Abstract

We suggest a novel scheme for measurement-device-independent (MDI) continuous-variable quantum key distribution (CVQKD) by integrating plug-and-play (PP) configuration with dual-phase modulation (DPM). With these techniques, MDI-CVQKD system has the ability to overcome a number of impractical problems with no extra performance penalty. In particular, the synchronous loophole of different lasers from Alice and Bob can be elegantly eliminated in the plug-and-play configuration, which gives birth to the convenient implementation when comparing to the Gaussian-modulated coherent-state protocol. Moreover, All LO-aimed attacks can be well defended since the local oscillator (LO) is locally generated. By taking advantage of DPM, the performance degeneration caused by the practical polarization-sensitive amplitude modulator can be eliminated. We also derive the security bounds for the proposed scheme against optimal Gaussian collective attacks. By taking the finite-size effect into account, we show that almost all raw keys generated by the proposed scheme can be exploited for the final secret key generation so that the secret key rate can be increased without sacrificing a part of raw keys for parameter estimation. In addition, we give an experimental concept of the proposed scheme which can be deemed guideline for final implementation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
[Crossref]

Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
[Crossref]

Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
[Crossref]

2017 (2)

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
[Crossref]

Y. Guo, Q. Liao, D. Huang, and G. H. Zeng, “Quantum relay schemes for continuous-variable quantum key distribution,” Phys. Rev. A 95, 042326 (2017).
[Crossref]

2016 (4)

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

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
[Crossref]

Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
[Crossref]

M. Gessner, L. Pezzé, and A. Smerzi, “Efficient entanglement criteria for discrete, continuous, and hybrid variables,” Phys. Rev. A 94(2), 020101 (2016).
[Crossref]

2015 (6)

S. Takeda, M. Fuwa, P. van Loock, and A. Furusawa, “Entanglement swapping between discrete and continuous variables,” Phys. Rev. Lett. 114(10), 100501 (2015).
[Crossref] [PubMed]

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
[Crossref]

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent states,” Phys. Rev. Lett. 114, 070501 (2015).
[Crossref] [PubMed]

2014 (5)

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
[Crossref]

H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (2014).
[Crossref]

M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
[Crossref]

P. Huang, J. Fang, and G. H. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (2014).
[Crossref]

2013 (7)

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]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

H. Qin, R. Kumar, and R. Alleaume, “Saturation attack on continuous-variable quantum key distribution system,” Proc. SPIE 8899(2), 717–718 (2013).

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

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
[Crossref]

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110, 030502 (2013).
[Crossref] [PubMed]

C. Weedbrook, “Continuous-variable quantum key distribution with entanglement in the middle,” Phys. Rev. A 87, 022308 (2013).
[Crossref]

2012 (4)

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
[Crossref] [PubMed]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (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, 621 (2012).
[Crossref]

2011 (1)

A. Leverrier and P. Grangier, “Erratum: Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation [Phys. Rev. Lett. 102, 180504 (2009)],” Phys. Rev. Lett. 106259902 (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)

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102, 110504 (2009).
[Crossref] [PubMed]

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

2008 (1)

S. Pirandola, S. L. Braunstein, and S. Lloyd, “Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography,” Phys. Rev. Lett. 101, 200504 (2008).
[Crossref] [PubMed]

2007 (1)

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
[Crossref] [PubMed]

2006 (4)

J. Y. Bang and M. S. Berger, ”Quantum mechanics and the generalized uncertainty principle,” Phys. Rev. D 74(12), 125012 (2006).
[Crossref]

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

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian Quantum States,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

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

2005 (3)

M. Navascués and A. Acín, “SecurityBounds for continuous variables quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).
[Crossref]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

X. F. Mo, B. Zhu, Z. F. Han, Y. Z. Gui, and G. C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30(19), 2632–2634 (2005).
[Crossref] [PubMed]

2003 (1)

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3(7), 535–552 (2003).

2002 (2)

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

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

1982 (1)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature (London) 299(5886), 802–803 (1982).
[Crossref]

Acín, A.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
[Crossref] [PubMed]

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

M. Navascués and A. Acín, “SecurityBounds for continuous variables quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).
[Crossref]

Alleaume, R.

H. Qin, R. Kumar, and R. Alleaume, “Saturation attack on continuous-variable quantum key distribution system,” Proc. SPIE 8899(2), 717–718 (2013).

Andersen, U. L.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

Bang, J. Y.

J. Y. Bang and M. S. Berger, ”Quantum mechanics and the generalized uncertainty principle,” Phys. Rev. D 74(12), 125012 (2006).
[Crossref]

Bennett, C. H.

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

Berger, M. S.

J. Y. Bang and M. S. Berger, ”Quantum mechanics and the generalized uncertainty principle,” Phys. Rev. D 74(12), 125012 (2006).
[Crossref]

Berta, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
[Crossref] [PubMed]

Brassard, G.

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

Braunstein, S. L.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

S. Pirandola, S. L. Braunstein, and S. Lloyd, “Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography,” Phys. Rev. Lett. 101, 200504 (2008).
[Crossref] [PubMed]

Brunner, N.

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

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
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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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Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
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Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
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Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
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Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
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Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
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H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
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H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (2014).
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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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X. F. Mo, B. Zhu, Z. F. Han, Y. Z. Gui, and G. C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30(19), 2632–2634 (2005).
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Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
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Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
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Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
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Y. Guo, Q. Liao, D. Huang, and G. H. Zeng, “Quantum relay schemes for continuous-variable quantum key distribution,” Phys. Rev. A 95, 042326 (2017).
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Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
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D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
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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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Huang, P.

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
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Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
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Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
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P. Huang, J. Fang, and G. H. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
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S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
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X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (2014).
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X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
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X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
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P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
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Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
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P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
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Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
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A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent states,” Phys. Rev. Lett. 114, 070501 (2015).
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A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110, 030502 (2013).
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F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
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A. Leverrier and P. Grangier, “Erratum: Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation [Phys. Rev. Lett. 102, 180504 (2009)],” Phys. Rev. Lett. 106259902 (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]

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

Li, H. S.

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
[Crossref]

Li, H. W.

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
[Crossref]

H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (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]

Li, R. J.

Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
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Li, Z. Y.

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
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Liang, L. M.

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
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X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
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Liao, Q.

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
[Crossref]

Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
[Crossref]

Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
[Crossref]

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
[Crossref]

Y. Guo, Q. Liao, D. Huang, and G. H. Zeng, “Quantum relay schemes for continuous-variable quantum key distribution,” Phys. Rev. A 95, 042326 (2017).
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Lim, C. C.

M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
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Lin, D. K.

D. Huang, P. Huang, D. K. Lin, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Scientific Reports,  6, 19201 (2016).
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Lloyd, S.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (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 (2012).
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S. Pirandola, S. L. Braunstein, and S. Lloyd, “Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography,” Phys. Rev. Lett. 101, 200504 (2008).
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Lo, H. K.

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
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M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
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H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
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C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable security against coherent attacks,” arXiv:1704.07924 (2017).

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Parameter estimation with almost no public communication for continuous-variable quantum key distribution,” arXiv: 1712.00743 (2017).

Ma, X. C.

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
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Massar, S.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
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Mo, X. F.

Moon, S.

Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
[Crossref]

Navascués, M.

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

M. Navascués and A. Acín, “SecurityBounds for continuous variables quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).
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M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, Cambridge University, Cambridge, (2000).

Oh, K.

Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
[Crossref]

Ottaviani, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable security against coherent attacks,” arXiv:1704.07924 (2017).

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Parameter estimation with almost no public communication for continuous-variable quantum key distribution,” arXiv: 1712.00743 (2017).

Papanastasiou, P.

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Parameter estimation with almost no public communication for continuous-variable quantum key distribution,” arXiv: 1712.00743 (2017).

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable security against coherent attacks,” arXiv:1704.07924 (2017).

Pawlowski, M.

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
[Crossref]

Peng, X.

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
[Crossref]

Pezzé, L.

M. Gessner, L. Pezzé, and A. Smerzi, “Efficient entanglement criteria for discrete, continuous, and hybrid variables,” Phys. Rev. A 94(2), 020101 (2016).
[Crossref]

Pirandola, S.

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[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, 621 (2012).
[Crossref]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

S. Pirandola, S. L. Braunstein, and S. Lloyd, “Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography,” Phys. Rev. Lett. 101, 200504 (2008).
[Crossref] [PubMed]

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Parameter estimation with almost no public communication for continuous-variable quantum key distribution,” arXiv: 1712.00743 (2017).

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable security against coherent attacks,” arXiv:1704.07924 (2017).

Pironio, S.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
[Crossref] [PubMed]

Qi, B.

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
[Crossref]

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref] [PubMed]

Qian, L.

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
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Qin, H.

H. Qin, R. Kumar, and R. Alleaume, “Saturation attack on continuous-variable quantum key distribution system,” Proc. SPIE 8899(2), 717–718 (2013).

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, 621 (2012).
[Crossref]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

Renner, R.

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110, 030502 (2013).
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R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102, 110504 (2009).
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Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Scarani, V.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
[Crossref] [PubMed]

Scholz, V. B.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
[Crossref] [PubMed]

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, 621 (2012).
[Crossref]

Sharma, V.

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

Smerzi, A.

M. Gessner, L. Pezzé, and A. Smerzi, “Efficient entanglement criteria for discrete, continuous, and hybrid variables,” Phys. Rev. A 94(2), 020101 (2016).
[Crossref]

Spedalieri, G.

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

Sun, S. H.

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

Symul, T.

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

Takeda, S.

S. Takeda, M. Fuwa, P. van Loock, and A. Furusawa, “Entanglement swapping between discrete and continuous variables,” Phys. Rev. Lett. 114(10), 100501 (2015).
[Crossref] [PubMed]

Tamaki, K.

M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Tomamichel, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
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Tualle-Brouri, R.

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3(7), 535–552 (2003).

van Loock, P.

S. Takeda, M. Fuwa, P. van Loock, and A. Furusawa, “Entanglement swapping between discrete and continuous variables,” Phys. Rev. Lett. 114(10), 100501 (2015).
[Crossref] [PubMed]

Wang, S.

H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (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]

Wang, T.

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
[Crossref]

Wang, Y.

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
[Crossref]

Weedbrook, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[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]

C. Weedbrook, “Continuous-variable quantum key distribution with entanglement in the middle,” Phys. Rev. A 87, 022308 (2013).
[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, 621 (2012).
[Crossref]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

Wenger, J.

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3(7), 535–552 (2003).

Werner, R. F.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).
[Crossref] [PubMed]

Wolf, M. M.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian Quantum States,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

Woo, M.

Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
[Crossref]

Wootters, W. K.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature (London) 299(5886), 802–803 (1982).
[Crossref]

Xie, C. L.

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
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Xu, F. H.

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
[Crossref]

M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
[Crossref]

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
[Crossref]

Yin, Z. Q.

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
[Crossref]

H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (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]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Zeng, G. H.

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
[Crossref]

Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
[Crossref]

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
[Crossref]

Y. Guo, Q. Liao, D. Huang, and G. H. Zeng, “Quantum relay schemes for continuous-variable quantum key distribution,” Phys. Rev. A 95, 042326 (2017).
[Crossref]

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
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D. Huang, P. Huang, D. K. Lin, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Scientific Reports,  6, 19201 (2016).
[Crossref] [PubMed]

P. Huang, J. Fang, and G. H. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

Zhang, Y. C.

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
[Crossref]

Zhou, J.

Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
[Crossref]

Zhou, Y. M.

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
[Crossref]

Zhu, B.

Zurek, W. H.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature (London) 299(5886), 802–803 (1982).
[Crossref]

Nat. Commun. (1)

M. Curty, F. H. Xu, W. Cui, C. C. Lim, K. Tamaki, and H. K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5(4), 643–648 (2014).
[Crossref]

Nat. Photon. (2)

F. H. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photon. 9(12), 772 (2015).
[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photon. 9, 397 (2015).
[Crossref]

Nature (London) (1)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature (London) 299(5886), 802–803 (1982).
[Crossref]

New J. Phys. (1)

Q. Liao, Y. Guo, D. Huang, P. Huang, and G. H. Zeng, “Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection,” New J. Phys. 20(2), 023015 (2018).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

Y. Guo, R. J. Li, Q. Liao, J. Zhou, and D. Huang, “Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier,” Phys. Lett. A 382(6), 372–381 (2018).
[Crossref]

Phys. Rev. A (17)

Y. Choi, O. Kwon, M. Woo, K. Oh, S. W. Han, Y. S. Kim, and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93, 032319 (2016).
[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]

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. H. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95, 032304 (2017).
[Crossref]

C. Weedbrook, “Continuous-variable quantum key distribution with entanglement in the middle,” Phys. Rev. A 87, 022308 (2013).
[Crossref]

M. Gessner, L. Pezzé, and A. Smerzi, “Efficient entanglement criteria for discrete, continuous, and hybrid variables,” Phys. Rev. A 94(2), 020101 (2016).
[Crossref]

P. Huang, J. Fang, and G. H. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

X. C. Ma, S. H. Sun, M. S. Jiang, M. Gui, and L. M. Liang, “Gaussian-modulated coherent-state measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 042335 (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]

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

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

X. C. Ma, S. H. Sun, M. S. Jiang, and L. M. Liang, “Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems,” Phys. Rev. A 88, 022339 (2013).
[Crossref]

Z. Y. Li, Y. C. Zhang, F. H. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
[Crossref]

C. Ottaviani, G. Spedalieri, S. L. Braunstein, and S. Pirandola, “Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration,” Phys. Rev. A 91, 022320 (2015).
[Crossref]

Y. Guo, Q. Liao, D. Huang, and G. H. Zeng, “Quantum relay schemes for continuous-variable quantum key distribution,” Phys. Rev. A 95, 042326 (2017).
[Crossref]

H. W. Li, Z. Q. Yin, M. Pawlowski, G. C. Guo, and Z. F. Han, “Detection efficiency and noise in a semi-device-independent randomness-extraction protocol,” Phys. Rev. A 91, 032305 (2015).
[Crossref]

H. W. Li, Z. Q. Yin, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, “Quantum key distribution based on quantum dimension and independent devices,” Phys. Rev. A 89, 032302 (2014).
[Crossref]

D. Huang, P. Huang, T. Wang, H. S. Li, Y. M. Zhou, and G. H. Zeng, “Continuous-variable quantum key distribution based on a plug-and-play dual-phase-modulated coherent-states protocol,” Phys. Rev. A 94, 032305 (2016).
[Crossref]

Phys. Rev. D (1)

J. Y. Bang and M. S. Berger, ”Quantum mechanics and the generalized uncertainty principle,” Phys. Rev. D 74(12), 125012 (2006).
[Crossref]

Phys. Rev. Lett. (17)

S. Takeda, M. Fuwa, P. van Loock, and A. Furusawa, “Entanglement swapping between discrete and continuous variables,” Phys. Rev. Lett. 114(10), 100501 (2015).
[Crossref] [PubMed]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[Crossref] [PubMed]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref] [PubMed]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
[Crossref] [PubMed]

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

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

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

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian Quantum States,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

M. Navascués and A. Acín, “SecurityBounds for continuous variables quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).
[Crossref]

S. Pirandola, S. L. Braunstein, and S. Lloyd, “Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography,” Phys. Rev. Lett. 101, 200504 (2008).
[Crossref] [PubMed]

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Proc. SPIE (1)

H. Qin, R. Kumar, and R. Alleaume, “Saturation attack on continuous-variable quantum key distribution system,” Proc. SPIE 8899(2), 717–718 (2013).

Quantum Inf Process (1)

Q. Liao, Y. Guo, C. L. Xie, D. Huang, P. Huang, and G. H. Zeng, “Composable security of unidimensional continuous-variable quantum key distribution,” Quantum Inf Process,  17, 113 (2018).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Schematic diagrams of (a) traditional MDI-CVQKD protocol. Alice and Bob prepare coherent states independently, and send them to Charlie for Bell state measurement. (b) PP MDI-CVQKD protocol. Charlie initially launches pulses to Alice and Bob, and then Alice and Bob reflect back the pulses to Charlie after Gaussian modulation. (c) PP DPM-based MDI-CVQKD protocol. Charlie still initially launches pulses to Alice and Bob, Alice and Bob respectively use dual-phase-modulation strategy to encode the information and subsequently send the pulses back to Charlie. AM, Amplitude modulator; PM, Phase modulator; FM, Faraday mirror; BS, Beam splitter; BSM, Bell state measurement.
Fig. 2
Fig. 2 Entanglement-based model of MDI-CVQKD protocol with entangling cloner attacks. Alice and Bob respectively generate EPR pairs and send them to the third party Charlie through the untrusted quantum channel. Charlie measures the incoming modes using BSM and subsequently sends the measurement result back to Alice and Bob. ε is excess noise and η is the transmittance of the quantum channel.
Fig. 3
Fig. 3 Entanglement-based model of PP DPM-based MDI-CVQKD protocol with entangling cloner attacks. Charlie prepares two EPR pairs and sends one mode of each to Alice and Bob through the untrusted quantum channel, respectively. Alice and Bob displace the incoming modes according to the public BSM result and subsequently measure them with respective heterodyne detections.
Fig. 4
Fig. 4 The performance of MDI-CVQKD protocols. Blue solid line and red dashed line denote the asymptotic secret key rate and the tolerable excess noise of the proposed PP DPM-based MDI-CVQKD protocol as a function of transmission distance from Alice to Bob, respectively. As a comparison, blue dotted line denotes the asymptotic secret key rate of traditional MDI-CVQKD protocol in [27]. The simulation parameters are set as follows: modulation variance is V = 20, reconciliation efficiency is β = 95% and excess noise for blue solid line is ε = 0.001.
Fig. 5
Fig. 5 Finite-size secret key rate of the proposed PP DPM-based MDI-CVQKD protocol as a function of transmission distance. Solid lines show the secret key rate generated from almost all raw keys (N = n), dashed lines show the secret key rate using conventional finite-size calculation (N = 2n). From left to right, both lines correspond to block lengths of N = 104, 105, 106, 107 and 108. The parameters are set as same as Fig. 4.
Fig. 6
Fig. 6 Experimental concept of the PP DPM-based MDI-CVQKD protocol. CW, Continuous-wave laser; BS, Beam splitter; PM, Phase modulator; PBS, Polarizing beam splitter; DL, Delay line; FM, Faraday mirror; PD, Photoelectric detector; BSM, Bell state measurement.

Equations (25)

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x A = x A k x A ( γ ) , p A = p A k p A ( γ ) , x B = x B k x B ( γ ) , p B = p B k p B ( γ ) .
J FM = [ cos θ sin θ sin θ cos θ ] [ 1 0 0 1 ] [ cos θ sin θ sin θ cos θ ] = [ cos ( 2 θ ) sin ( 2 θ ) sin ( 2 θ ) cos ( 2 θ ) ] .
R = T ( δ ) J FM T ( δ ) = e i ( φ o + φ e ) J FM ,
T ( ± δ ) = [ cos δ sin δ ± sin δ cos δ ] [ e i φ o 0 0 e i φ e ] [ cos δ ± sin δ sin δ cos δ ] .
J PM A 1 + FM A 1 = T ( δ ) J PM A 1 x R J PM A 1 y T ( δ ) = ς A 1 e i ( φ A 1 ) R ,
J PM A 2 + FM A 2 = T ( δ ) J PM A 2 x R J PM A 2 y T ( δ ) = ς A 2 e i ( φ A 2 ) R ,
Alice out = 1 2 Alice in ( J PM A 1 + FM A 1 + J PM A 2 + FM A 2 ) = 1 2 ( ς A 1 Alice in e i ( φ A 1 ) + ς A 2 Alice in e i ( φ A 2 ) ) R .
Alice out = ς Alice in exp [ i ( φ A 1 + φ A 2 ) 2 ] cos ( φ A 1 φ A 2 2 ) R .
Bob out = ς Bob in exp [ i ( φ B 1 + φ B 2 ) 2 ] cos ( φ B 1 φ B 2 2 ) R .
ρ A 2 E 1 B 2 E 2 = a , b [ P ( a ) | a a | ψ A 2 E 1 a P ( b ) | b b | ψ B 2 E 2 b ] n .
K asym = β I ( A : B ) χ E ,
Γ A B G = [ a 𝕀 c σ z c σ z b 𝕀 ] = [ [ T 1 V + ( 1 T 1 ) W 1 ] 𝕀 T 1 T 2 ( V 2 1 ) σ 2 T 1 T 2 ( V 2 1 ) σ 2 [ T 2 V + ( 1 T 2 ) W 2 ] 𝕀 ] ,
I ( A : B ) = log 2 [ b + 1 b + 1 c 2 / ( a + 1 ) ] .
χ E = S ( E ) S ( E | A ) .
S ( A B ) = G [ ( λ 1 1 ) / 2 ] + G [ ( λ 2 1 ) / 2 ] ,
λ 1 , 2 2 = 1 2 [ Δ ± Δ 2 4 D 2 ] ,
Γ X Y Z = [ X 0 c X Z 0 Y c Y Z c X Z T c Y Z T Z ] ,
Z = [ x Z 2 x Z p Z x Z p Z p Z 2 ] ,
c X Z = [ x A x Z x A p Z p A x Z p A x Z ] , c Y Z = [ x B x z x B p Z p B x Z p B A x Z ]
K fini = n N [ β I ( A : B ) S PE Δ ( n ) ] ,
Δ ( n ) = ( 2 dim + 3 ) log 2 ( 2 / ¯ ) n + 2 n log 2 ( 1 / P A ) ,
Γ PE = ( V 𝕀 t Z σ z t Z σ z ( t 2 V + σ 2 ) 𝕀 ) ,
t ^ ~ ( t , σ 2 i = 1 m x i 2 ) and m σ ^ 2 σ 2 ~ χ 2 ( m 1 ) ,
t min = η z PE / 2 1 + η ε m X , σ max 2 = 1 + η ε + z PE / 2 2 ( 1 + η ε ) m ,
erf ( x ) = 2 π 0 x e t 2 d t .

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