671–6683 (2011). [CrossRef] [PubMed]
17. F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A83, 053822 (2011). [CrossRef]
18. Y.-X. Zhang, Y.-G. Wang, J.-C. Xu, J.-Y. Wang, and J.-J Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun.284, 1132–1138 (2011). [CrossRef]
19. Y. Wang, Y. Zhang, J. Wang, and J. Jia, “Degree of polarization for quantum light field propagating through non-Kolmogorov turbulence,” Opt. Laser Technol.43, 776–780 (2011). [CrossRef]
20. We note that a security analysis of such a plane-wave encoding scheme has been presented earlier for the case of a continuous-variable protocol by L. Zhang, C. Silberhorn, and I. A. Walmsley, “Secure quantum key distribution using continuous variables of single photons,” Phys. Rev. Lett.100, 110504 (2008). In the present paper we discretize the propagation direction to better compare our results to those of earlier work based on an OAM basis. [CrossRef] [PubMed]
21. W. A. Miller, “Efficient photon sorter in a high-dimensional state space,” Quantum Inf. Comput.11, 0313–0325 (2011).
22. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very short and very long exposures,” J. Opt. Soc. Am.56, 1372–1379 (1966). [CrossRef]
23. The propagation of light through atmospheric turbulence is reviewed by P. W. Milonni, “Adaptive optics for astronomy,” Am. J. Phys.67, 476–485 (1999). [CrossRef]

Am. J. Phys.

• The propagation of light through atmospheric turbulence is reviewed by P. W. Milonni, “Adaptive optics for astronomy,” Am. J. Phys.67, 476–485 (1999). [CrossRef]

Appl. Opt.

• M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt.47, A33–A41 (2008). [CrossRef]

J. Opt. Soc. Am.

• D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very short and very long exposures,” J. Opt. Soc. Am.56, 1372–1379 (1966). [CrossRef]

J. Opt. Soc. Am. A

• G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A25, 225–260 (2008). [CrossRef]

J. Phys. A

• M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002). [CrossRef]

Nat. Photonics

• N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics1, 165–171 (2007). [CrossRef]

Nature

• A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001). [CrossRef] [PubMed]

New J. Phys.

• C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys.9, 94 (2007). [CrossRef]
• J. Leach, M. R. Denis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys.7, 55 (2005). [CrossRef]
• C. Bonato, A. Tomaello, V. Da Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2009). [CrossRef]

Opt. Commun.

• Y.-X. Zhang, Y.-G. Wang, J.-C. Xu, J.-Y. Wang, and J.-J Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun.284, 1132–1138 (2011). [CrossRef]

Opt. Express

• B.-J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express19, 6671–6683 (2011). [CrossRef] [PubMed]

Opt. Laser Technol.

• Y. Wang, Y. Zhang, J. Wang, and J. Jia, “Degree of polarization for quantum light field propagating through non-Kolmogorov turbulence,” Opt. Laser Technol.43, 776–780 (2011). [CrossRef]

Opt. Lett.

• G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett.34, 142–144 (2009). To allow straightforward comparison between the OAM and plane-wave cases, in the present article we use notation similar to that of this earlier paper. [CrossRef] [PubMed]

Phys. Rev. A

• B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A74, 062104 (2006). [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. A45, 8185–8189 (1992). [CrossRef] [PubMed]
• F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A83, 053822 (2011). [CrossRef]

Phys. Rev. Lett.

• G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88, 013601 (2002). [CrossRef] [PubMed]
• N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002). [CrossRef] [PubMed]
• C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett.94, 153901 (2005). [CrossRef] [PubMed]
• We note that a security analysis of such a plane-wave encoding scheme has been presented earlier for the case of a continuous-variable protocol by L. Zhang, C. Silberhorn, and I. A. Walmsley, “Secure quantum key distribution using continuous variables of single photons,” Phys. Rev. Lett.100, 110504 (2008). In the present paper we discretize the propagation direction to better compare our results to those of earlier work based on an OAM basis. [CrossRef] [PubMed]

Quantum Inf. Comput.

• W. A. Miller, “Efficient photon sorter in a high-dimensional state space,” Quantum Inf. Comput.11, 0313–0325 (2011).

Science

• 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,” Science329, 662–665 (2010). [CrossRef] [PubMed]

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