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Construction methods of nonlocal sets of orthogonal product states on multipartite quantum systems |
| Guang-Bao Xu(徐光宝)1, Zhao-Xia Zhong(仲昭霞)1, Yu-Guang Yang(杨宇光)2, and Dong-Huan Jiang(姜东焕)3,† |
1 College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China;
2 Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China;
3 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China |
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Abstract Nonlocal set of orthogonal product states (OPSs) can improve the confidentiality of information when it is used to design quantum cryptographic protocols. It is a difficult question how to construct a nonlocal set of OPSs on general multipartite and high dimensional quantum systems. Different from the previous works, we first present a novel method for constructing a nonlocal product set with $3d-2$ members on $\mathbb{C}^{d}\otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ quantum system for $d\ge 3$. Then, we extend this construction method to $\mathbb C^{d_{1}} \otimes \mathbb C^{d_{2} } \otimes \mathbb C^{d_{3} }$ quantum system and ${\otimes_{i=1}^{n}} \mathbb C^{d_{i} } $ quantum system respectively, where $3\le d_{1} \le d_{2}\le d_{3}\le \dots \le d_{n}$ and $n \geq 3$. The nonlocal set of OPSs constructed by our method contains fewer elements than those constructed by the existing methods, except for one special case. More importantly, the set of states constructed by our method has a completely different structure from those constructed by the existing methods since our nonlocal set does not contain a ``stopper" state. Our result is helpful to further understand the different structures of nonlocal sets on multipartite systems.
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Received: 13 April 2025
Revised: 23 May 2025
Accepted manuscript online: 26 May 2025
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PACS:
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03.67.Mn
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(Entanglement measures, witnesses, and other characterizations)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 62171264), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2023MF080), and the Natural Science Foundation of Beijing (Grant No. 4252014). |
Corresponding Authors:
Dong-Huan Jiang
E-mail: donghuan_jiang@163.com
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Cite this article:
Guang-Bao Xu(徐光宝), Zhao-Xia Zhong(仲昭霞), Yu-Guang Yang(杨宇光), and Dong-Huan Jiang(姜东焕) Construction methods of nonlocal sets of orthogonal product states on multipartite quantum systems 2025 Chin. Phys. B 34 110307
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[1] Bennett C H, DiVincenzo D P, Fuchs C A, Mor T, Rains E, Shor P W, Smolin J A and Wootters W K 1999 Phys. Rev. A 59 1070
[2] Walgate J and Hardy L 2002 Phys. Rev. Lett. 89 147901
[3] Sen K, Halder S and Sen U 2004 Phys. Rev. A 109 012415
[4] Zhang Z C, Gao F, Tian G J, Cao T Q and Wen Q Y 2014 Phys. Rev. A 90 022313
[5] Zhang X Q, Tan X Q, Weng J and Li Y J 2016 Sci. Rep. 6 28864
[6] Xu G B, Zhu Y Y, Jiang D H and Yang Y G 2023 Physica A 619 128734
[7] Halder S and Srivastava C 2020 Phys. Rev. A 101 052313
[8] Cohen S M 2023 Phys. Rev. A 107 012401
[9] Ghosal P, Ghosal A, Ghosh S B and Mukherjee A 2024 Phys. Rev. A 109 052617
[10] Yu S X and Oh C H 2015 arXiv: 1502.01274[hep-ph]
[11] Zhang Z C, Gao F, Qin S J, Yang Y H and Wen Q Y 2015 Phys. Rev. A 92 012332
[12] Wang Y L, Li M S, Zheng Z J and Fei S M 2015 Phys. Rev. A 92 032313
[13] Xu G B and Jiang D H 2021 Quantum Inf. Process. 20 128
[14] Xu G B, Zhu Y Y, Jiang D H and Yang Y G 2023 Physica A 619 128734
[15] Bhunia A, Chattopadhyay I and Sarkar D 2021 Quantum Inf. Process. 20 45
[16] Yuan P, Tian G J and Sun X M 2020 Phys. Rev. A 102 042228
[17] Cao H Q, Li M S and Zuo H J 2023 Phys. Rev. A 108 012418
[18] Halder S and Sengupta R 2020 Phys. Rev. A 101 012311
[19] Banik M, Guha T, Alimuddin M, Kar G, Halder S and Bhattacharya S 2021 Phys. Rev. Lett. 126 210505
[20] De Rinaldi S 2004 Phys. Rev. A 70 022309
[21] Chen P X and Li C Z 2004 Phys. Rev. A 70 022306
[22] Bennett C H, DiVincenzo D P, Mor T, Shor P W, Smolin J A and Terhal M 1999 Phys. Rev. Lett. 82 5385
[23] Niset J and Cerf N J 2006 Phys. Rev. A 74 052103
[24] Xu G B, Wen Q Y, Qin S J, Yang Y H and Gao F 2017 Phys. Rev. A 93 032341
[25] Zhu Y Y, Jiang D H, Xu G B and Yang Y G 2023 Physica A 624 128956
[26] Wang Y L, Li M S, Zheng Z J and Fei S M 2017 Quantum Inf. Process. 16 5
[27] Zuo H J, Liu J H, Zhen X F and Fei S M 2021 Quantum Inf. Process. 20 382
[28] Jiang D H and Xu G B 2020 Phys. Rev. A 102 032211
[29] Zhen X F, Fei S M and Zuo H J 2022 Phys. Rev. A 106 062432
[30] Zhang Y Q, Jiang D H, Yang Y G and Xu G B 2024 Quantum Inf. Process. 23 391
[31] Halder S, Banik M, Agrawal S and Bandyopadhyay S 2019 Phys. Rev. Lett. 122 040403
[32] Rout S, Maity A G, Mukherjee A, Halder S and Banik M 2021 Phys. Rev. A 104 052433
[33] Ma T, Zhao M J, Wang Y K and Fei S M 2014 Sci. Rep. 4 6336
[34] Xu G B, Yang Y H, Wen Q Y, Qin S J and Gao F 2016 Sci. Rep. 6 31048
[35] Yu N, Duan R Y and Ying M S 2012 Phys. Rev. Lett. 109 020506
[36] Horodecki M, Sen A, Sen U and Horodecki K 2003 Phys. Rev. Lett. 90 047902
[37] DiVincenzo D P, Mor T, Shor P W, Smolin J A and Terhal B M 2003 Commun. Math. Phys. 238 379
[38] Ye F, Zhou Z T and Li Y B 2022 Quantum Inf. Process. 21 327
[39] Jiang D H, Xu Y L and Xu G B 2019 Int. J. Theor. Phys. 58 1036
[40] Guo R and Cheng X G 2022 Quantum Inf. Process. 21 37
[41] Wei C Y, Cai X Q, Wang T Y, Qin S J, Gao F and Wen Q Y 2020 IEEE J. Sel. Area. Comm. 38 517
[42] Wei C Y, Cai X Q, Liu B, Wang T Y and Gao F 2018 IEEE T. Comput. 67 2
[43] Xu G, Kong D L, Zhang K J, Xu S Y, Cao Y B, Mao Y H, Duan J Y, Kang J W and Chen X B 2025 IEEE I. T. J. 12 2530 |
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