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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
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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
Figure 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.
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[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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