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Chin. Phys. B, 2022, Vol. 31(8): 080303    DOI: 10.1088/1674-1056/ac6017
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Finite-key analysis of practical time-bin high-dimensional quantum key distribution with afterpulse effect

Yu Zhou(周雨)1,2, Chun Zhou(周淳)1,2,†, Yang Wang(汪洋)1,2, Yi-Fei Lu(陆宜飞)1,2, Mu-Sheng Jiang(江木生)1,2, Xiao-Xu Zhang(张晓旭)1,2, and Wan-Su Bao(鲍皖苏)1,2,‡
1 Henan Key Laboratory of Quantum Information and Cryptography, SSF IEU, Zhengzhou 450001, China;
2 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Abstract  High-dimensional quantum resources provide the ability to encode several bits of information on a single photon, which can particularly increase the secret key rate rate of quantum key distribution (QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations. Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.
Keywords:  high-dimensional      time-bin      finite-key analysis      intensity fluctuations      afterpulse effect  
Received:  27 January 2022      Revised:  18 March 2022      Accepted manuscript online:  23 March 2022
PACS:  03.67.Dd (Quantum cryptography and communication security)  
  03.67.Hk (Quantum communication)  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0309702), the National Natural Science Foundation of China (Grant Nos. 62101597, 61605248, 61675235, and 61505261), the China Postdoctoral Science Foundation (Grant No. 2021M691536), the Natural Science Foundation of Henan Province, China (Grant Nos. 202300410534 and 202300410532), and the Anhui Initiative Fund in Quantum Information Technologies.
Corresponding Authors:  Chun Zhou, Wan-Su Bao     E-mail:;

Cite this article: 

Yu Zhou(周雨), Chun Zhou(周淳), Yang Wang(汪洋), Yi-Fei Lu(陆宜飞), Mu-Sheng Jiang(江木生), Xiao-Xu Zhang(张晓旭), and Wan-Su Bao(鲍皖苏) Finite-key analysis of practical time-bin high-dimensional quantum key distribution with afterpulse effect 2022 Chin. Phys. B 31 080303

[1] Bennett C H and Brassard G 1984 Theor. Comput. Sci. 560 7
[2] Lo H K and Chau H F 1999 Science 283 2050
[3] Raska M 2016 Nanyang Technological University RSIS 223
[4] Courtland R 2016 IEEE Spectrum 53 11
[5] Fan-Yuan G J, Lu F Y, Wang S, Yin Z Q, He D Y, Zhou Z, Teng J, Chen W, Guo G C and Han Z F 2021 Photon. Res. 9 1881
[6] Wang S, Yin Z Q, He D Y, Chen W, Wang R Q, Ye P, Zhou Y, Fan-Yuan G J, Wang F X and Zhu Y G 2022 Nat. Photon. 16 154
[7] Mower J, Zhang Z, Desjardins P, Lee C, Shapiro J H and Englund D 2013 Phys. Rev. A 87 062322
[8] Mirhosseini M, Magana-Loaiza O S, O sullivan M N, Rodenburg B, Malik M, Lavery M P, Padgett M J, Gauthier D J and Boyd R W 2015 New J. Phys. 17 033033
[9] Ding Y, Bacco D, Dalgaard K, Cai X, Zhou X, Rottwitt K and Oxenlowe L K 2017 npj Quantum Information 3 1
[10] Sit A, Bouchard F, Fickler R, Gagnon-Bischoff J, Larocque H, Heshami K, Elser D, Peuntinger C, Gunthner K and Heim B 2017 Optica 4 1006
[11] Zhang L, Silberhorn C and Walmsley I A 2008 Phys. Rev. Lett. 100 110504
[12] Tittel W, Brendel J, Zbinden H and Gisin N 2000 Phys. Rev. Lett. 84 4737
[13] Mair A, Vaziri A, Weihs G and Zeilinger A 2001 Nature 412 313
[14] Zhang Y, Roux F S, Konrad T, Agnew M, Leach J and Forbes A 2016 Sci. Adv. 2 e1501165
[15] Cerf N J, Bourennane M, Karlsson A and Gisin N 2002 Phys. Rev. Lett. 88 127902
[16] Erhard M, Krenn M and Zeilinger A 2020 Nat. Rev. Phys. 2 365
[17] Islam N T, Cahall C, Aragoneses A, Lezama A, Kim J and Gauthier D J 2017 Phys. Rev. Appl. 7 044010
[18] Islam N T, Lim C C W, Cahall C, Qi B, Kim J and Gauthier D J 2019 Quantum Science and Technology 4 035008
[19] Vagniluca I, Da Lio B, Rusca D, Cozzolino D, Ding Y, Zbinden H, Zavatta A, Oxenlowe L K and Bacco D 2020 Phys. Rev. Appl. 14 014051
[20] Rusca D, Boaron A, Grunenfelder F, Martin A and Zbinden H 2018 Appl. Phys. Lett. 112 171104
[21] Brassard G, Lutkenhaus N, Mor T and Sanders B C 2000 Phys. Rev. Lett. 85 1330
[22] Gisin N, Fasel S, Kraus B, Zbinden H and Ribordy G 2006 Phys. Rev. A 73 022320
[23] Makarov V, Anisimov A and Skaar J 2006 Phys. Rev. A 74 022313
[24] Lamas-Linares A and Kurtsiefer C 2007 Opt. Express 15 9388
[25] Zhao Y, Fung C H F, Qi B, Chen C and Lo H K 2008 Phys. Rev. A 78 042333
[26] Lydersen L, Wiechers C, Wittmann C, Elser D, Skaar J and Makarov V 2010 Nat. Photon. 4 686
[27] Li H W, Wang S, Huang J Z, Chen W, Yin Z Q, Li F Y, Zhou Z, Liu D, Zhang Y, Guo G C, Bao W S and Han Z F 2011 Phys. Rev. A 84 062308
[28] Bugge A N, Sauge S, Ghazali A M M, Skaar J, Lydersen L and Makarov V 2014 Phys. Rev. Lett. 112 070503
[29] Huang A, Navarrete A, Sun S H, Chaiwongkhot P, Curty M and Makarov V 2019 Phys. Rev. Appl. 12 064043
[30] Hwang W Y 2003 Phys. Rev. Lett. 91 057901
[31] Wang X B 2005 Phys. Rev. Lett. 94 230503
[32] Lo H K, Ma X and Chen K 2005 Phys. Rev. Lett. 94 230504
[33] Wang X B, Peng C Z, Zhang J, Yang L and Pan J W 2008 Phys. Rev. A 77 042311
[34] Zhou C, Bao W and Fu X 2010 Science China Information Sciences 53 2485
[35] Fan-Yuan G J, Wang C, Wang S, Yin Z Q, Liu H, Chen W, He D Y, Han Z F and Guo G C 2018 Phys. Rev. Appl. 10 064032
[36] Fan-Yuan G J, Wang S, Yin Z Q, Chen W, He D Y, Guo G C and Han Z F 2020 Quantum Engineering 2 e56
[37] Papapanos C, Zavitsanos D, Giannoulis G, Raptakis A, Kouloumentas C and Avramopoulos H 2020 arXiv:201003358[hep-ph]
[38] Hayashi M and Tsurumaru T 2012 New J. Phys. 14 093014
[39] Tomamichel M, Lim C C W, Gisin N and Renner R 2012 Nat. Commun. 3 634
[40] Hayashi M and Nakayama R 2014 New J. Phys. 16 063009
[41] Wang Y, Bao W S, Zhou C, Jiang M S and Li H W 2016 Phys. Rev. A 94 032335
[42] Azuma K 1967 Tohoku Mathematical J. Second Series 19 357
[43] Sedziak-Kacprowicz K, Czerwinski A and Kolenderski P 2020 Phys. Rev. A 102 052420
[44] Peronio P, Acconcia G, Rech I and Ghioni M 2015 Rev. Sci. Instrum. 86 113101
[45] Muller-Quade J and Renner R 2009 New J. Phys. 11 085006
[46] Ma X, Qi B, Zhao Y and Lo H K 2005 Phys. Rev. A 72 012326
[47] Wang X B, Yang L, Peng C Z and Pan J W 2009 New J. Phys. 11 075006
[48] Wang S, Zhang S L, Li H W, Yin Z Q, Zhao Y B, Chen W, Han Z F and Guo G C 2009 Phys. Rev. A 79 062309
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