Abstract

We show that partially trusting the phase noise associated with estimation uncertainty in a local local oscillator continuous-variable quantum key distribution (LLO-CVQKD) system allows one to exchange higher secure key rates than in the case of untrusted phase noise. However, this opens a security loophole through the manipulation of the reference pulse amplitude. We label this as a “reference pulse attack,” which is applicable to all LLO-CVQKD systems if the phase noise is trusted. We show that, at the optimal reference pulse intensity level, Eve achieves unity attack efficiency at 23.8 km and 32.0 km while using lossless and 0.14 dB/km loss channels, respectively, for her attack. However, to maintain the performance enhancement from partially trusting the phase noise, countermeasures have been proposed. As a result, the LLO-CVQKD system with partially trusted phase noise owns a superior key rate at 20 km by an order 9.5, and an extended transmission distance by 45%, compared to the phase noise untrusted system.

© 2019 Optical Society of America

Full Article  |  PDF Article
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    [Crossref]
  4. H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
    [Crossref]
  5. 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]
  6. A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102, 180504 (2009).
    [Crossref]
  7. 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, 621–669 (2012).
    [Crossref]
  8. E. Diamanti and A. Leverrier, “Distributing secret keys with quantum continuous variables: principle, security and implementations,” Entropy 17, 6072–6092 (2015).
    [Crossref]
  9. D. Huang, P. Huang, D. Lin, C. Wang, and G. Zeng, “High-speed continuous-variable quantum key distribution without sending a local oscillator,” Opt. Lett. 40, 3695–3698 (2015).
    [Crossref]
  10. Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (2011).
    [Crossref]
  11. D. Huang, J. Fang, C. Wang, P. Huang, and G. Zeng, “A wideband balanced homodyne detector for high speed continuous variable quantum key distribution systems,” in 3rd International Conference on Quantum Cryptography, Waterloo, Ontario, 2013.
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  13. A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81, 062343 (2010).
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  14. X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
    [Crossref]
  15. J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
    [Crossref]
  16. H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94, 012325 (2016).
    [Crossref]
  17. 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, 041009 (2015).
    [Crossref]
  18. D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
    [Crossref]
  19. S. Kleis, M. Rueckmann, and C. G. Schaeffer, “Continuous variable quantum key distribution with a real local oscillator using simultaneous pilot signals,” Opt. Lett. 42, 1588–1591 (2017).
    [Crossref]
  20. A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95, 012316 (2017).
    [Crossref]
  21. T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
    [Crossref]
  22. F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
    [Crossref]
  23. B. Qi and C. C. W. Lim, “Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator,” Phys. Rev. Appl. 9, 054008 (2018).
    [Crossref]
  24. 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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
    [Crossref]
  25. A. S. Holevo, “Bounds for the quantity of information transmitted by a quantum communication channel,” Problemy Peredachi Informatsii 9, 3–11 (1973).
  26. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
    [Crossref]
  27. J. Von Neumann and M. E. Rose, Mathematical Foundations of Quantum Mechanics, Investigations in Physics, No. 2 (Princeton University, 1955).
  28. G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
    [Crossref]
  29. S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (2009).
    [Crossref]
  30. Y. Tamura, H. Sakuma, K. Morita, M. Suzuki, Y. Yamamoto, K. Shimada, Y. Honma, K. Sohma, T. Fujii, and T. Hasegawa, “Lowest-ever 0.1419-dB/km loss optical fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th5D.1.

2018 (3)

T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
[Crossref]

F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
[Crossref]

B. Qi and C. C. W. Lim, “Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator,” Phys. Rev. Appl. 9, 054008 (2018).
[Crossref]

2017 (2)

S. Kleis, M. Rueckmann, and C. G. Schaeffer, “Continuous variable quantum key distribution with a real local oscillator using simultaneous pilot signals,” Opt. Lett. 42, 1588–1591 (2017).
[Crossref]

A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95, 012316 (2017).
[Crossref]

2016 (1)

H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94, 012325 (2016).
[Crossref]

2015 (4)

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, 041009 (2015).
[Crossref]

D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
[Crossref]

E. Diamanti and A. Leverrier, “Distributing secret keys with quantum continuous variables: principle, security and implementations,” Entropy 17, 6072–6092 (2015).
[Crossref]

D. Huang, P. Huang, D. Lin, C. Wang, and G. Zeng, “High-speed continuous-variable quantum key distribution without sending a local oscillator,” Opt. Lett. 40, 3695–3698 (2015).
[Crossref]

2014 (2)

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
[Crossref]

2013 (1)

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

2012 (1)

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, 621–669 (2012).
[Crossref]

2011 (1)

Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (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, 062343 (2010).
[Crossref]

2009 (3)

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (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, 1301–1350 (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, 180504 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

2006 (1)

M. Navascués, F. Grosshans, and A. Acin, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref]

2004 (1)

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

2003 (1)

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]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref]

1973 (1)

A. S. Holevo, “Bounds for the quantity of information transmitted by a quantum communication channel,” Problemy Peredachi Informatsii 9, 3–11 (1973).

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Acin, A.

M. Navascués, F. Grosshans, and A. Acin, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref]

Adesso, G.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

Alléaume, R.

A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95, 012316 (2017).
[Crossref]

H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94, 012325 (2016).
[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, 1301–1350 (2009).
[Crossref]

Bennett, C. H.

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

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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 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, 041009 (2015).
[Crossref]

Brassard, G.

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

Brif, C.

D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
[Crossref]

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]

Camacho, R. M.

D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
[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, 621–669 (2012).
[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, 1301–1350 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

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]

Chen, W.

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Chi, Y.-M.

Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (2011).
[Crossref]

Coles, P. J.

D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
[Crossref]

Curty, M.

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

Debuisschert, T.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Diamanti, E.

E. Diamanti and A. Leverrier, “Distributing secret keys with quantum continuous variables: principle, security and implementations,” Entropy 17, 6072–6092 (2015).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

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, 1301–1350 (2009).
[Crossref]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref]

Fang, J.

D. Huang, J. Fang, C. Wang, P. Huang, and G. Zeng, “A wideband balanced homodyne detector for high speed continuous variable quantum key distribution systems,” in 3rd International Conference on Quantum Cryptography, Waterloo, Ontario, 2013.

Fossier, S.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Fujii, T.

Y. Tamura, H. Sakuma, K. Morita, M. Suzuki, Y. Yamamoto, K. Shimada, Y. Honma, K. Sohma, T. Fujii, and T. Hasegawa, “Lowest-ever 0.1419-dB/km loss optical fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th5D.1.

Fung, C.-H. F.

F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
[Crossref]

García-Patrón, R.

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, 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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Grangier, P.

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

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

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

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]

Grice, W.

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, 041009 (2015).
[Crossref]

Grosshans, F.

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

M. Navascués, F. Grosshans, and A. Acin, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref]

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]

Gui, M.

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
[Crossref]

Guo, G.-C.

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Han, Z.-F.

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Hasegawa, T.

Y. Tamura, H. Sakuma, K. Morita, M. Suzuki, Y. Yamamoto, K. Shimada, Y. Honma, K. Sohma, T. Fujii, and T. Hasegawa, “Lowest-ever 0.1419-dB/km loss optical fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th5D.1.

Hentschel, M.

F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
[Crossref]

Holevo, A. S.

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J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
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F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
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Liu, W.

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F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
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B. Qi and C. C. W. Lim, “Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator,” Phys. Rev. Appl. 9, 054008 (2018).
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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, 041009 (2015).
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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, 621–669 (2012).
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D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
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D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5, 041010 (2015).
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X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
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Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (2011).
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J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
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T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
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J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
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J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
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T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
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T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
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X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
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Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (2011).
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Adv. Quantum Technol. (1)

F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, “Continuous-variable quantum key distribution with Gaussian modulation—the theory of practical implementations,” Adv. Quantum Technol. 1, 1800011 (2018).
[Crossref]

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Entropy (1)

E. Diamanti and A. Leverrier, “Distributing secret keys with quantum continuous variables: principle, security and implementations,” Entropy 17, 6072–6092 (2015).
[Crossref]

J. Phys. B (1)

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B 42, 114014 (2009).
[Crossref]

Nat. Photonics (1)

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

Nature (1)

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]

New J. Phys. (1)

Y.-M. Chi, B. Qi, W. Zhu, L. Qian, H.-K. Lo, S.-H. Youn, A. I. Lvovsky, and L. Tian, “A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution,” New J. Phys. 13, 013003 (2011).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (8)

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[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 25km with an all-fiber continuous variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

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

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, Y. L. Zhou, and L. M. Liang, “Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator,” Phys. Rev. A 89, 032310 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94, 012325 (2016).
[Crossref]

A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95, 012316 (2017).
[Crossref]

T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97, 012310 (2018).
[Crossref]

Phys. Rev. Appl. (1)

B. Qi and C. C. W. Lim, “Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator,” Phys. Rev. Appl. 9, 054008 (2018).
[Crossref]

Phys. Rev. Lett. (3)

M. Navascués, F. Grosshans, and A. Acin, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
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Figures (8)

Fig. 1.
Fig. 1. Practical LLO-CVQKD setup. The signal pulse (blue) and phase reference pulse (green) are transmitted through the optical channel and undergo same attenuation. At Bob, the received signals are interfered with the LO (black) to extract quadrature values.
Fig. 2.
Fig. 2. General process of phase rotation and estimation. At Bob, the actual relative phase φS (green angle) of the quantum signal (1,3) and estimated relative phase φR (blue angle) from reference pulse (2,4) are added to the initial phase. φestiR is used to estimate the phase difference φS between two free-running lasers.
Fig. 3.
Fig. 3. Secret key rate comparison of the realistic and paranoid security noise models. The simulation parameters are selected to match the parameters used in recent LLO-CVQKD experiments [17]. Alice modulation variance VA=4 and reference pulse intensity ER2/VA=100.
Fig. 4.
Fig. 4. Reference pulse attack schematic diagram. At the output of Alice, Eve separates the reference pulse to the low-loss channel (blue) and the quantum pulse to the normal fiber (red). She recombines the pulses at the input of Bob. The dashed green lines show the less-attenuated path reference pulses.
Fig. 5.
Fig. 5. Phase noise with (blue dashed line) and without (red dashed line) attack variation at different reference path attenuation coefficient. Excess noise tolerance is generated by an attack. Simulations are performed in the collective attack and VA=4, ERef2/VA=100, and L=20  km.
Fig. 6.
Fig. 6. Mutual information in the realistic model versus channel lengths. The insecure region expands with an increase in the transmission distance. The zero-loss (vacuum) channel maximizes the information gain by Eve. A 100% attack efficiency is achieved from 23.8 km and 32.0 km for 0 and 0.14 dB/km attenuation factors.
Fig. 7.
Fig. 7. Mutual information variations for different reference path attenuation coefficients. Simulations are performed for a collective attack, with (a) untrusted phase noise assumption and (b) trusted phase noise assumption.
Fig. 8.
Fig. 8. Updated trusted phase noise model performance comparison at different reference pulse intensities. The black line represents the key rate performance under the untrusted phase noise model. The blue line shows the trusted phase noise model performance without considering the loophole we discovered in this paper. The red solid line and dashed line, respectively, demonstrate the resultant secure key performance at practically the lowest fiber loss 0.14 dB/km and the idealistic lossless fiber 0 dB/km after upgrading the noise model in this paper. The different pulse intensity ratios are (a) 50, (b) 100, (c) 200, and (d) 300. All other parameters we chose are identical to the values shown in Section 2.C. The upgraded noise model provides an enhanced secure key under the trusted phase noise model to the untrusted case with any reference pulse intensity.

Equations (28)

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XBR=Tη2(XARcosφestiR+PARsinφestiR)
PBR=Tη2(XARsinφestiR+PARcosφestiR).
φR_esti=tan1(PBRXBR).
Vdrift=2π(ΔvA+ΔvB)frep,
Vesti=var(φR_estiφR)=(χtot+1)ERef2.
ξphaseVA*(χtot+1ERef2+2πΔvA+ΔvBfrep).
(XB^PB^)=Tη2[(cosφR_estisinφR_estisinφR_esticosφR_esti)(XAPA)+(Xξ+XNPξ+PN)]+(xelepele).
Kcollective=βIABχBE,
χhetT=[1+(1η)+2Vele]η+Tξesti.
χlineT=1T1+ξe+ξdrift+ξAM+ξADC.
χlineu=χlineT+ξesti,
χhetu=χhetTTξesti.
χtot=χline+χhetT.
IAB=log2VBVB|A=log2V+χtot1+χtot.
χBE=S(E)S(E|B).
χBE=i=12G(λi12)i=35G(λi12),
A=V2(12T)+2T+T2(V+χline)2,
B=[T(Vχline+1)]2.
C=1(T(V+χtot))2[Aχhet2+B+1+2χhet(VB+T(V+χline))+2T(V21)],
D=(V+BχhetT(V+χtot))2.
ξestiattack=VA*χtot+1η*Tlowη*TstdERef2=ξestistd*TstdTlow,
ξtole=ξestistdξestiattack=VA*χtot+1ERef2*(1110(αstdαlow)*L/10).
ξtot=ξe+ξeattack+ξphaseξtole+ξdrift+ξAM+ξADC.
(XBattack^PBattack^)=Tη2[(cosφRPA^sinφRPA^sinφRPA^cosφRPA^)(XAPA)+(Xξ+Xξadd+XNPξ+Pξadd+PN)]+(xelepele)
IAB=log2V+χtot1+χtot=log2V+χtattack1+χtattack=IABest.
χhetattack=[1+(1η)+2Vele]η+T(ξestiξtole)
χlineattack=1T1+ξe+ξdrift+ξAM+ξADC+ξeattack,
Keff=χBEattackχBEestIABestχBEest.

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