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Free-space quantum key distribution (QKD) allows two distant parties to share secret keys with information-theoretic security, which can pave the way for satellite-ground quantum communication to set up a global network for sharing secret message. However, free-space channels in the presence of atmospheric turbulence are affected by losses and fluctuating transmissivity which further affect the quantum bit error rate and the secure key rate. To implement free-space QKD, it is indispensable to study the effect of atmospheric turbulence. Different models have been used to describe the probability distribution for channel transmission coefficient under atmospheric turbulence, including the log-normal distribution and K distribution. In this paper, we focus on free space measurement-device-independent quantum key distribution (MDI-QKD) under K-distributed strong atmospheric turbulence. The MDI-QKD can close all loopholes on detection and achieve a similar performance to QKD, relying on time-reversed version of entanglement-based QKD protocol. Threshold post-selection method is adopted to restrain detrimental effects of the atmospheric turbulence, which is based on the selection of the intervals with higher channel transmissivity. By combining the general MDI-QKD system model with this method, we present a framework for the optimal choice of threshold. Our simulation result shows that the optimal threshold is dependent on the turbulence intensity and expected channel loss. Furthermore, compared with the original MDI-QKD protocols, the proposed protocol with threshold post-selection method can acquire a considerable better performance in key rate, especially in regions of high turbulence and high loss. What is more, this is instructive to the building of a practical free-space MDI-QKD system with better performance.
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Keywords:
- strong atmospheric turbulence /
- K-distributed model /
- measurement-device-independent quantum key distribution /
- free space
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图 1 自由空间测量设备无关量子密钥分发模型示意图(BS, 50 : 50光分束器; PBS, 偏振光分束器; D1H, D2H, D1V, D2V, 单光子探测器; U1 (U2), Alice和Bob的大气信道)
Figure 1. Free space MDI-QKD diagram. BS, 50 : 50 beam splitter; PBS, polarized beam splitter; D1H, D2H, D1V, D2V, single-photon detector; U1 (U2), Alice and Bob’s atmospheric channel.
图 2
$\alpha $ 与闪烁系数$\sigma _{\rm{I}}^{\rm{2}}$ 的关系Figure 2. Relationship between
$\alpha $ and scintillation coefficient$\sigma _{\rm{I}}^2$ .
图 3 最佳阈值
$\eta _{\rm{T}}^{{\rm{opt}}}$ 与信道参数$\alpha $ 、平均传输率${\eta _0}$ 的关系Figure 3. Relationship of optimal threshold value
$\eta _{\rm{T}}^{{\rm{opt}}}$ to channel parameter$\alpha $ and average transmission rate${\eta _0}$ .
图 4 强湍流下MDI-QKD密钥率与阈值、信道参数的关系
Figure 4. Relationship of key rate of MDI-QKD under strong turbulence to threshold and channel parameters.
图 5 强湍流下MDI-QKD密钥率与信道损耗间的关系
Figure 5. Relationship between key rate of MDI-QKD under strong turbulence and channel loss.
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[1] Shannon C E 1949 Bell Syst. Tech. J. 28 656
Google Scholar
[2] Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441
Google Scholar
[3] Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quantum Inf. Comput. 4 325
[4] Xu G, Chen X B, Dou Z, Yang Y X, Li Z P 2015 Quantum Inf. Process. 14 2959
Google Scholar
[5] 东晨, 赵尚弘, 赵卫虎, 石磊, 赵顾颢 2014 物理学报 63 030302
Google Scholar
Dong C, Zhao S H, Zhao W H, Shi L, Zhao G H 2014 Acta Phys. Sin. 63 030302
Google Scholar
[6] 东晨, 赵尚弘, 董毅, 赵卫虎, 赵静 2014 物理学报 63 170303
Google Scholar
Dong C, Zhao S H, Dong Y, Zhao W H, Zhao J 2014 Acta Phys. Sin. 63 170303
Google Scholar
[7] Chen X B, Tang X, Xu G, Dou Z, Chen Y L, Yang Y X 2018 Quantum Inf. Process. 17 225
Google Scholar
[8] Chen X B, Sun Y R, Xu G, Jia H Y, Qu Z G, Yang Y X 2017 Quantum Inf. Process. 16 244
Google Scholar
[9] Xu G, Chen X B, Li J, Wang C, Yang Y X, Li Z P 2015 Quantum Inf. Process. 14 4297
Google Scholar
[10] Chen X B, Wang Y L, Xu G, Yang Y X 2019 IEEE Access 7 13634
Google Scholar
[11] Yin H L, Chen T Y, Yu Z W, Liu H, You L X, Zhou Y H, Chen S J, Mao Y, Huang M Q, Zhang W J, Chen H, Li M J, Nolan D, Zhou F, Jiang X, Wang Z, Zhang Q, Wang X B, Pan J W 2016 Phys. Rev. Lett. 117 190501
Google Scholar
[12] Bedington R, Arrazola J M, Ling A 2017 EPJ Quantum Inf. 3 30
Google Scholar
[13] Buttler W T, Hughes R J, Lamoreaux S K, Morgan G L, Nordholt J E, Peterson C G 2000 Phys. Rev. Lett. 84 5652
Google Scholar
[14] Richard J H, Jane E N, Derek D, Charles G P 2002 New J. Phys. 4 43
[15] Manderbach S T, Weier H, Fürst M, Ursin R, Tiefenbacher F, Scheidl T, Perdigues J, Sodnik Z; Kurtsiefer C, Rarity J G, Zeilinger A, Weinfurter H 2007 Phys. Rev. Lett. 98 010504
Google Scholar
[16] Liao S K, Yong H L, Liu C, Shentu G L, Li D D, Lin J, Dai H, Zhao S Q, Li B, Guan J Y, Chen W, Gong Y H, Li Y, Lin Z H, Pan G S, Pelc S J, Fejer M M, Zhang W Z, Liu W Y, Yin J, Ren J G, Wang X B, Zhang Q, Peng C Z, Pan J W 2017 Nat. Photon. 11 509
[17] Vallone G, Bacco D, Dequal, D, Gaiarin S, Luceri V, Bianco G, Villoresi P 2015 Phys. Rev. Lett. 115 040502
Google Scholar
[18] Oi D K, Ling A, Vallone G, Villoresi P, Greenland S, Kerr E, Macdonald M, Weinfurter H, Kuiper H, Charbon E, Ursin R 2017 EPJ Quantum Technol. 4 6
Google Scholar
[19] Liao S K, Cai W Q, Liu W Y, Zhang L, Li Y, Ren J G, Yin J, Shen Q, Cao Y, Li Z P, Li F Z, Chen X W, Sun L H, Jia J J, Wu J C, Jiang X J, Wang J F, Huang Y M, Wang Q, Zhou Y L, Deng L, Xi T, Ma L, Hu T, Zhang Q, Chen Y A, Liu N L, Wang X B, Zhu Z C, Lu C Y, Shu R, Peng C Z, Wang J Y, Pan J W 2017 Nature 549 43
Google Scholar
[20] Yin J, Cao Y, Li Y H, Liao S K, Zhang L, Ren J G, Cai W Q, Liu W Y, Li B, Dai H, Li G B, Lu Q M, Gong Y H, Xu Y, Li S L, Li F Z, Yin Y Y, Jiang Z Q, Li M, Jia J J, Ren G, He D, Zhou Y L, Zhang X X, Wang N, Chang X, Zhu Z C, Liu N L, Chen Y A, Lu C Y, Shu R, Peng C Z, Wang J Y, Pan J W 2017 Science 356 1140
Google Scholar
[21] Ren J G, Xu P, Yong H L, Zhang L, Liao S K, Yin J, Liu W Y, Cai W Q, Yang M, Li L, Yang K X, Han X, Yao Y Q, Li J, Wu H Y, Wan S, Liu L, Liu D Q, Kuang Y W, He Z P, Shang P, Guo C, Zheng R H, Tian K, Zhu Z C, Liu N L, Lu C Y, Shu R, Chen Y A, Peng C Z, Wang J Y, Pan J W 2017 Nature 549 70
Google Scholar
[22] Liao S K, Cai W Q, Handsteiner J, Liu B, Yin J, Zhang L, Rauch D, Fink M, Ren J G, Liu W Y, Li Y, Shen Q, Cao Y, Li F Z, Wang J F, Huang Y M, Deng L, Xi T, Ma L, Hu T, Li L, Liu N L, Koidl F, Wang P, Chen Y A, Wang X B, Steindorfer M, Kirchner G, Lu C Y, Shu R, Ursin R, Scheidl T, Peng C Z, Wang J Y, Zeilinger A, Pan J W 2018 Phys. Rev. Lett. 120 030501
Google Scholar
[23] Carrasco-Casado A, Fernández V, Denisenko N 2016 Free-Space Quantum Key Distribution (Switzerland: Springer International Publishing) pp589−607
[24] Hill R J, Frehlich R G 1997 J. Opt. Soc. Am. A 14 1530
Google Scholar
[25] Lyke S D, Voelz D G, Roggemann M C 2009 Appl. Opt. 48 6511
Google Scholar
[26] Mclaren J R, Thomas J C, Mackintosh J L, Mudge K A, Grant K J, Clare B A, Cowley W G 2012 Appl. Opt. 51 5996
Google Scholar
[27] Kiasaleh K 2006 IEEE Trans. Commun. 54 604
Google Scholar
[28] Vallone G, Marangon D G, Canale M, Vallone G, Marangon D G, Canale M, Savorgnan I, Bacco D, Barbieri M, Calimani S, Barbieri C, Laurenti N, Villoresi P 2015 Phys. Rev. A 91 042320
[29] Erven C, Heim B, Meyerscott E, Bourgoin J P, Laflamme R, Weihs G, Jennewein T 2012 New J. Phys. 14 129401
[30] Wang W, Xu F, Lo H K 2018 Phys. Rev. A 97 32337
Google Scholar
[31] Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503
Google Scholar
[32] Ma X, Razavi M 2012 Phys. Rev. A 86 062319
Google Scholar
[33] Niu M, Cheng J, Holzman J F 2011 IEEE Trans. Commun. 59 664
Google Scholar
[34] Bourgoin J, Meyerscott E, Higgins B L, Helou B, Erven C, Hübel H, Kumar B, Hudson D, D'Souza I, Girard R, Laflamme R, Jennewein T 2014 New J. Phys. 16 069502
Google Scholar
[35] Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007
Google Scholar
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