Abstract

We investigate a multiple spatial modes based quantum key distribution (QKD) scheme that employs multiple independent parallel beams through a marine free-space optical channel over open ocean. This approach provides the potential to increase secret key rate (SKR) linearly with the number of channels. To improve the SKR performance, we describe a back-propagation mode (BPM) method to mitigate the atmospheric turbulence effects. Our simulation results indicate that the secret key rate can be improved significantly by employing the proposed BPM-based multi-channel QKD scheme.

© 2016 Optical Society of America

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Vladyslav C. Usenko, Christian Peuntinger, Bettina Heim, Kevin Günthner, Ivan Derkach, Dominique Elser, Christoph Marquardt, Radim Filip, and Gerd Leuchs
Opt. Express 26(24) 31106-31115 (2018)

References

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  1. C. H. Bennett, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE Conference on Computer System and Signal Processing (IEEE, 1984), pp. 175–179.
  2. R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  6. B. A. Bash, N. Chandrasekaran, J. H. Shapiro, and S. Guha, “Quantum key distribution using multiple Gaussian focused beams,” https://arxiv.org/abs/1604.08582 .
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    [Crossref]
  8. Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
    [Crossref] [PubMed]
  9. S. Hammel, “Reference vertical atmospheric turbulence profiles,” SPAWAR Systems Center Pacific Internal Report.
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: trends and applications,” in Optical Imaging and Metrology: Advanced Technologies (John Wiley & Sons, 2012).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (2)

Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
[Crossref] [PubMed]

X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Secret key rates and optimization of BB84 and decoy state protocols over time-varying free-space optical channels,” IEEE Photonics J. 8(3), 1–13 (2016).

2015 (2)

J. P. Bourgoin, B. L. Higgins, N. Gigov, C. Holloway, C. J. Pugh, S. Kaiser, M. Cranmer, and T. Jennewein, “Free-space quantum key distribution to a moving receiver,” Opt. Express 23(26), 33437–33447 (2015).
[Crossref] [PubMed]

J. Liu and J. Wang, “Demonstration of polarization-insensitive spatial light modulation using a single polarization-sensitive spatial light modulator,” Sci. Rep. 5, 9959 (2015).
[Crossref] [PubMed]

2014 (1)

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), e213 (2014).
[Crossref]

2013 (2)

M. Mirhosseini, O. S. Magaña-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21(25), 30196–30203 (2013).
[Crossref] [PubMed]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

2012 (1)

2009 (1)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

2008 (1)

2004 (1)

2002 (2)

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

2000 (1)

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

1998 (1)

1989 (1)

U. Piomelli, J. L. Balint, and J. M. Wallace, “On the validity of Taylor’s hypothesis for wall‐bounded flows,” Phys. Fluids A Fluid Dyn. 1(3), 609–611 (1989).
[Crossref]

1982 (1)

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
[Crossref]

Bagnoud, V.

Balint, J. L.

U. Piomelli, J. L. Balint, and J. M. Wallace, “On the validity of Taylor’s hypothesis for wall‐bounded flows,” Phys. Fluids A Fluid Dyn. 1(3), 609–611 (1989).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE Conference on Computer System and Signal Processing (IEEE, 1984), pp. 175–179.

Bourgoin, J. P.

Boyd, R. W.

Bruno, T. L.

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Chen, C.

Chu, D.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), e213 (2014).
[Crossref]

Cranmer, M.

Derkacs, D.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

Desjardins, P.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Ding, J.

Djordjevic, I. B.

Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
[Crossref] [PubMed]

X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Secret key rates and optimization of BB84 and decoy state protocols over time-varying free-space optical channels,” IEEE Photonics J. 8(3), 1–13 (2016).

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Dymale, R. C.

Englund, D.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Fried, D. L.

Gigov, N.

Gong, L. Y.

Gruneisen, M. T.

Higgins, B. L.

Holloway, C.

Hughes, R. J.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

Jankevics, A.

Jennewein, T.

Kaiser, S.

Landers, F.

Leach, J.

Lee, C.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Levine, B. M.

Liu, J.

J. Liu and J. Wang, “Demonstration of polarization-insensitive spatial light modulation using a single polarization-sensitive spatial light modulator,” Sci. Rep. 5, 9959 (2015).
[Crossref] [PubMed]

Lütkenhaus, N.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

Magaña-Loaiza, O. S.

Malik, M.

Martinsen, E. A.

Miller, W. A.

Mirhosseini, M.

Mower, J.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Neifeld, M. A.

X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Secret key rates and optimization of BB84 and decoy state protocols over time-varying free-space optical channels,” IEEE Photonics J. 8(3), 1–13 (2016).

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
[Crossref]

Nordholt, J. E.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Peterson, C. G.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

Piomelli, U.

U. Piomelli, J. L. Balint, and J. M. Wallace, “On the validity of Taylor’s hypothesis for wall‐bounded flows,” Phys. Fluids A Fluid Dyn. 1(3), 609–611 (1989).
[Crossref]

Pugh, C. J.

Qu, Z.

Rodenburg, B.

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Shapiro, J. H.

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Sun, X.

X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Secret key rates and optimization of BB84 and decoy state protocols over time-varying free-space optical channels,” IEEE Photonics J. 8(3), 1–13 (2016).

Sweiti, A. M.

Toledo-Quinones, M.

Wallace, J. M.

U. Piomelli, J. L. Balint, and J. M. Wallace, “On the validity of Taylor’s hypothesis for wall‐bounded flows,” Phys. Fluids A Fluid Dyn. 1(3), 609–611 (1989).
[Crossref]

Wang, J.

J. Liu and J. Wang, “Demonstration of polarization-insensitive spatial light modulation using a single polarization-sensitive spatial light modulator,” Sci. Rep. 5, 9959 (2015).
[Crossref] [PubMed]

Wirth, A.

You, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), e213 (2014).
[Crossref]

Zhang, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), e213 (2014).
[Crossref]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Zhao, S. M.

Zheng, B. Y.

Zuegel, J. D.

Appl. Opt. (2)

IEEE Photonics J. (1)

X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Secret key rates and optimization of BB84 and decoy state protocols over time-varying free-space optical channels,” IEEE Photonics J. 8(3), 1–13 (2016).

J. Opt. Soc. Am. (1)

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

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
[Crossref]

Light Sci. Appl. (1)

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), e213 (2014).
[Crossref]

New J. Phys. (2)

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4(1), 43 (2002).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Fluids A Fluid Dyn. (1)

U. Piomelli, J. L. Balint, and J. M. Wallace, “On the validity of Taylor’s hypothesis for wall‐bounded flows,” Phys. Fluids A Fluid Dyn. 1(3), 609–611 (1989).
[Crossref]

Phys. Rev. A (2)

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87(6), 062322 (2013).
[Crossref]

Rev. Mod. Phys. (1)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Sci. Rep. (1)

J. Liu and J. Wang, “Demonstration of polarization-insensitive spatial light modulation using a single polarization-sensitive spatial light modulator,” Sci. Rep. 5, 9959 (2015).
[Crossref] [PubMed]

Other (8)

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: trends and applications,” in Optical Imaging and Metrology: Advanced Technologies (John Wiley & Sons, 2012).

C. H. Bennett, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE Conference on Computer System and Signal Processing (IEEE, 1984), pp. 175–179.

R. K. Tyson, Principles of Adaptive Optics (CRC, 2015).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

B. A. Bash, N. Chandrasekaran, J. H. Shapiro, and S. Guha, “Quantum key distribution using multiple Gaussian focused beams,” https://arxiv.org/abs/1604.08582 .

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” https://arxiv.org/abs/1402.7113 .
[Crossref]

S. Hammel, “Reference vertical atmospheric turbulence profiles,” SPAWAR Systems Center Pacific Internal Report.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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Figures (9)

Fig. 1
Fig. 1 Multi-channel QKD system diagrams. (a) Parallel channel setup, (b) Receiver-side adaptive optics (RXAO) scheme, (c) Back-propagation mode (BPM)-based transmitter setup. BS: Beam splitter. DM: Deformable mirror. LC-SLM: Liquid crystal spatial light modulator.
Fig. 2
Fig. 2 SKR versus transmitter separation for different values of turbulence strength. This data demonstrates the existence of an optimal transmitter separation for each value of turbulence strength.
Fig. 3
Fig. 3 Optimized secret key rates of multi-channel QKD for different number of channels.
Fig. 4
Fig. 4 SKR Comparison between multi-channel QKD with RXAO and without RXAO. Solid lines: SKR without RXAO. Dash lines: SKR with RXAO.
Fig. 5
Fig. 5 SKR Comparison between multi-channel QKD with RXAO and BPM scheme.
Fig. 6
Fig. 6 Anisoplanatism in BPM scheme. (a) Angular anisoplanatism, (b) Temporal anisoplanatism (displacement anisoplanatism).
Fig. 7
Fig. 7 Simulated pilot signal detector plane intensity profile of BPM scheme with different number of probing sources and time delays. Results are shown with Cn2 of 10−15 (σR2 = 16) and the transverse wind speed of 5m/s.
Fig. 8
Fig. 8 Turbulence temporal effect of SKR in BPM scheme. Results are shown with Cn2 of 10−15 (σR2 = 16) and the transverse wind speed of 5m/s.
Fig. 9
Fig. 9 SKR comparison between multi-channel QKD with RXAO and BPM scheme with temporal effect. The black dotted lines connecting cross marks are used to denote the SKRs of time delays ranging from 4.8 msec to 9.6 msec.

Equations (4)

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Φ n ( κ )=0.033 C n 2 [ 1+1.802( κ/ κ l )0.254 ( κ/ κ l ) 7/6 ] e κ 2 / κ l 2 ( κ 2 + κ 0 2 ) 11 /6 .
SKR=max{ 1 2 [ p det ( 1h( Q det ) ) p s h( Q s ) p m ],0 }.
w( x,y )= j=1 N a j Z j ( x,y ) .
w shaped =conj( w bp )exp{i2π x( x det x prob )+y( y det y prob ) λf }.

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