基于矩阵乘积压缩态的动态可扩展秘密共享方案

赖红; 万林春

doi:10.7498/aps.73.20240191

摘要

目前, 基于纠缠态的量子秘密共享(quantum secret sharing, QSS)方案未充分利用纠缠态的概率振幅潜力. 然而, 纠缠态的概率振幅是量子信息学的一个关键特性, 在量子计算和量子通信等领域有着广泛的应用潜力. 值得注意的是, 纠缠态可以通过矩阵乘积态(matrix product state, MPS)有效表达. 利用MPS对纠缠态进行表征, 能够准确地揭示与概率振幅相关的纠缠特性. 本研究证明利用MPS表征纠缠态, 可以将一个W态压缩为一个单光子和一个矩阵, 展示一种新的技术路径. 此外, 本研究还提出MPS与秘密共享方案之间的创新互操作性, 即通过压缩允许量子份额与共享的量子态之间形成非一对一的映射关系. 这种方法可能提供一种更高效的方式来实现量子信息的编码和传输, 对于量子秘密共享尤为重要. 同时, 我们提出的QSS方案具有动态特性, 能够根据需要轻松地添加或移除参与者, 以更好地适应参与者需求的变化, 并在实际应用场景中展现出更高的实用性和适应性. 本文的方案能够在保持高效纠缠利用的同时, 满足系统的多元需求, 包括但不限于通信安全性、数据传输率和系统的可扩展性.

关键词:

Abstract

Currently, quantum secret sharing (QSS) schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication. It is worth noting that entangled states can be effectively represented by matrix product states (MPSs). The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude.This study first focuses on the representation of the W state by using MPS, an approach that allows us to determine the key conditions for W state to achieve quantum advantage in QSS. Subsequently, this research demonstrates that by representing entangled states with MPS, a W state can be compressed into a single photon state and a simplified matrix form, presenting an innovative technical path.Moreover, one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states (represented by photons) into a unified state represented by a single photon. This characteristic endows our scheme with scalability and flexibility, meaning that the group of participants can be easily expanded or reduced according to their specific needs. The addition of new participants is managed by Alice, who is responsible for the distribution of quantum state shares. On the other hand, when a participant leaves the group, their old quantum state share can be simply ignored in the process of recovering the secret's quantum state, thereby simplifying the management process.Through this strategy, we can not only make effective use of entangled resources but also meet the various requirements of the system, including but not limited to communication security, data transfer rates, and system scalability. This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.

Keywords:

matrix product compressed state /
probability amplitude of entangled states /
scalability /
dynamism

作者及机构信息

赖红,
万林春

西南大学计算机与信息科学学院, 重庆　400715

通信作者: 赖红, hlai@swu.edu.cn

基金项目: 国家自然科学基金(批准号: 61702427, 62301454)、重庆市自然科学基金(批准号: CSTB2022NSCQ-MSX0749, CSTB2023NSCQ-MSX0739)和西南大学2022年校级教改项目(批准号: 2022JY086) 资助的课题.

Authors and contacts

College of Computer and Information Science, Southwest University, Chongqing 400715, China

Corresponding author: Lai Hong, hlai@swu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61702427, 62301454), the Natural Science Foundation of Chongqing, China (Grant Nos. CSTB2022NSCQ-MSX0749, CSTB2023NSCQ-MSX0739), and the Southwest University’s 2022School-Level Teaching Reform Program, China (Grant No. 2022JY086).

文章全文 : translate this paragraph

参考文献

[1]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829 Google Scholar
[2]	Greenberger D M, Horne M A, Zeilinger A 1989 Bell's Theorem, Quantum Theory and Conceptions of the Universe (Dordrecht: Springer) pp69–72
[3]	Tittel W, Zbinden H, Gisin N 2001 Phys. Rev. A 63 042301 Google Scholar
[4]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307 Google Scholar
[5]	Hsu J L, Chong S K, Hwang T, et al. 2013 Quantum Inf. Process. 12 331 Google Scholar
[6]	Singh S K, Srikanth R 2005 Phys. Rev. A 71 012328 Google Scholar
[7]	Markham D, Sanders B C 2008 Phys. Rev. A 78 042309 Google Scholar
[8]	Bagherinezhad S, Karimipour V 2003 Phys. Rev. A 67 044302 Google Scholar
[9]	Gaertner S, Kurtsiefer C, Bourennane M, Weinfurter H 2007 Phys. Rev. Lett. 98 020503 Google Scholar
[10]	Bell B A, Markham D, Herrera-Martí D A, Marin A, Wadsworth W J, Rarity J G, Tame M S 2014 Nat. Commun. 5 5480 Google Scholar
[11]	Ampatzis M, Andronikos T 2022 Symmetry 14 1692 Google Scholar
[12]	Lai H, Pieprzyk J, Pan L 2022 Phys. Rev. A 106 052403 Google Scholar
[13]	Shen A, Cao X Y, Wang Y, Fu Y, Gu J, Liu W B, Weng C X, Yin H L, Chen Z B 2023 Sci. China Phys. Mech. Astron. 66 260311 Google Scholar
[14]	Singh P, Chakrabarty I 2023 arXiv: 2305.06062 [quant-ph]
[15]	Song X, Li C 2023 J. Electron. Inform. Technol. 46 1109 Google Scholar
[16]	Liu L L, Tsai C W, Hwang T 2012 Int. J. Theor. Phys. 51 2291 Google Scholar
[17]	Tsai C W, Hwang T 2010 Opt. Commun. 283 4397 Google Scholar
[18]	Li C L, Fu Y, Liu W B, Xie Y M, Li B H, Zhou M G, Yin H L, Chen Z B 2023 Phys. Rev. Res. 5 033077 Google Scholar
[19]	Singh P, Chakrabarty I 2024 Phys. Rev. A 109 032406 Google Scholar
[20]	Ma R H, Gao F, Cai B B, Lin S 2024 Adv. Quantum Technol. 7 2300273 Google Scholar
[21]	Dür W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314 Google Scholar
[22]	Joo J, Park Y J, Lee J, Jang J, Kim I 2005 J. Korean Phys. Soc. 46 763
[23]	Pérez García D, Verstraete F, Wolf M M, Cirac J I 2007 Quantum Inf. Comput. 7 401
[24]	Sutherland B 1971 J. Math. Phys. 12 246 Google Scholar
[25]	Biamonte J 2020 arXiv: 1912.10049v2 [quant-ph]
[26]	Schollwöck U 2011 Ann. Phys. 326 96 Google Scholar
[27]	Eisert J 2013 arXiv: 1308.3318 [quant-ph]
[28]	Islam R, Ma R, Preiss P M, Tai M E, Lukin A, Rispoli M, Greiner M 2015 Nature 528 77 Google Scholar
[29]	Lai H, Pieprzyk J, Pan L, Li Y 2023 Quantum Inf. Process. 22 235 Google Scholar
[30]	Hughes R J, Nordholt J E, Derkacs D, Peterson C G 2002 New J. Phys. 4 43 Google Scholar
[31]	Jennewein T, Simon C, Weihs G, Weinfurter H, Zeilinger A 2000 Phys. Rev. Lett. 84 4729 Google Scholar
[32]	Stucki D, Gisin N, Guinnard O, Ribordy G, Zbinden H 2002 New J. Phys. 4 41 Google Scholar
[33]	Beveratos A, Brouri R, Gacoin T, Villing A, Poizat J P, Grangier P 2002 Phys. Rev. Lett. 89 187901 Google Scholar

施引文献

图 1 压缩量子态秘密共享示意图, 即一个特定的MPS被分解为多个部分, 每一部分都被压缩成一个单光子和一个矩阵, 并分别发送给各个参与者, 参与者在接收到这些部分后, 可以将其解压缩回原始的特定矩阵乘积态

Fig. 1. Diagram of compressed quantum state secret sharing: A specific MPS is divided into several parts, each of which is compressed into a single photon and a matrix, and then sent to individual participants. Upon receiving these parts, participants can decompress them back into the original matrix product state.

下载: 全尺寸图片幻灯片

表 1 本文协议与文献[1, 15, 16]中的协议比较, 其中${N_{{\text{NP}}}}$表示量子参与者的数量

Table 1. Comparison of our scheme with the schemes in Ref. [1, 15, 16], where ${N_{{\text{NP}}}}$ denotes the number of photons for quantum participants.

	协议^[1]	协议^[15]	协议^[16]	本文协议
分享的秘密	GHZ态	W态	经典序列	W态的MPS
秘密份额压缩	否	是	是	是
纠缠系数的使用	否	否	否	是
动态性	否	是	是	是
可扩展性	否	否	否	是
非唯一映射性	否	否	否	是
参与者集合的伸缩性	否	否	否	是
N_NPQ	n	n	n	1
秘密份额重复利用	否	否	否	是
分享秘密更新	否	否	否	是

下载: 导出CSV

[1]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829 Google Scholar
[2]	Greenberger D M, Horne M A, Zeilinger A 1989 Bell's Theorem, Quantum Theory and Conceptions of the Universe (Dordrecht: Springer) pp69–72
[3]	Tittel W, Zbinden H, Gisin N 2001 Phys. Rev. A 63 042301 Google Scholar
[4]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307 Google Scholar
[5]	Hsu J L, Chong S K, Hwang T, et al. 2013 Quantum Inf. Process. 12 331 Google Scholar
[6]	Singh S K, Srikanth R 2005 Phys. Rev. A 71 012328 Google Scholar
[7]	Markham D, Sanders B C 2008 Phys. Rev. A 78 042309 Google Scholar
[8]	Bagherinezhad S, Karimipour V 2003 Phys. Rev. A 67 044302 Google Scholar
[9]	Gaertner S, Kurtsiefer C, Bourennane M, Weinfurter H 2007 Phys. Rev. Lett. 98 020503 Google Scholar
[10]	Bell B A, Markham D, Herrera-Martí D A, Marin A, Wadsworth W J, Rarity J G, Tame M S 2014 Nat. Commun. 5 5480 Google Scholar
[11]	Ampatzis M, Andronikos T 2022 Symmetry 14 1692 Google Scholar
[12]	Lai H, Pieprzyk J, Pan L 2022 Phys. Rev. A 106 052403 Google Scholar
[13]	Shen A, Cao X Y, Wang Y, Fu Y, Gu J, Liu W B, Weng C X, Yin H L, Chen Z B 2023 Sci. China Phys. Mech. Astron. 66 260311 Google Scholar
[14]	Singh P, Chakrabarty I 2023 arXiv: 2305.06062 [quant-ph]
[15]	Song X, Li C 2023 J. Electron. Inform. Technol. 46 1109 Google Scholar
[16]	Liu L L, Tsai C W, Hwang T 2012 Int. J. Theor. Phys. 51 2291 Google Scholar
[17]	Tsai C W, Hwang T 2010 Opt. Commun. 283 4397 Google Scholar
[18]	Li C L, Fu Y, Liu W B, Xie Y M, Li B H, Zhou M G, Yin H L, Chen Z B 2023 Phys. Rev. Res. 5 033077 Google Scholar
[19]	Singh P, Chakrabarty I 2024 Phys. Rev. A 109 032406 Google Scholar
[20]	Ma R H, Gao F, Cai B B, Lin S 2024 Adv. Quantum Technol. 7 2300273 Google Scholar
[21]	Dür W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314 Google Scholar
[22]	Joo J, Park Y J, Lee J, Jang J, Kim I 2005 J. Korean Phys. Soc. 46 763
[23]	Pérez García D, Verstraete F, Wolf M M, Cirac J I 2007 Quantum Inf. Comput. 7 401
[24]	Sutherland B 1971 J. Math. Phys. 12 246 Google Scholar
[25]	Biamonte J 2020 arXiv: 1912.10049v2 [quant-ph]
[26]	Schollwöck U 2011 Ann. Phys. 326 96 Google Scholar
[27]	Eisert J 2013 arXiv: 1308.3318 [quant-ph]
[28]	Islam R, Ma R, Preiss P M, Tai M E, Lukin A, Rispoli M, Greiner M 2015 Nature 528 77 Google Scholar
[29]	Lai H, Pieprzyk J, Pan L, Li Y 2023 Quantum Inf. Process. 22 235 Google Scholar
[30]	Hughes R J, Nordholt J E, Derkacs D, Peterson C G 2002 New J. Phys. 4 43 Google Scholar
[31]	Jennewein T, Simon C, Weihs G, Weinfurter H, Zeilinger A 2000 Phys. Rev. Lett. 84 4729 Google Scholar
[32]	Stucki D, Gisin N, Guinnard O, Ribordy G, Zbinden H 2002 New J. Phys. 4 41 Google Scholar
[33]	Beveratos A, Brouri R, Gacoin T, Villing A, Poizat J P, Grangier P 2002 Phys. Rev. Lett. 89 187901 Google Scholar

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