Abstract

Continuous variable quantum key distribution (CV QKD) is a promising candidate for the deployment of quantum cryptography. At present, the longest distance is limited to ∼100 km at fiber-based quantum channel. We investigated in depth the realistic rate–distance limit (RDL) of CV QKD, considering reconciliation efficiency, finite-size effect, and realistic excess noise under collective attack. It is shown that the excess noise generated on Bob’s side degrades significantly the transmission distance and we verify it in experiment. The improvement in RDL by reconciliation efficiency depends on the excess noise level, considerable increase of RDL by improving the reconciliation efficiency occurs only for relative large excess noises. A convergence modulation variance, useful in calculation simplification, is found. Furthermore, we restudy the finite-size analysis and eliminates a loophole arising from the Holevo-bound information monotonicity and a safe RDL is guaranteed. Based on the revised finite-size analysis, the optimum ratio determining the amount of data used for parameter estimation is analyzed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
  4. S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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  5. M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
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  6. K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68(2), 022317 (2003).
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  7. D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
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  8. D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
    [Crossref]
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    [Crossref]
  11. D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63(2), 022309 (2001).
    [Crossref]
  12. C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88(16), 167902 (2002).
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  15. C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
    [Crossref] [PubMed]
  16. R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
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  17. J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
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  21. V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
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  22. C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
    [Crossref]
  23. B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
  24. D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
    [Crossref] [PubMed]
  25. X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
    [Crossref]
  26. 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]
  27. N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
    [Crossref]
  28. P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
    [Crossref] [PubMed]
  29. D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
    [Crossref] [PubMed]
  30. Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
    [Crossref]
  31. F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
    [Crossref]
  32. M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography,” NPJ Quantum Inf. 4, 21 (2018).
    [Crossref]
  33. P. Wang, X. Y. Wang, J. Q. Li, and Y. M. Li, “Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions,” Opt. Express 25(23), 27995–28009 (2017).
    [Crossref]
  34. Z. Qu, I. B. Djordjevic, and M. A. Neifeld, “RF-subcarrier-assisted four-state continuous variable QKD based on coherent detection,” Opt. Lett. 41(23), 5507–5510 (2016).
    [Crossref] [PubMed]
  35. A. Leverrier and P. Grangier, “Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation,” Phys. Rev. A 83(4), 042312 (2011).
    [Crossref]
  36. A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
    [Crossref]
  37. P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite-size analysis of measurement-device-independent quantum cryptography with continuous variables,” Phys. Rev. A 96(4), 042332 (2017).
    [Crossref]
  38. X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
    [Crossref]
  39. P. Jouguet, S. K. Jacques, E. Diamanti, and A. Leverrier, “Analysis of imperfections in practical continuous-variable quantum key distribution,” Phys. Rev. A 86(3), 032309 (2012).
    [Crossref]
  40. J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Controlling excess noise in fiber-optics continuous-variable quantum key distribution,” Phys. Rev. A 72(5), 050303(R) (2005).
    [Crossref]

2018 (4)

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
[Crossref] [PubMed]

N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
[Crossref]

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography,” NPJ Quantum Inf. 4, 21 (2018).
[Crossref]

2017 (6)

P. Wang, X. Y. Wang, J. Q. Li, and Y. M. Li, “Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions,” Opt. Express 25(23), 27995–28009 (2017).
[Crossref]

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
[Crossref]

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
[Crossref] [PubMed]

P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite-size analysis of measurement-device-independent quantum cryptography with continuous variables,” Phys. Rev. A 96(4), 042332 (2017).
[Crossref]

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
[Crossref]

2016 (4)

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

Z. Qu, I. B. Djordjevic, and M. A. Neifeld, “RF-subcarrier-assisted four-state continuous variable QKD based on coherent detection,” Opt. Lett. 41(23), 5507–5510 (2016).
[Crossref] [PubMed]

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

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[Crossref] [PubMed]

2015 (4)

R. kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17(4), 043027 (2015).
[Crossref]

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
[Crossref]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

2013 (2)

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

2012 (3)

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[Crossref] [PubMed]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

P. Jouguet, S. K. Jacques, E. Diamanti, and A. Leverrier, “Analysis of imperfections in practical continuous-variable quantum key distribution,” Phys. Rev. A 86(3), 032309 (2012).
[Crossref]

2011 (1)

A. Leverrier and P. Grangier, “Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation,” Phys. Rev. A 83(4), 042312 (2011).
[Crossref]

2010 (1)

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
[Crossref]

2009 (2)

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]

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]

2007 (1)

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
[Crossref]

2006 (1)

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[Crossref] [PubMed]

2005 (2)

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Controlling excess noise in fiber-optics continuous-variable quantum key distribution,” Phys. Rev. A 72(5), 050303(R) (2005).
[Crossref]

2004 (1)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

2003 (2)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68(2), 022317 (2003).
[Crossref]

2002 (2)

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88(16), 167902 (2002).
[Crossref] [PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref] [PubMed]

2001 (2)

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311(2001).
[Crossref]

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63(2), 022309 (2001).
[Crossref]

1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303(R) (1999).
[Crossref]

Alléaume, R.

Bacco, D.

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

Bai, Z. L.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
[Crossref]

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
[Crossref]

Banchi, L.

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
[Crossref] [PubMed]

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 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.

Bettelli, S.

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Bloch, M.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
[Crossref]

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Bowen, W. P.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

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.

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

Brunner, H. H.

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Brunner, N.

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

Castaneda, M. A. U.

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
[Crossref]

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[Crossref] [PubMed]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311(2001).
[Crossref]

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]

Christensen, J. B.

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

Comandar, L. C.

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Debuisschert, T.

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B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

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M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
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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).
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C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
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N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
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S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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[Crossref]

Pooser, R.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Poppe, A.

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Preskill, J.

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63(2), 022309 (2001).
[Crossref]

Qi, B.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Qin, H.

R. kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17(4), 043027 (2015).
[Crossref]

Qu, Z.

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303(R) (1999).
[Crossref]

Rottwitt, K.

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

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]

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

Shields, A. J.

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
[Crossref] [PubMed]

Silberhorn, C.

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88(16), 167902 (2002).
[Crossref] [PubMed]

Stucki, D.

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

Symul, T.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

Tualle-Brouri, R.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[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]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
[Crossref]

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Controlling excess noise in fiber-optics continuous-variable quantum key distribution,” Phys. Rev. A 72(5), 050303(R) (2005).
[Crossref]

Usenko, V. C.

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311(2001).
[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]

Waks, E.

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68(2), 022317 (2003).
[Crossref]

Wang, C.

C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
[Crossref]

Wang, D.

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Wang, N.

N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
[Crossref]

Wang, P.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
[Crossref]

P. Wang, X. Y. Wang, J. Q. Li, and Y. M. Li, “Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions,” Opt. Express 25(23), 27995–28009 (2017).
[Crossref]

Wang, S. F.

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
[Crossref]

Wang, T.

Wang, X. Y.

N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
[Crossref]

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
[Crossref]

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
[Crossref]

P. Wang, X. Y. Wang, J. Q. Li, and Y. M. Li, “Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions,” Opt. Express 25(23), 27995–28009 (2017).
[Crossref]

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
[Crossref]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

Yamamoto, Y.

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68(2), 022317 (2003).
[Crossref]

Yang, S. S.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
[Crossref]

Yu, S.

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Yuan, Z. L.

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
[Crossref] [PubMed]

Zbinden, H.

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

Zeng, G.

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[Crossref] [PubMed]

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

C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
[Crossref]

Zhang, L. M.

M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography,” NPJ Quantum Inf. 4, 21 (2018).
[Crossref]

Zhang, X. Y.

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Zhang, Y. C.

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Zhao, Y. J.

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Zhou, Y.

Appl. Phys. Lett. (1)

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, “Fast and simple one-way quantum key distribution,” Appl. Phys. Lett. 87(19), 194108 (2005).
[Crossref]

Chin. Phys. B. (1)

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B. 26(4), 040303 (2017).
[Crossref]

Chin. Phys. Lett. (1)

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
[Crossref]

IEEE Photonic Tech. Lett. (1)

F. Karinou, H. H. Brunner, C. F. Fung, L. C. Comandar, S. Bettelli, D. Hillerkuss, M. Kuschnerov, S. Mikroulis, D. Wang, C. X M. Peev, and A. Poppe, “Toward the integration of CV quantum key distribution in deployed optical networks,” IEEE Photonic Tech. Lett. 30(7), 650–653 (2018).
[Crossref]

Nat. Commun. (1)

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
[Crossref] [PubMed]

Nat. Photonics (1)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

Nature (2)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–407 (2018).
[Crossref] [PubMed]

New J. Phys. (2)

R. kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17(4), 043027 (2015).
[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]

NPJ Quantum Inf. (1)

M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography,” NPJ Quantum Inf. 4, 21 (2018).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev A (1)

X. Y. Zhang, Y. C. Zhang, Y. J. Zhao, X. Y. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev A 96(4), 042334 (2017).
[Crossref]

Phys. Rev. A (12)

P. Jouguet, S. K. Jacques, E. Diamanti, and A. Leverrier, “Analysis of imperfections in practical continuous-variable quantum key distribution,” Phys. Rev. A 86(3), 032309 (2012).
[Crossref]

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Controlling excess noise in fiber-optics continuous-variable quantum key distribution,” Phys. Rev. A 72(5), 050303(R) (2005).
[Crossref]

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
[Crossref]

A. Leverrier and P. Grangier, “Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation,” Phys. Rev. A 83(4), 042312 (2011).
[Crossref]

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
[Crossref]

P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite-size analysis of measurement-device-independent quantum cryptography with continuous variables,” Phys. Rev. A 96(4), 042332 (2017).
[Crossref]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
[Crossref]

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68(2), 022317 (2003).
[Crossref]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303(R) (1999).
[Crossref]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311(2001).
[Crossref]

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63(2), 022309 (2001).
[Crossref]

Phys. Rev. Applied (1)

N. Wang, S. N. Du, W. Y. Liu, X. Y. Wang, Y. M. Li, and K. C. Peng, “Long-Distance Continuous-Variable Quantum Key Distribution with Entangled States,” Phys. Rev. Applied 10(6), 064028 (2018).
[Crossref]

Phys. Rev. Lett. (4)

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88(16), 167902 (2002).
[Crossref] [PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref] [PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref] [PubMed]

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[Crossref] [PubMed]

Phys. Rev. X (1)

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Rev. Mod. Phys. (2)

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]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

Sci. Rep. (2)

C. Wang, D. Huang, P. Huang, D. Lin, J. Peng, and G. Zeng, “25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel,” Sci. Rep. 5, 14607 (2015).
[Crossref]

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

Sci. Reports (1)

D. Bacco, J. B. Christensen, M. A. U. Castaneda, Y. H. Ding, S. Forchhammer, K. Rottwitt, and L. K. Oxenlowe, “Two-dimensional distributed-phase-reference protocol for quantum key distribution,” Sci. Reports 6, 36756 (2016).
[Crossref]

Other (1)

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.

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Figures (9)

Fig. 1
Fig. 1 RDLs and experimental results for typical CV QKD protocols.
Fig. 2
Fig. 2 RDLs at different reconciliation efficiencies of 0.99 (red lines) and 0.95 (blue lines).
Fig. 3
Fig. 3 Optimal modulation variance versus the transmission distance at different reconciliation efficiencies and different excess noise levels. (a) The curves at different reconciliation efficiencies where ε = 0.01. (b) The curves at different excess noise where β = 0.99.
Fig. 4
Fig. 4 The RDLs with optimal modulation variances and convergence variances at different excess noise levels. (a) The y-axis is the secret key rate. (b) The y-axis is the ratio of the secret key rate at optimal modulation variance (OMV) to that at convergence modulation variance (CMV).
Fig. 5
Fig. 5 Various kinds of information versus the transmission efficiency.
Fig. 6
Fig. 6 (a) Tight and loose RDLs with different numbers of total samples. (b) The corresponding optimal ratio.
Fig. 7
Fig. 7 The reduction ratios RST and RPA versus the transmission distance with different total numbers of samples.
Fig. 8
Fig. 8 Realistic excess noise and RDLs as a function of distance in asymptotic (asy) and finite-size cases.
Fig. 9
Fig. 9 Entanglement-based scheme.

Tables (2)

Tables Icon

Table 1 Performance improvement arising from the enhanced reconciliation efficiency (from 0.95 to 0.99) versus different excess noise levels at a constant distance or secret key rate.

Tables Icon

Table 2 Excess noises at different transmission distances.

Equations (33)

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

Δ I = β I AB χ BE ,
Δ I AB f = ( n / N ) ( β I AB δ PE χ BE δ PE Δ ( n , δ PA ) ) ,
χ BE t | σ 2 < 0 and χ BE σ 2 | t > 0 ,
{ Δ I AB f = n N [ β I AB ( t min , σ max 2 ) χ BE ( t max , σ max 2 ) Δ ( n , δ PA ) ] , t max < t peak Δ I AB f = n N [ β I AB ( t min , σ max 2 ) χ BE ( t min , σ max 2 ) Δ ( n , δ PA ) ] , t min > t peak
I AB t | σ 2 > 0 and I AB σ 2 | t < 0 ,
Δ ST = β I AB χ BE ( β I AB δ PE χ BE δ PE ) ,
Δ PA = Δ ( n , δ PA ) .
Δ = Δ PA + Δ ST .
R ST = Δ ST / Δ and R PA = Δ P A / Δ .
y = t x + z ,
V B = η TV M + η T ( ε a + ε l ) + ε b + N 0 + ν e .
ε r = ( η T ( ε a + ε l ) + ε b ) / η T = ε a + ε l + ε b / η T .
γ AB 0 = [ V I V 2 1 σ z V 2 1 σ z V I ] ,
I = [ 1 0 0 1 ] and σ Z = [ 1 0 0 1 ] .
γ AB 1 = [ V I T ( V 2 1 ) σ z T ( V 2 1 ) σ z T ( V + χ line ) I ] ,
V N = 1 + ν e / ( 1 η ) .
γ AB = [ V I η T ( V 2 1 ) σ z η T ( V 2 1 ) σ z T ( V + χ tot ) I ] ,
Δ I = β I AB χ BE ,
I AB = 1 2 log 2 V A V A | B ,
γ A | B = γ A σ AB ( X γ B X ) MP σ AB T ,
X = [ 1 0 0 0 ] ;
γ AB = [ γ A σ AB σ AB T γ B ] .
χ B E = S ( ρ E ) S ( ρ E x B ) ,
S ( ρ ) = i G ( λ i 1 2 ) ,
γ AB = [ a I c σ z c σ 2 b I ] .
λ 1 , 2 = 1 2 [ Δ ± Δ 2 4 D 2 ] ,
Δ = a 2 + b 2 2 c 2 and D = a b c 2 .
γ ARH x B = γ ARH σ ARH ; B ( X γ B X ) MP σ A R H ; B T .
γ ARHB = [ γ ARH σ ARH ; B σ ARH ; B T γ B ] ,
γ ABRH = [ I S B 1 R 0 I ] [ γ AB 1 γ R 0 H ] [ I S B 1 R 0 I ] T ,
S B 1 R 0 = [ η I 1 η I 1 η I η I ] .
λ 3 , 4 = 1 2 [ A ± A 2 4 B 2 ] and λ 5 = 1 ,
A = 1 b + χ hom [ b + a D + χ hom Δ ] and B = D b + χ hom [ a + χ hom Δ ] .

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