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Constructing the three-qudit unextendible product bases with strong nonlocality |
| Bichen Che(车碧琛)1, Zhao Dou(窦钊)1,†, Xiubo Chen(陈秀波)1, Yu Yang(杨榆)2, Jian Li(李剑)2, and Yixian Yang(杨义先)1 |
1 Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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Abstract Unextendible product bases (UPBs) are interesting members of a family of orthogonal product bases. Here, we investigate the construction of 3-qudit UPBs with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the shift UPBs. By mapping the system to a Rubik's cube, we provide a general method of constructing UPBs in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to the ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in by Halder et al. [$Phys. Rev. Lett$. 122 040403 (2019)], indicating that there do exist UPBs that can exhibit strong quantum nonlocality without entanglement.
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Received: 10 September 2021
Revised: 20 December 2021
Accepted manuscript online: 12 January 2022
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PACS:
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03.67.-a
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(Quantum information)
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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03.65.Ud
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(Entanglement and quantum nonlocality)
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| Fund: This work was supported by the National Key R&D Program of China (Grant No. 2020YFB1805405), the 111 Project (Grant No. B21049), the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2019BDKFJJ014), and the Fundamental Research Funds for the Central Universities (Grant Nos. 2019XD-A02 and 2020RC38). |
Corresponding Authors:
Zhao Dou
E-mail: dou@bupt.edu.cn
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Cite this article:
Bichen Che(车碧琛), Zhao Dou(窦钊), Xiubo Chen(陈秀波), Yu Yang(杨榆), Jian Li(李剑), and Yixian Yang(杨义先) Constructing the three-qudit unextendible product bases with strong nonlocality 2022 Chin. Phys. B 31 060302
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[1] Walgate J, Short A J, Hardy L and Vedral V 2000 Phys. Rev. Lett. 85 4972
[2] Zhang C R, Hu M J and Xiang G Y 2020 Chin. Phys. Lett. 37 012103
[3] Rahaman R and Parker M G 2015 Phys. Lett. A 91 022330
[4] DiVincenzo D P, Leung D W and Terhal B M 1988 IEEE Trans. Inf. Theory 48 580
[5] Eggeling T and Werner R F 2002 Phys. Rev. Lett. 89 097905
[6] Cao H J and Song H S 2006 Chin. Phys. Lett. 23 290
[7] Li C Y, Li X H, Deng F G, Zhou P, Liang Y J and Zhou H Y 2006 Chin. Phys. Lett. 23 2896
[8] Xue C, Chen Z Y, Wu Y C and Guo G P 2021 Chin. Phys. Lett. 38 030302
[9] Furusawa A, Srensen J L, Braunstein S, Fuchs C A, Kimble H J and Polzik E S 1998 Science 282 706
[10] Karlsson A and Bourennane M 1998 Phys. Rev. A 58 4394
[11] Hu Y L, Zhang Z and Wu B 2021 Chin. Phys. B 30 020308
[12] Harrow A W, Hassidim A and Lloyd S 2009 Phys. Rev. Lett. 103 150502
[13] Wang G 2017 Phys. Rev. A 96 012335
[14] Bru D, D'Ariano G. M, Lewenstein M, Macchiavello C, Sen A and Sen U 2000 Phys. Rev. Lett. 93 210501
[15] 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. Lett. A 59 1070
[16] Jiao F and Hui Z 2001 Chin. Phys. B 19 100309
[17] Johnston N 2014 J. Phys. A: Math. Theor. 47 424034
[18] De Rinaldis S 2004 Phys. Rev. A 70 022309
[19] DiVincenzo D P, Mor T, Shor P W, Smolin J A and Terhal B M 2003 Commun. Math. Phys. 238 379
[20] Agrawal S, Halder S and Banik M 2020 Phys. Rev. A 99 032335
[21] Wieniak M, Pandya P, Sakarya O and Woloncewicz B 2020 Quantum Rep. 2 49
[22] Chen J and Johnston N 2015 Commun. Math. Phys. 333 351
[23] Bej P and Halder S 2021 Phys. Lett. A 386 126992
[24] Shi F and Zhang X and Chen L 2020 Phys. Rev. A 101 062329
[25] Shi F, Li M S, Hu M, Chen L, Yung M H, Wang Y L and Zhang X 2021 arXiv:2101.0073
[26] Sun Y and Chen L 2021 arXiv:2102.11553
[27] Augusiak R, Fritz T, Kotowski M, Kotowski M, Pawowski M, Lewenstein M and Acn A 2012 Phys. Rev. A 85 042113
[28] Fan H 2004 Phys. Rev. Lett. 92 177905
[29] Wang Y M, Li J G, Zou J and Xu B M 2016 Chin. Phys. B 25 120302
[30] Walgate J, Short A J, Hardy L and Vedral V 2000 Phys. Rev. Lett. 85 4972
[31] Bennett C H, DiVincenzo D P, Mor T, Shor P W, Smolin J A and Terhal B M 1999 Phys. Rev. Lett. 82 5385
[32] Zhang Z C, Zhang K J and Gao F 2017 Phys. Rev. A 95 052344
[33] Halder S, Banik M, Agrawal S and Bandyopadhyay S 2019 Phys. Rev. Lett. 122 040403
[34] Zhang Z C and Zhang X 2017 Phys. Rev. A 99 062108
[35] Shi F, Hu M, Chen L and Zhang X 2020 Phys. Rev. A 102 042202
[36] Gross J L and Yellen J 2003 Handbook of Graph Theory (Boca Raton: CRC Press) p. 1192
[37] Johnston N 2014 J. Phys. A: Math. Theor. 47 424034
[38] Belhaj A, Sedra M B and Segui A 2014 J. Phys. A: Math. Theor. 48 045401
[39] Markham D and Sanders B C 2008 Phys. Rev. A 78 042309
[40] Halder S, Banik M and Ghosh S 2019 Phys. Rev. A 99 062329
[41] Wang K and Chen L 2020 Quantum Inf. Process. 19 1
[42] Zhang Z C, Wu X and Zhang X 2020 Phys. Rev. A 101 022306
[43] Guo Y, Jia Y and Li X 2015 Quantum Inf. Process. 14 3553
[44] Halder S and Sengupta R 2019 Phys. Lett. A 383 2004
[45] Halder S and Sengupta R 2020 Phys. Rev. A 101 012311 |
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