Abstract

A high-speed four-state continuous-variable quantum key distribution (CV-QKD) system, enabled by wavelength-division multiplexing, polarization multiplexing, and orbital angular momentum (OAM) multiplexing, is studied in the presence of atmospheric turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns yielding Andrews’ spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and channel transmittance can be monitored directly by the D.C. level in our PNC stage. After the system calibration, a total SKR of >1.68 Gbit/s can be reached in the ideal system, featured with lossless channel and free of excess noise. In our experiment, based on commercial photodetectors, the minimum transmittances of 0.21 and 0.29 are required for OAM states of 2 (or −2) and 6 (or −6), respectively, to guarantee the secure transmission, while a total SKR of 120 Mbit/s can be obtained in case of mean transmittances.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  8. A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
    [Crossref]
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    [Crossref] [PubMed]
  10. F. Grosshans, “Collective attacks and unconditional security in continuous variable quantum key distribution,” Phys. Rev. Lett. 94(2), 020504 (2005).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  13. D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
    [Crossref] [PubMed]
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    [Crossref]
  15. H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
    [Crossref]
  16. Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Express 17(14), 12090–12108 (2009).
    [Crossref] [PubMed]
  17. A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
    [Crossref] [PubMed]
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    [Crossref]
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2016 (5)

2014 (1)

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

2013 (1)

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87(6), 062313 (2013).
[Crossref]

2012 (2)

H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
[Crossref]

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

2009 (5)

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[Crossref] [PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Express 17(14), 12090–12108 (2009).
[Crossref] [PubMed]

Q. Dinh Xuan, Z. Zhang, and P. L. Voss, “A 24 km fiber-based discretely signaled continuous variable quantum key distribution system,” Opt. Express 17(26), 24244–24249 (2009).
[Crossref] [PubMed]

2005 (2)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

F. Grosshans, “Collective attacks and unconditional security in continuous variable quantum key distribution,” Phys. Rev. Lett. 94(2), 020504 (2005).
[Crossref] [PubMed]

1998 (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

1992 (1)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Braunstein, S. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Debuisschert, T.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87(6), 062313 (2013).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Dinh Xuan, Q.

Djordjevic, I. B.

Fang, J.

H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
[Crossref]

Fossier, S.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Gomonay, H. V.

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Grangier, P.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[Crossref] [PubMed]

Grosshans, F.

F. Grosshans, “Collective attacks and unconditional security in continuous variable quantum key distribution,” Phys. Rev. Lett. 94(2), 020504 (2005).
[Crossref] [PubMed]

He, G.

H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
[Crossref]

Heid, M.

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

Heim, B.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Huang, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref] [PubMed]

Huang, P.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref] [PubMed]

Jouguet, P.

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87(6), 062313 (2013).
[Crossref]

Khan, I.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Killoran, N.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Kimble, H. J.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Kunz-Jacques, S.

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87(6), 062313 (2013).
[Crossref]

Leuchs, G.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Leverrier, A.

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[Crossref] [PubMed]

Lin, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref] [PubMed]

Liu, J.

Lutkenhaus, N.

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

Marquardt, Ch.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Neifeld, M. A.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Peuntinger, C.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Qu, Z.

Rigas, J.

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

Semenov, A. A.

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Sun, X.

Toppel, F.

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Tualle-Brouri, R.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Vasylyev, D. Yu.

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Villing, A.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Vogel, W.

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Voss, P. L.

Wang, J.

Wittmann, C.

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

Zeng, G.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref] [PubMed]

Zhang, H.

H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
[Crossref]

Zhang, Z.

Zhao, Y.

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

New J. Phys. (2)

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16(11), 113018 (2014).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (4)

A. A. Semenov, F. Toppel, D. Yu. Vasylyev, H. V. Gomonay, and W. Vogel, “Homodyne detection for atmosphere channels,” Phys. Rev. A 85(1), 013826 (2012).
[Crossref]

Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A 79(1), 012307 (2009).
[Crossref]

H. Zhang, J. Fang, and G. He, “Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers,” Phys. Rev. A 86(2), 022338 (2012).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87(6), 062313 (2013).
[Crossref]

Phys. Rev. Lett. (4)

F. Grosshans, “Collective attacks and unconditional security in continuous variable quantum key distribution,” Phys. Rev. Lett. 94(2), 020504 (2005).
[Crossref] [PubMed]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[Crossref] [PubMed]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
[Crossref] [PubMed]

Sci. Rep. (1)

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref] [PubMed]

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Other (3)

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

T. C .Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303(R) (1999).
[Crossref]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).

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Figures (6)

Fig. 1
Fig. 1 The schematic of the proposed 3D multiplexed four-state CV-QKD system. Inset (a) the optical spectrum after I/Q modulation; Inset (b) the concept of 3D multiplexing. PBS: polarization beam splitter, BS: beam splitter, MR: mirror, HWP: half-wave plate, IL: optical interleaver, OTF: optical tunable filter, LO: local oscillator laser, PNC: phase noise cancellation stage.
Fig. 2
Fig. 2 (a) PDF of the obtained on-axis intensity fluctuation and the analytical Gamma-Gamma distribution. (b) ICFs based on the target continuous path and our turbulent model.
Fig. 3
Fig. 3 (a) Probability distribution of the fluctuating channel transmittances for (a) OAM state of −2; (b) OAM state of 2;(c) OAM state of −6; (d) OAM state of 6.
Fig. 4
Fig. 4 Measured excess noise in cases of (a) OAM state of 2; (b) OAM state of 6.
Fig. 5
Fig. 5 Calculated SKRs in the ideal situation as a function of the modulation variance and channel transmittance in cases of (a) OAM state of 6; (b) OAM state of 2.
Fig. 6
Fig. 6 Experimental SKRs as a function of the modulation variance and channel transmittance in cases of (a) OAM state of 2; (b) OAM state of 6.

Equations (5)

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

i C ( t )( 1+ A 2 ) T 2 2 AI(t)cos( w 1 t π 4 )+ 2 AQ(t)cos( w 1 t π 4 )+ n C
ΔI=β I AB χ BE
I AB = log 2 ( V+ χ tot 1+ χ tot ).
χ BE =G( λ 1 1 2 )+G( λ 2 1 2 )G( λ 3 1 2 )G( λ 4 1 2 )
with V= V A +1, χ tot = χ line + χ het /T, χ line =1/T+ϵ1, χ het =(2+2 V el η)/η, G( x )=( x+1 ) log 2 ( x+1 )x log 2 (x), λ 1,2 = 1 2 (A± A 2 4B ) , λ 3,4 = 1 2 (C± C 2 4D ), A= V 2 + T 2 (V+ χ line ) 2 2T Z 4 2 , B= (T V 2 +TV χ line T Z 4 2 ) 2 , C= A χ het 2 +B+1+2 χ het [ V B +T( V+ χ line ) ]+2T Z 4 2 [T( V+ χ tot )] 2 , D= (V+ χ het B ) 2 [T( V+ χ tot )] 2 ξ 0,2 =1/2 e V A /2 [cosh( V A /2±cos( V A /2))], ξ 1,3 =1/2 e V A /2 [sinh( V A /2±sin( V A /2))].

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