Abstract

Here, we investigate the security of the practical one-way CVQKD and CV-MDI-QKD systems under laser seeding attack. In particular, Eve can inject a suitable light into the laser diodes of the light source modules in the two kinds of practical CVQKD systems, which results in the increased intensity of the generated optical signal. The parameter estimation under laser seeding attack shows that the secret key rates of these two schemes may be overestimated, which indicates that this attack can open a security loophole for Eve to successfully obtain information about secret key in these practical CVQKD systems. To close this loophole, we propose a real-time monitoring scheme to precisely evaluate the secret key rates of these schemes. The analysis results indicate the implementation of the proposed monitoring scheme can effectively resist this potential attack.

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

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References

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2019 (4)

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

H.-X. Ma, P. Huang, D.-Y. Bai, T. Wang, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation,” Phys. Rev. A 99, 022322 (2019).
[Crossref]

P. Wang, X. Wang, and Y. Li, “Continuous-variable measurement-device-independent quantum key distribution using modulated squeezed states and optical amplifiers,” Phys. Rev. A 99, 042309 (2019).
[Crossref]

Y. Zheng, P. Huang, A. Huang, J. Peng, and G. Zeng, “Practical security of continuous-variable quantum key distribution with reduced optical attenuation,” Phys. Rev. A 100, 012313 (2019).
[Crossref]

2018 (9)

H.-X. Ma, P. Huang, D.-Y. Bai, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Continuous-variable measurement-device-independent quantum key distribution with photon subtraction,” Phys. Rev. A 97, 042329 (2018).
[Crossref]

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks,” Phys. Rev. A 97, 052327 (2018).
[Crossref]

Z. Chen, Y. Zhang, G. Wang, Z. Li, and H. Guo, “Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks,” Phys. Rev. A 98, 012314 (2018).
[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]

T. Wang, P. Huang, Y. Zhou, W. Liu, H. Ma, S. Wang, and G. Zeng, “High key rate continuous-variable quantum key distribution with a real local oscillator,” Opt. Express 26, 2794–2806 (2018).
[Crossref] [PubMed]

W. Liu, P. Huang, J. Peng, J. Fan, and G. Zeng, “Integrating machine learning to achieve an automatic parameter prediction for practical continuous-variable quantum key distribution,” Phys. Rev. A 97, 022316 (2018).
[Crossref]

H. Qin, R. Kumar, V. Makarov, and R. Alléaume, “Homodyne-detector-blinding attack in continuous-variable quantum key distribution,” Phys. Rev. A 98, 012312 (2018).
[Crossref]

C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
[Crossref]

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
[Crossref]

2017 (4)

W. Liu, X. Wang, N. Wang, S. Du, and Y. Li, “Imperfect state preparation in continuous-variable quantum key distribution,” Phys. Rev. A 96, 042312 (2017).
[Crossref]

W. Liu, J. Peng, P. Huang, D. Huang, and G. Zeng, “Monitoring of continuous-variable quantum key distribution system in real environment,” Opt. Express 25, 19429–19443 (2017).
[Crossref] [PubMed]

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

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

2016 (4)

V. Makarov, J.-P. Bourgoin, P. Chaiwongkhot, M. Gagné, T. Jennewein, S. Kaiser, R. Kashyap, M. Legré, C. Minshull, and S. Sajeed, “Creation of backdoors in quantum communications via laser damage,” Phys. Rev. A 94, 030302 (2016).
[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]

C. Wang, P. Huang, D. Huang, D. Lin, and G. Zeng, “Practical security of continuous-variable quantum key distribution with finite sampling bandwidth effects,” Phys. Rev. A 93, 022315 (2016).
[Crossref]

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

2015 (7)

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

P. Huang, D.-k. Lin, D. Huang, and G.-H. Zeng, “Security of continuous-variable quantum key distribution with imperfect phase compensation,” Int. J. Theor. Phys. 54, 2613–2622 (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).

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).

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] [PubMed]

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, 397–402 (2015).
[Crossref]

S.-H. Sun, F. Xu, M.-S. Jiang, X.-C. Ma, H.-K. Lo, and L.-M. Liang, “Effect of source tampering in the security of quantum cryptography,” Phys. Rev. A 92, 022304 (2015).
[Crossref]

2014 (5)

Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution using squeezed states,” Phys. Rev. A 90, 052325 (2014).
[Crossref]

A. N. Bugge, S. Sauge, A. M. M. Ghazali, J. Skaar, L. Lydersen, and V. Makarov, “Laser damage helps the eavesdropper in quantum cryptography,” Phys. Rev. Lett. 112, 070503 (2014).
[Crossref] [PubMed]

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]

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

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

2013 (6)

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

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]

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]

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]

2012 (3)

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]

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

J. Yang, B. Xu, and H. Guo, “Source monitoring for continuous-variable quantum key distribution,” Phys. Rev. A 86, 042314 (2012).
[Crossref]

2011 (1)

Y. Shen, X. Peng, J. Yang, and H. Guo, “Continuous-variable quantum key distribution with gaussian source noise,” Phys. Rev. A 83, 052304 (2011).
[Crossref]

2010 (2)

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

V. C. Usenko and R. Filip, “Feasibility of continuous-variable quantum key distribution with noisy coherent states,” Phys. Rev. A 81, 022318 (2010).
[Crossref]

2009 (2)

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

2008 (1)

R. Filip, “Continuous-variable quantum key distribution with noisy coherent states,” Phys. Rev. A 77, 022310 (2008).
[Crossref]

2007 (2)

B. Qi, L.-L. Huang, L. Qian, and H.-K. Lo, “Experimental study on the gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76, 052323 (2007).
[Crossref]

J. Lodewyck, T. Debuisschert, R. García-Patrón, R. Tualle-Brouri, N. J. Cerf, and P. Grangier, “Experimental Implementation of Non-Gaussian Attacks on a Continuous-Variable Quantum-Key-Distribution System,” Phys. Rev. Lett. 98, 030503 (2007).
[Crossref] [PubMed]

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] [PubMed]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

2000 (1)

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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).
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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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V. Makarov, J.-P. Bourgoin, P. Chaiwongkhot, M. Gagné, T. Jennewein, S. Kaiser, R. Kashyap, M. Legré, C. Minshull, and S. Sajeed, “Creation of backdoors in quantum communications via laser damage,” Phys. Rev. A 94, 030302 (2016).
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H.-K. Lo and H. F. Chau, “Unconditional Security of Quantum Key Distribution over Arbitrarily Long Distances,” Science 283, 2050–2056 (1999).
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J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (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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Z. Chen, Y. Zhang, G. Wang, Z. Li, and H. Guo, “Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks,” Phys. Rev. A 98, 012314 (2018).
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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).

Curty, M.

A. Huang, Á. Navarrete, S.-H. Sun, P. Chaiwongkhot, M. Curty, and V. Makarov, “Laser seeding attack in quantum key distribution,” arXiv preprint arXiv:1902.09792 [quant-ph] (2019).

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S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
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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).
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P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photon. 7, 378–381 (2013).
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P. Jouguet, S. Kunz-Jacques, E. Diamanti, and A. Leverrier, “Analysis of imperfections in practical continuous-variable quantum key distribution,” Phys. Rev. A 86, 032309 (2012).
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S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
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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).
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W. Liu, X. Wang, N. Wang, S. Du, and Y. Li, “Imperfect state preparation in continuous-variable quantum key distribution,” Phys. Rev. A 96, 042312 (2017).
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A. Huang, R. Li, V. Egorov, S. Tchouragoulov, K. Kumar, and V. Makarov, “Laser damage attack against optical attenuators in quantum key distribution,” arXiv preprint arXiv:1905.10795 [quant-ph] (2019).

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A. K. Ekert, “Quantum Cryptography Based on Bell’s Theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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W. Liu, P. Huang, J. Peng, J. Fan, and G. Zeng, “Integrating machine learning to achieve an automatic parameter prediction for practical continuous-variable quantum key distribution,” Phys. Rev. A 97, 022316 (2018).
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V. Makarov, J.-P. Bourgoin, P. Chaiwongkhot, M. Gagné, T. Jennewein, S. Kaiser, R. Kashyap, M. Legré, C. Minshull, and S. Sajeed, “Creation of backdoors in quantum communications via laser damage,” Phys. Rev. A 94, 030302 (2016).
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X.-L. Pang, A.-L. Yang, C.-N. Zhang, J.-P. Dou, H. Li, J. Gao, and X.-M. Jin, “Hacking measurement-device-independent quantum key distribution via injection locking,” arXiv preprint arXiv:1902.10423 [quant-ph] (2019).

Gao, X.

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
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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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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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J. Lodewyck, T. Debuisschert, R. García-Patrón, R. Tualle-Brouri, N. J. Cerf, and P. Grangier, “Experimental Implementation of Non-Gaussian Attacks on a Continuous-Variable Quantum-Key-Distribution System,” Phys. Rev. Lett. 98, 030503 (2007).
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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, 397–402 (2015).
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A. N. Bugge, S. Sauge, A. M. M. Ghazali, J. Skaar, L. Lydersen, and V. Makarov, “Laser damage helps the eavesdropper in quantum cryptography,” Phys. Rev. Lett. 112, 070503 (2014).
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P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photon. 7, 378–381 (2013).
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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, 062343 (2010).
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S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
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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).
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J. Lodewyck, T. Debuisschert, R. García-Patrón, R. Tualle-Brouri, N. J. Cerf, and P. Grangier, “Experimental Implementation of Non-Gaussian Attacks on a Continuous-Variable Quantum-Key-Distribution System,” Phys. Rev. Lett. 98, 030503 (2007).
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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).
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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).

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).
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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).
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Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution using squeezed states,” Phys. Rev. A 90, 052325 (2014).
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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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J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (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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Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
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Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
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Z. Chen, Y. Zhang, G. Wang, Z. Li, and H. Guo, “Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks,” Phys. Rev. A 98, 012314 (2018).
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X. Zhang, Y. Zhang, Y. Zhao, X. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 96, 042334 (2017).
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C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
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J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (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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Y. Zheng, P. Huang, A. Huang, J. Peng, and G. Zeng, “Practical security of continuous-variable quantum key distribution with reduced optical attenuation,” Phys. Rev. A 100, 012313 (2019).
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A. Huang, R. Li, V. Egorov, S. Tchouragoulov, K. Kumar, and V. Makarov, “Laser damage attack against optical attenuators in quantum key distribution,” arXiv preprint arXiv:1905.10795 [quant-ph] (2019).

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A. Huang, Á. Navarrete, S.-H. Sun, P. Chaiwongkhot, M. Curty, and V. Makarov, “Laser seeding attack in quantum key distribution,” arXiv preprint arXiv:1902.09792 [quant-ph] (2019).

Huang, D.

C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
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D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41, 3511–3514 (2016).
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C. Wang, P. Huang, D. Huang, D. Lin, and G. Zeng, “Practical security of continuous-variable quantum key distribution with finite sampling bandwidth effects,” Phys. Rev. A 93, 022315 (2016).
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P. Huang, D.-k. Lin, D. Huang, and G.-H. Zeng, “Security of continuous-variable quantum key distribution with imperfect phase compensation,” Int. J. Theor. Phys. 54, 2613–2622 (2015).
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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).
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J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (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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H.-X. Ma, P. Huang, D.-Y. Bai, T. Wang, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation,” Phys. Rev. A 99, 022322 (2019).
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Y. Zheng, P. Huang, A. Huang, J. Peng, and G. Zeng, “Practical security of continuous-variable quantum key distribution with reduced optical attenuation,” Phys. Rev. A 100, 012313 (2019).
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W. Liu, P. Huang, J. Peng, J. Fan, and G. Zeng, “Integrating machine learning to achieve an automatic parameter prediction for practical continuous-variable quantum key distribution,” Phys. Rev. A 97, 022316 (2018).
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H.-X. Ma, P. Huang, D.-Y. Bai, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Continuous-variable measurement-device-independent quantum key distribution with photon subtraction,” Phys. Rev. A 97, 042329 (2018).
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D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41, 3511–3514 (2016).
[Crossref] [PubMed]

C. Wang, P. Huang, D. Huang, D. Lin, and G. Zeng, “Practical security of continuous-variable quantum key distribution with finite sampling bandwidth effects,” Phys. Rev. A 93, 022315 (2016).
[Crossref]

P. Huang, D.-k. Lin, D. Huang, and G.-H. Zeng, “Security of continuous-variable quantum key distribution with imperfect phase compensation,” Int. J. Theor. Phys. 54, 2613–2622 (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).
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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. 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).
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C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
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Xu, B.

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
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S.-H. Sun, F. Xu, M.-S. Jiang, X.-C. Ma, H.-K. Lo, and L.-M. Liang, “Effect of source tampering in the security of quantum cryptography,” Phys. Rev. A 92, 022304 (2015).
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Z. Li, Y.-C. Zhang, F. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89, 052301 (2014).
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X.-L. Pang, A.-L. Yang, C.-N. Zhang, J.-P. Dou, H. Li, J. Gao, and X.-M. Jin, “Hacking measurement-device-independent quantum key distribution via injection locking,” arXiv preprint arXiv:1902.10423 [quant-ph] (2019).

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J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (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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Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
[Crossref]

X. Zhang, Y. Zhang, Y. Zhao, X. Wang, S. Yu, and H. Guo, “Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 96, 042334 (2017).
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Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution using squeezed states,” Phys. Rev. A 90, 052325 (2014).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

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Y. Zheng, P. Huang, A. Huang, J. Peng, and G. Zeng, “Practical security of continuous-variable quantum key distribution with reduced optical attenuation,” Phys. Rev. A 100, 012313 (2019).
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C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
[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]

T. Wang, P. Huang, Y. Zhou, W. Liu, H. Ma, S. Wang, and G. Zeng, “High key rate continuous-variable quantum key distribution with a real local oscillator,” Opt. Express 26, 2794–2806 (2018).
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W. Liu, J. Peng, P. Huang, D. Huang, and G. Zeng, “Monitoring of continuous-variable quantum key distribution system in real environment,” Opt. Express 25, 19429–19443 (2017).
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D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41, 3511–3514 (2016).
[Crossref] [PubMed]

C. Wang, P. Huang, D. Huang, D. Lin, and G. Zeng, “Practical security of continuous-variable quantum key distribution with finite sampling bandwidth effects,” Phys. Rev. A 93, 022315 (2016).
[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] [PubMed]

Zeng, G.-H.

H.-X. Ma, P. Huang, D.-Y. Bai, T. Wang, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation,” Phys. Rev. A 99, 022322 (2019).
[Crossref]

H.-X. Ma, P. Huang, D.-Y. Bai, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Continuous-variable measurement-device-independent quantum key distribution with photon subtraction,” Phys. Rev. A 97, 042329 (2018).
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P. Huang, D.-k. Lin, D. Huang, and G.-H. Zeng, “Security of continuous-variable quantum key distribution with imperfect phase compensation,” Int. J. Theor. Phys. 54, 2613–2622 (2015).
[Crossref]

Zhang, C.-N.

X.-L. Pang, A.-L. Yang, C.-N. Zhang, J.-P. Dou, H. Li, J. Gao, and X.-M. Jin, “Hacking measurement-device-independent quantum key distribution via injection locking,” arXiv preprint arXiv:1902.10423 [quant-ph] (2019).

Zhang, L.

C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
[Crossref]

Zhang, X.

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

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

Zhang, Y.

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
[Crossref]

Z. Chen, Y. Zhang, G. Wang, Z. Li, and H. Guo, “Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks,” Phys. Rev. A 98, 012314 (2018).
[Crossref]

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

Zhang, Y.-C.

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

Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution using squeezed states,” Phys. Rev. A 90, 052325 (2014).
[Crossref]

Zhao, W.

C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
[Crossref]

Zhao, Y.

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
[Crossref]

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

Zheng, Y.

Y. Zheng, P. Huang, A. Huang, J. Peng, and G. Zeng, “Practical security of continuous-variable quantum key distribution with reduced optical attenuation,” Phys. Rev. A 100, 012313 (2019).
[Crossref]

Zheng, Z.

Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50 km commercial fiber,”Quantum Sci. Technol. 4, 035006 (2019).
[Crossref]

Zhou, Y.

Int. J. Theor. Phys. (1)

P. Huang, D.-k. Lin, D. Huang, and G.-H. Zeng, “Security of continuous-variable quantum key distribution with imperfect phase compensation,” Int. J. Theor. Phys. 54, 2613–2622 (2015).
[Crossref]

J. Phys. B (2)

Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2018).
[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]

Nat. Photon. (2)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photon. 7, 378–381 (2013).
[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, 397–402 (2015).
[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] [PubMed]

New J. Phys. (1)

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

C. Xie, Y. Guo, Q. Liao, W. Zhao, D. Huang, L. Zhang, and G. Zeng, “Practical security analysis of continuous-variable quantum key distribution with jitter in clock synchronization,” Phys. Lett. A 382, 811–817 (2018).
[Crossref]

Phys. Rev. A (31)

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

W. Liu, X. Wang, N. Wang, S. Du, and Y. Li, “Imperfect state preparation in continuous-variable quantum key distribution,” Phys. Rev. A 96, 042312 (2017).
[Crossref]

R. Filip, “Continuous-variable quantum key distribution with noisy coherent states,” Phys. Rev. A 77, 022310 (2008).
[Crossref]

V. C. Usenko and R. Filip, “Feasibility of continuous-variable quantum key distribution with noisy coherent states,” Phys. Rev. A 81, 022318 (2010).
[Crossref]

Y. Shen, X. Peng, J. Yang, and H. Guo, “Continuous-variable quantum key distribution with gaussian source noise,” Phys. Rev. A 83, 052304 (2011).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 The schematic diagram of the laser seeding attack. CD Circuit, current driver circuit; CW Laser, continuous-wave laser; LD, laser diode; PC, polarization controller; P(t), the power of the optical signal emitted by a laser diode without the laser seeding attack; (t), the power of the optical signal emitted by a laser diode with the attack; A, the generated signal without the attack; , the generated signal with attack; I, the intensity of the pulse signal generated by the light source module without the attack; , the intensity of the pulse signal generated by the light source module with the attack.
Fig. 2
Fig. 2 The expression of the transmitted Gaussian-modulated coherent states in the phase space under the lase seeding attack.
Fig. 3
Fig. 3 Secret key rate vs transmission distance under different powers g of the laser seeding attack when ε = 0.01, 0.05, respectively. Solid curves from top to bottom represent the relations between the evaluated secret key rate Ke and the transmission distance. Dotted curves show the corresponding practical secret key rate Kp vs transmission distance under different situations. The fiber loss is 0.2 dB/km.
Fig. 4
Fig. 4 EB scheme of the CV-MDI-QKD protocols. EPR, two-mode squeezed state; Het, heterodyne detection; Hom, homodyne detection; D(β), displacement operation.
Fig. 5
Fig. 5 Secret key rate as a function of the transmission distance from Alice to Bob for different excess noise in the symmetric case, where LAC = LBC. Solid curves from top to bottom represent the relations between the evaluated secret key rate Km,e and the transmission distance when εAC = εBC = 0.01, 0.05. Dotted curves show the corresponding practical secret key rate Km,p versus transmission distance. The fiber loss is 0.2 dB/km.
Fig. 6
Fig. 6 Secret key rate vs the transmission distance from Alice to Bob for different excess noise environments in the extreme asymmetric case, where LBC = 0. Solid curves from top to bottom represent the relations between the evaluated secret key rate Km,e and the transmission distance when εAC = εBC = 0.01,0.05. Dotted curves show the corresponding practical secret key rate K m , p versus transmission distance.
Fig. 7
Fig. 7 The structure of the real-time monitoring scheme against the laser seeding attack in Alice’s apparatus for the one-way CVQKD stsyems. AM, amplitude modulator; PM, phase modulator; BS, beam splitter; PBS, polarizing beam splitter; FM, faraday mirror; DL, delay line; LO, local oscillator; VOA, variable optical attenuator; PD, photodiode.

Equations (21)

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I = μ 0 T P ( t ) d t ,
| α A 0 = | α A 0 | e i θ = x A 0 + i p A 0 , x A 0 = | α A 0 | cos θ , p A 0 = | α A 0 | sin θ ,
x A 0 = g x A 0 , p A 0 = g p A 0 , V A 0 = g V A 0 ,
x A 0 = t A C x A 0 + z A C , p A 0 = t A C p A 0 + z A C , x B 0 = t B C x B 0 + z B C , p B 0 = t B C p B 0 + z B C ,
x A 0 2 = p A 0 2 = V x A 0 = V p A 0 , x B 0 2 = p B 0 2 = V x B 0 = V p B 0 , x C 2 = p D 2 = 1 2 η ( T A C V x A 0 + T B C V x B 0 ) + N 0 + V e l + 1 2 η ( T A C ξ A C + T B C ξ B C ) , x A 0 x C = η T A C 2 V x A 0 , p B 0 p D = η T B C 2 V p B 0 , x C x D = p C p D = 1 2 η ( T A C V x A 0 T B C V x B 0 ) + 1 2 η ( T A C ξ A C T B C ξ B C ) .
x C 2 + x C x D = η T A C V x A 0 + η T A C ξ A C + N 0 + V e l , p D 2 p C p D = η T B C V x B 0 + η T B C ξ B C + N 0 + V e l .
T A C = 2 x A 0 x C 2 η x A 0 2 2 , T B C = 2 p B 0 p D 2 η p B 0 2 2 , ε A C = x C 2 + x C x D N 0 ν e l N 0 2 ( x A 0 x C / x A 0 2 ) 2 N 0 x A 0 2 N 0 , ε B C = p D 2 p C p D N 0 ν e l N 0 2 ( p B 0 p D / p B 0 2 ) 2 N 0 p B 0 2 N 0 .
x A 0 = g x A 0 , p A 0 = g p A 0 , x B 0 = g x B 0 , p B 0 = g p B 0 , x C = g x C , p C = g p C , x D = g x D , p D = g p D .
T A C = 2 x A 0 x C 2 η x A 0 2 2 = g T A C , T B C = 2 p B 0 p D 2 η p B 0 2 2 = g T B C , ε A C = ( x C ) 2 + x C x D N 0 ν e l N 0 2 ( x A 0 x C / x A 0 2 ) 2 N 0 x A 0 2 N 0 = ε A C g , ε B C = ( p D ) 2 p C p D N 0 ν e l N 0 2 ( p B 0 p D / p B 0 2 ) 2 N 0 p B 0 2 N 0 = ε B C g .
ξ P I R , A C = ξ t , A C + 2 u N 0 ,
ε P I R , A C = ε t , A C + 2 u .
ε P I R , A C = ε t , A C + 0.2 g .
I A B h e t = 2 × 1 2 log 2 V B m h e t V B m | A m h e t = log 2 T m ( V A + 1 + χ line , m ) + 1 T m ( 1 + χ line , m ) + 1 ,
Γ A B m = [ ( V A + 1 ) I T m [ ( V A + 1 ) 2 1 ] σ Z T m [ ( V A + 1 ) 2 1 ] σ Z ( T m V A + 1 + T m ε m ) I ] ,
T m = T A C 2 k 2 , ε m = 1 + 1 T A C [ 2 + T B C ( ε B C 2 ) + T A C ( ε B C 1 ) ] + 1 T A C ( 2 k V B T B C V B + 2 ) 2 .
ε m = T B C T A C ( ε B C 2 ) + ε A C + 2 T A C .
χ B E = G ( λ m , 1 1 2 ) + G ( λ m , 2 1 2 ) G ( λ m , 3 1 2 ) .
λ m , 1 , 2 2 = 1 2 ( A m ± A m 2 4 B m ) , λ m , 3 = ( T m ε m + 2 ) ( V A + 1 ) T m V A T m ( ε m + V A ) + 2 ,
A m = ( V A + 1 ) 2 2 T m ( V A 2 + 2 V A ) + ( T m V A + T m ε m + 1 ) 2 , B m = [ ( T m ε m + 1 ) ( V A + 1 ) T m V A ] 2 .
K m = β I A B h e t χ B E .
V A = g V A , V B = g V B , T m = g T A C V B T B C ( g V B + 2 ) , ε m = T B C T A C ( ε B C g 2 ) + ε A C g + 2 g T A C .

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