Abstract

Inspired by recent demonstrations of orbital angular momentum-(OAM)-based single-photon communications, we propose two quantum-channel models: (i) the multidimensional quantum-key distribution model and (ii) the quantum teleportation model. Both models employ operator-sum representation for Kraus operators derived from OAM eigenkets transition probabilities. These models are highly important for future development of quantum-error correction schemes to extend the transmission distance and improve date rates of OAM quantum communications. By using these models, we calculate corresponding quantum-channel capacities in the presence of atmospheric turbulence.

© 2012 Optical Society of America

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References

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2012

2010

2009

2008

V. P. Aksenov and Ch. E. Pogutsa, Quantum Electron. 38, 343 (2008).
[CrossRef]

2007

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

2005

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

1999

J. J.-L. Ting, Phys. Lett. A 259, 349 (1999).
[CrossRef]

Aksenov, V. P.

V. P. Aksenov and Ch. E. Pogutsa, Quantum Electron. 38, 343 (2008).
[CrossRef]

Boyd, R. W.

Cuang, J.

Y. Zhang, G. Zhao, J. Xu, and J. Cuang, in 2009 Conference on Communications and Mobile Computing (IEEE, 2009), p. 477.

Ding, J.

Djordjevic, I. B.

I. B. Djordjevic, Quantum Information Processing and Quantum Error Correction (Elsevier/Academic, 2012).

Dudley, A.

Forbes, A.

Gong, L. Y.

Kitajima, S.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Kondo, Y.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Konrad, T.

Lavery, M. P. J.

Leach, J.

Malik, M.

Mirhosseini, M.

Nakahara, M.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Nock, M.

O’Sullivan, M.

Padgett, M. J.

Paterson, C.

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Pogutsa, Ch. E.

V. P. Aksenov and Ch. E. Pogutsa, Quantum Electron. 38, 343 (2008).
[CrossRef]

Rodenburg, B.

Roux, F. S.

Shibata, F.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Tanimura, S.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Ting, J. J.-L.

J. J.-L. Ting, Phys. Lett. A 259, 349 (1999).
[CrossRef]

Tyler, G. A.

Uchiyama, C.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Xu, J.

Y. Zhang, G. Zhao, J. Xu, and J. Cuang, in 2009 Conference on Communications and Mobile Computing (IEEE, 2009), p. 477.

Zhang, Y.

Y. Zhang, G. Zhao, J. Xu, and J. Cuang, in 2009 Conference on Communications and Mobile Computing (IEEE, 2009), p. 477.

Zhao, G.

Y. Zhang, G. Zhao, J. Xu, and J. Cuang, in 2009 Conference on Communications and Mobile Computing (IEEE, 2009), p. 477.

Zhao, S. M.

Zheng, B. Y.

J. Phys. Soc. Jpn.

Y. Kondo, M. Nakahara, S. Tanimura, S. Kitajima, C. Uchiyama, and F. Shibata, J. Phys. Soc. Jpn. 76, 074002 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

J. J.-L. Ting, Phys. Lett. A 259, 349 (1999).
[CrossRef]

Phys. Rev. Lett.

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Quantum Electron.

V. P. Aksenov and Ch. E. Pogutsa, Quantum Electron. 38, 343 (2008).
[CrossRef]

Other

I. B. Djordjevic, Quantum Information Processing and Quantum Error Correction (Elsevier/Academic, 2012).

Y. Zhang, G. Zhao, J. Xu, and J. Cuang, in 2009 Conference on Communications and Mobile Computing (IEEE, 2009), p. 477.

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Figures (3)

Fig. 1.
Fig. 1.

The OAM quantum-channel models for L=1: (a) MQKD model (|ψm=|m) and (b) quantum teleportation model.

Fig. 2.
Fig. 2.

Quantum-channel capacity for MQKD model (i) against the atmospheric turbulence strength (in terms of telescope diameter D over Fried’s coherence diameter r0).

Fig. 3.
Fig. 3.

QCCs against the atmospheric turbulence strength for various superposition states using the quantum teleportation model (ii).

Equations (15)

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

|+1=[100],|0=[010],and|1=[001].
|ψin=m=LLαm|m,s.t.m=LLαm2=1.
ρs=[p+1000p0000p1].
pm,n=sΔ=1π01dρρ02πdθexp[3.44(Dr0)5/3](ρsinθ2)5/3cosΔθ,
E(r)=E0W(rR)eimθ,
ρsUρs.
ξ(ρs)=TrEUs,E(ρs|0E0E|)Us,E,
ξ(ρs)=iEiρsEi.
iEiEi=I.
V(ρs)=m,npm,nUm,nρsUm,n.
Em,n=pm,nUm,n.
Ei,j,k=p+1,ip0,jp1,k(|i+1|+|j0|+|k1|),i,j,k{1,0,+1}.
C(ρs)=max{pj,ρj}{S[V(ρs)]jpjS[V(ρj)]},ρs=jpjρj,
|+1+|12,|+1+2|0|16,and|+1+|0+|13.
|1+|22,|2+2|1|26,|2+|1+3|0+|212,|2|1+|0+4|1+|225,|2+|1|0+|1+|25.

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