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Discrete modulation continuous variable measurement device independent quantum key distribution scheme has good compatibility with efficient error correction codes, which leads to high reconciliation efficiency even at low signal-to-noise ratio. Besides, the implementation of this protocol is simpler than that of Gaussian modulation scheme. However, the quantum efficiency of homodyne detector commonly used in the experiment is only 0.6, which will seriously affect the practical application performance of discrete modulation continuous variable measurement device independent quantum key distribution scheme. To solve this problem, we propose a discrete modulation continuous variable measurement device independent quantum key distribution scheme based on realistic detector compensation. In our scheme, for the outputs of two quantum channels, each adopts a phase sensitive amplifier to compensate for the corresponding realistic homodyne detector. The simulation results show that the phase sensitive amplifier can well compensate for the quantum efficiency of the realistic detector and effectively improve the performance of the discrete modulation continuous variable measurement device independent quantum key distribution scheme with realistic detector in terms of secret key rate and secure transmission distance. The proposed protocol provides an effective method for promoting the practical development of the discrete modulation continuous variable measurement device independent quantum key distribution scheme.
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Keywords:
- discrete modulation /
- continuous variable /
- measurement device independent quantum key distribution /
- realistic detector compensation
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图 1 基于实际探测器的离散调制CV-MDI-QKD方案图,
$D(\delta )$ 表示置换操作Figure 1. Schematic diagram of the discrete modulation CV-MDI-QKD based on realistic detector,
$D(\delta )$ represents displacement operation.
图 2
$W$ (${W_4}$ 和${W_{{\text{EPR}}}}$ )与调制方差${V_{\text{M}}}$ 的关系Figure 2. Relationship between
$W$ (${W_4}$ and${W_{{\text{EPR}}}}$ ) and the modulation variance${V_{\text{M}}}$ .
图 3 基于PSA的离散调制CV-MDI-QKD实际探测器补偿方案图, PSA为相位敏感放大器
Figure 3. Schematic diagram of discrete modulation CV-MDI-QKD with realistic detector compensation based on PSA, where PSA is the phase-sensitive amplifier.
图 4 在对称情况以及不同的PSA增益参数
$G$ 下所提出方案的安全密钥率与传输距离的关系Figure 4. Relationship between the security key rate and transmission distance of the proposed scheme in the symmetric case with different PSA gain
$G$ .
图 5 极端非对称情况下所提出方案的安全密钥率与PSA增益参数
$G$ 及传输距离${L_{AC}}$ 的关系Figure 5. Relationship between the secret key rate and the PSA gain
$G$ , transmission distance${L_{AC}}$ of the proposed scheme in the extreme asymmetric case.
图 6 极端非对称情况以及不同的PSA增益参数
$G$ 下所提出方案的安全密钥率与传输距离的关系Figure 6. Relationship between the secret key rate and the transmission distance of the proposed scheme in the extreme asymmetric case with different PSA gain G.
图 7 极端非对称情况以及不同PSA增益参数
$G$ 下所提出方案的安全密钥率与协商效率$\beta $ 的关系Figure 7. Relationship between the secret key rate and the reconciliation efficiency
$\beta $ of the proposed scheme in the extreme asymmetric case with different PSA gain$G$ . -
[1] Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002
Google Scholar
[2] Lo H K, Curty M, Tamaki K 2014 Nat. Photonics 8 595
Google Scholar
[3] Liu H, Jiang C, Zhu H T, Zou M, Yu Z W, Hu X L, Xu H, Ma S, Han Z, Chen J P, Dai Y, Tang S B, Zhang W, Li H, You L, Wang Z, Hua Y, Hu H, Zhang H, Zhou F, Zhang Q, Wang X B, Chen T Y, Pan J W 2021 Phys. Rev. Lett. 126 250502
Google Scholar
[4] Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shaari J S, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photon. 12 1012
Google Scholar
[5] Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Han Z Y, Ma S Z, Hu X L, Li Y H, Liu H, Zhou F, Jiang H F, Chen T Y, Li H, You L X, Wang Z, Wang X B, Zhang Q, Pan J W 2021 Nat. Photonics 15 570
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[7] Fang X T, Zeng P, Liu H, Zou M, Wu W J, Tang Y L, Sheng Y J, Xiang Y, Zhang W, Li H, Wang Z, You L, Li M J, Chen H, Chen Y A, Zhang Q, Peng C Z, Ma X, Chen T Y, Pan J W 2020 Nat. Photonics 14 422
Google Scholar
[8] Laudenbach F, Pacher C, Fung C H F, Poppe A, Peev M, Schrenk B, Hentschel M, Walther P, Hübel H 2018 Adv. Quantum Technol. 1 1800011
Google Scholar
[9] Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501
Google Scholar
[10] 钟海, 叶炜, 吴晓东, 郭迎 2021 物理学报 70 020301
Google Scholar
Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin 70 020301
Google Scholar
[11] Wu X, Wang Y, Guo Y, Zhong H, Huang D 2021 Phys. Rev. A 103 032604
Google Scholar
[12] Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902
Google Scholar
[13] Wang T, Zuo Z, Li L, Huang P, Guo Y, Zeng G 2022 Phys. Rev. Appl. 18 014064
Google Scholar
[14] Liu C, Zhu C, Nie M, Yang H, Pei C 2022 Opt. Express 30 14798
Google Scholar
[15] Jing F, Liu X, Wang X, Lu Y, Wu T, Li K, Dong C 2022 Opt. Express 30 8075
Google Scholar
[16] Sarmiento S, Etcheverry S, Aldama J, López I H, Vidarte L T, Xavier G B, Nolan D A, Stone J S, Li M J, Loeber D, Pruneri V 2022 New J. Phys. 24 063011
Google Scholar
[17] García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503
Google Scholar
[18] Navascués M, Grosshans F, Acín A 2006 Phys. Rev. Lett. 97 190502
Google Scholar
[19] Pirandola S, Braunstein S L, Lloyd S 2008 Phys. Rev. Lett. 101 200504
Google Scholar
[20] Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504
Google Scholar
[21] Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343
Google Scholar
[22] Leverrier A 2015 Phys. Rev. Lett. 114 070501
Google Scholar
[23] Huang D, Huang P, Lin D, Zeng G 2016 Sci. Rep. 6 19201
Google Scholar
[24] Zhang Y, Chen Z, Pirandola S, Wang X, Zhou C, Chu B, Zhao Y, Xu B, Yu S, Guo H 2020 Phys. Rev. Lett. 125 010502
Google Scholar
[25] Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378
Google Scholar
[26] Huang D, Lin D, Wang C, Liu W, Fang S, Peng J, Huang P, Zeng G 2015 Opt. Express 23 17511
Google Scholar
[27] Huang D, Huang P, Li H, Wang T, Zhou Y, Zeng G 2016 Opt. Lett. 41 3511
Google Scholar
[28] Filip R 2008 Phys. Rev. A 77 022310
Google Scholar
[29] Yuan Z L, Dynes J F, Shields A J 2010 Nat. Photonics 4 800
Google Scholar
[30] Jouguet P, Kunz-Jacques S, Diamanti E 2013 Phys. Rev. A 87 062313
Google Scholar
[31] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 88 022339
Google Scholar
[32] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 87 052309
Google Scholar
[33] Qin H, Kumar R, Alléaume R 2016 Phys. Rev. A 94 012325
Google Scholar
[34] Braunstein S L, Pirandola S 2012 Phys. Rev. Lett. 108 130502
Google Scholar
[35] Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503
Google Scholar
[36] Wang X B 2013 Phys. Rev. A 87 012320
Google Scholar
[37] Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007
Google Scholar
[38] Curty M, Xu F, Cui W, Lim C C W, Tamaki K, Lo H K 2014 Nat. Commun. 5 3732
Google Scholar
[39] Lupo C, Ottaviani C, Papanastasiou P, Pirandola S 2018 Phys. Rev. Lett. 120 220505
Google Scholar
[40] Ferreira da S T, Vitoreti D, Xavier G B, do Amaral G C, Temporao G P, von derWeid J P 2013 Phys. Rev. A 88 052303
Google Scholar
[41] Cao Y, Li Y H, Yang K X, Jiang Y F, Li S L, Hu X L, Abulizi M, Li C L, Zhang W, Sun Q C, Liu W Y, Jiang X, Liao S K, Ren J G, Li H, You L, Wang Z, Yin J, Lu C Y, Wang X B, Zhang Q, Peng C Z, Pan J W 2020 Phys. Rev. Lett. 125 260503
Google Scholar
[42] Xu F, Qi B, Liao Z, Lo H K 2013 Appl. Phys. Lett. 103 061101
Google Scholar
[43] Li Z, Zhang Y C, Xu F, Peng X, Guo H 2014 Phys. Rev. A 89 052301
Google Scholar
[44] Ma X C, Sun S H, Jiang M S, Gui M, Liang L M 2014 Phys. Rev. A 89 042335
Google Scholar
[45] Zhang Y C, Li Z, Yu S, Gu W, Peng X, Guo H 2014 Phys. Rev. A 90 052325
Google Scholar
[46] Wu X D, Wang Y J, Huang D, Guo Y 2020 Front. Phys. 15 31601
Google Scholar
[47] Pirandola S, Ottaviani C, Spedalieri G, Weedbrook C, Braunstein S L, Lloyd S, Gehring T, Jacobsen C S, Andersen U L 2015 Nat. Photonics 9 397
Google Scholar
[48] Richardson T J, Shokrollahi M A, Urbanke R 2001 IEEE Trans. Inf. Theory 47 619
Google Scholar
[49] Leverrier A, Alléaume R, Boutros J, Zémor G, Grangier P 2008 Phys. Rev. A 77 042325
Google Scholar
[50] Jouguet P, Kunz-Jacques S, Leverrier A 2011 Phys. Rev. A 84 062317
Google Scholar
[51] Milicevic M, Chen F, Zhang L M, Gulak P. G 2018 npj Quantum Inf. 4 21
Google Scholar
[52] Ma H X, Huang P, Bai D Y, Wang T, Wang S Y, Bao W S, Zeng G H 2019 Phys. Rev. A 99 022322
Google Scholar
[53] Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305
Google Scholar
[54] Leverrier A, Grangier P 2009 Phys. Rev. Lett. 102 180504
Google Scholar
[55] Polkinghorne R E S, Ralph T C 1999 Phys. Rev. Lett. 83 2095
Google Scholar
[56] Pirandola S 2013 New J. Phys. 15 113046
Google Scholar
[57] Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B 42 114014
Google Scholar
[58] Pirandola S, Laurenza R, Ottaviani C, Banchi L 2017 Nat. Commun. 8 15043
Google Scholar
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