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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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[3] Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quantum Inf. Comput. 4 325
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[5] 东晨, 赵尚弘, 赵卫虎, 石磊, 赵顾颢 2014 物理学报 63 030302Google Scholar
Dong C, Zhao S H, Zhao W H, Shi L, Zhao G H 2014 Acta Phys. Sin. 63 030302Google Scholar
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[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 1530Google Scholar
[25] Lyke S D, Voelz D G, Roggemann M C 2009 Appl. Opt. 48 6511Google 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 5996Google Scholar
[27] Kiasaleh K 2006 IEEE Trans. Commun. 54 604Google 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 32337Google Scholar
[31] Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503Google Scholar
[32] Ma X, Razavi M 2012 Phys. Rev. A 86 062319Google Scholar
[33] Niu M, Cheng J, Holzman J F 2011 IEEE Trans. Commun. 59 664Google 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 069502Google Scholar
[35] Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007Google Scholar
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[1] Shannon C E 1949 Bell Syst. Tech. J. 28 656Google Scholar
[2] Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441Google 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 2959Google Scholar
[5] 东晨, 赵尚弘, 赵卫虎, 石磊, 赵顾颢 2014 物理学报 63 030302Google Scholar
Dong C, Zhao S H, Zhao W H, Shi L, Zhao G H 2014 Acta Phys. Sin. 63 030302Google Scholar
[6] 东晨, 赵尚弘, 董毅, 赵卫虎, 赵静 2014 物理学报 63 170303Google Scholar
Dong C, Zhao S H, Dong Y, Zhao W H, Zhao J 2014 Acta Phys. Sin. 63 170303Google Scholar
[7] Chen X B, Tang X, Xu G, Dou Z, Chen Y L, Yang Y X 2018 Quantum Inf. Process. 17 225Google Scholar
[8] Chen X B, Sun Y R, Xu G, Jia H Y, Qu Z G, Yang Y X 2017 Quantum Inf. Process. 16 244Google Scholar
[9] Xu G, Chen X B, Li J, Wang C, Yang Y X, Li Z P 2015 Quantum Inf. Process. 14 4297Google Scholar
[10] Chen X B, Wang Y L, Xu G, Yang Y X 2019 IEEE Access 7 13634Google 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 190501Google Scholar
[12] Bedington R, Arrazola J M, Ling A 2017 EPJ Quantum Inf. 3 30Google 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 5652Google 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 010504Google 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 040502Google 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 6Google 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 43Google 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 1140Google 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 70Google 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 030501Google 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 1530Google Scholar
[25] Lyke S D, Voelz D G, Roggemann M C 2009 Appl. Opt. 48 6511Google 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 5996Google Scholar
[27] Kiasaleh K 2006 IEEE Trans. Commun. 54 604Google 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 32337Google Scholar
[31] Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503Google Scholar
[32] Ma X, Razavi M 2012 Phys. Rev. A 86 062319Google Scholar
[33] Niu M, Cheng J, Holzman J F 2011 IEEE Trans. Commun. 59 664Google 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 069502Google Scholar
[35] Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007Google Scholar
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