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In a practical quantum communication system, the security of signal source of continuous-variable quantum key distribution may be jeopardized due to device flaws and hidden attacks. In this paper, an improved scheme for Gaussian-modulated continuous-variable quantum key distribution based on an untrusted entangled source is proposed. In particular, the entanglement source is placed in an untrusted quantum channel to simulate that it is controlled by an eavesdropper, thereby verifying the security of Gaussian-modulated continuous-variable quantum key distribution in a complex environment. This work in detail analyzes the influence of untrusted entanglement source on practical Gaussian-modulated continuous-variable quantum key distribution system, and the numerical simulation shows that the performance of Gaussian-modulated continuous-variable quantum key distribution will dramatically decrease once the entanglement source has moved out of the sender, and it will slightly rise as the untrusted entanglement source slowly moves away from the sender. This paper further introduces two kinds of optical amplifiers, which are phase-sensitive amplifier and phase-insensitive amplifier, to compensate for the imperfection of the coherent detector. These amplifiers are beneficial to enhancing the quantum efficiency of the receiver’s detector. Specifically, the security key rate of Gaussian-modulated continuous-variable quantum key distribution with homodyne detection can be well improved by phase-sensitive amplifier, and the security key rate of Gaussian-modulated continuous-variable quantum key distribution with heterodyne detection can be well improved by phase-insensitive amplifier. To summary, this paper proposes a scheme for Gaussian-modulated continuous-variable quantum key distribution with untrusted entanglement source, experimental results show that the proposed scheme can generate secure quantum keys even if the Gaussian entanglement source is untrusted, and the two optical amplifiers can effectively improve the quantum efficiency of the detector at the receiver. This work aims to promote the practical process of the Gaussian-modulated continuous-variable quantum key distribution system and provide theoretical guidance for the practical implementation and application of the Gaussian-modulated continuous-variable quantum key distribution system.
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Keywords:
- continuous-variable quantum key distribution /
- untrusted entanglement source /
- optical amplifier /
- quantum communication
[1] Zhou N R, Li J F, Yu Z B, Gong L H, Farouk A 2016 Quantum Inf. Process 16 4
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图 1 基于不可信纠缠源的GMCVQKD的方案图
Figure 1. Scheme diagram of the GMCVQKD based on untrusted entanglement source.
图 2 纠缠源可信的GMCVQKD的方案图
Figure 2. Scheme diagram of the GMCVQKD with trusted entanglement source.
图 3 零差探测下不可信纠缠源的GMCVQKD方案的与原始GMCVQKD方案的性能对比 (a) 两种方案的安全密钥率与传输距离的关系; (b)两种方案的互信量与传输距离的关系; (c)两种方案的Holevo界与传输距离的关系
Figure 3. The performance comparison between the GMCVQKD scheme with an untrusted entanglement source and the original GMCVQKD scheme under homodyne detection: (a) The relationship between the security key rate and transmission distance of the two schemes; (b) the relationship between mutual information and transmission distance of the two schemes; (c) the relationship between Holevo bound and transmission distance of two schemes.
图 4 零差探测下基于不可信纠缠源的GMCVQKD方案在不同纠缠源距离下的性能 (a)所提方案的安全密钥率与传输距离的关系; (b)所提方案的Holevo界与传输距离的关系
Figure 4. Performance of the GMCVQKD scheme based on an untrusted entanglement source with homodyne detection at different entanglement source distances: (a) Relationship between the security key rate of the proposed scheme and the transmission distance; (b) relationship between the Holevo bound of the proposed scheme and the transmission distance.
图 5 零差探测下基于不可信纠缠源的GMCVQKD方案在不同过噪声下的性能
Figure 5. The performance of the GMCVQKD scheme based on an untrusted entanglement source under different excess noise.
图 6 外差探测下基于不可信纠缠源的GMCVQKD方案在不同纠缠源距离下的性能 (a) 所提方案的安全密钥率与传输距离的关系; (b)所提方案的Holevo界与传输距离的关系
Figure 6. Performance of the GMCVQKD scheme based on an untrusted entanglement source with heterodyne detection at different entanglement source distances: (a) Relationship between the security key rate of the proposed scheme and the transmission distance; (b) relationship between the Holevo bound of the proposed scheme and the transmission distance.
图 7 PSA的模型
Figure 7. Model of PSA.
图 8 零差探测与PSA组合后的安全密钥率
Figure 8. Security key rate for the combination of homodyne detection and PSA.
图 9 PIA的模型
Figure 9. Model of PIA.
图 10 外差探测与PIA组合后的安全密钥率
Figure 10. Security key rate for the combination of heterodyne detection and PIA.
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[1] Zhou N R, Li J F, Yu Z B, Gong L H, Farouk A 2016 Quantum Inf. Process 16 4
[2] Scarani V, Bechmann-Pasquinucci H, Cerf N J, Dušek M, Lütkenhaus N, Peev M 2009 Rev. Mod. Phys. 81 1301
Google Scholar
[3] Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145
Google Scholar
[4] Gong L H, Li J F, Zhou N R 2018 Laser Phys. Lett. 15 105204
Google Scholar
[5] Liao Q, Liu H J, Zhu L J, Guo Y 2021 Phys. Rev. A 103 032410
Google Scholar
[6] Liao Q, Liu H J, Gong Y P, Wang Z, Peng Q Q, Guo Y 2022 Opt. Express 30 3876
Google Scholar
[7] 宋汉冲, 龚黎华, 周南润 2012 61 154206
Google Scholar
Song H C, Gong L H, Zhou N R 2012 Acta Phys. Sin. 61 154206
Google Scholar
[8] Zhou N R, Wang L J, Ding J, Gong L H, Zuo X W 2010 Int. J. Theor. Phys. 49 2035
Google Scholar
[9] Guo Y, Liao Q, Wang Y J, Huang D, Huang P, Zeng G H 2017 Phys. Rev. A 95 032304
Google Scholar
[10] 钟海, 叶炜, 吴晓东, 郭迎 2021 70 020301
Google Scholar
Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301
Google Scholar
[11] Lance A M, Symul T, Sharma V, Weedbrook C, Ralph T C, Lam P K 2005 Phys. Rev. Lett. 95 180503
Google Scholar
[12] Ma X C, Sun S H, Jiang M S, Gui M, Liang L M 2014 Phys. Rev. A 89 042335
Google Scholar
[13] Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902
Google Scholar
[14] Leverrier A 2015 Phys. Rev. Lett. 114 070501
Google Scholar
[15] Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343
Google Scholar
[16] Jouguet P, Kunz-Jacques S, Diamanti E 2013 Phys. Rev. A 87 062313
Google Scholar
[17] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 88 022339
Google Scholar
[18] Qin H, Kumar R, Alléaume R 2016 Phys. Rev. A 94 012325
Google Scholar
[19] Huang J Z, Weedbrook C, Yin Z Q, Wang S, Li H W, Chen W, Guo G C, Han Z F 2013 Phys. Rev. A 87 062329
Google Scholar
[20] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 87 052309
Google Scholar
[21] Qin H, Kumar R, Makarov V, Alléaume R 2018 Phys. Rev. A 98 012312
Google Scholar
[22] Zhou N R, Zhang T F, Xie X W, Wu J Y 2023 Signal Process. Image Commun. 110 116891
Google Scholar
[23] Liao Q, Xiao G, Zhong H, Guo Y 2020 New J. Phys. 22 083086
Google Scholar
[24] Weedbrook C 2013 Phys. Rev. A 87 022308
Google Scholar
[25] Liao Q, Xiao G, Xu C G, Xu Y, Guo Y 2020 Phys. Rev. A 102 032604
Google Scholar
[26] Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B: At., Mol. Opt. Phys. 42 114014
Google Scholar
[27] Zhang H, Fang J, He G Q 2012 Phys. Rev. A 86 022338
Google Scholar
[28] Wu X D, Wang Y J, Liao Q, Zhong H, Guo Y 2019 Entropy 21 333
Google Scholar
[29] Pirandola S, Braunstein S L, Lloyd S 2008 Phys. Rev. Lett. 101 200504
[30] García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503
Google Scholar
[31] Navascués M, Grosshans F, Acín A 2006 Phys. Rev. Lett. 97 190502
Google Scholar
[32] Huang D, Huang P, Lin D K, Zeng G H 2016 Sci. Rep. 6 19201
Google Scholar
[33] Huang D, Lin D K, Wang C, Liu W Q, Fang S H, Peng J Y, Huang P, Zeng G H 2015 Opt. Express 23 017511
Google Scholar
[34] Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378
Google Scholar
[35] Huang L Y, Zhang Y C, Huang Y D, Jiang T W, Yu S 2019 Phys. B: At. Mol. Opt. Phys. 52 225502
Google Scholar
[36] Zhang Y C, Li Z Y, Weedbrook C, Yu S, Gu W Y, Sun M Z, Peng X, Guo H 2014 J. Phys. B: At., Mol. Opt. Phys. 47 035501
Google Scholar
[37] Guo Y, Li R J, Liao Q, Zhou J, Huang D 2018 Phys. Lett. A 382 372
Google Scholar
[38] Blandino R, Leverrier A, Barbieri M, Etesse J, Grangier P, Tualle-Brouri R 2012 Phys. Rev. A 86 012327
Google Scholar
[39] Bencheikh K, Lopez O, Abram I, Levenson J A 1995 Appl. Phys. Lett. 66 399
Google Scholar
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