Parameterized monogamy and polygamy relations of multipartite entanglement

doi:10.1088/1674-1056/acf300

中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120303-120303.doi: 10.1088/1674-1056/acf300

Parameterized monogamy and polygamy relations of multipartite entanglement

Zhong-Xi Shen(沈中喜)^1,†, Ke-Ke Wang(王珂珂)^1,‡, and Shao-Ming Fei(费少明)^1,2,§

1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2 Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany

收稿日期:2023-06-12 修回日期:2023-08-08 接受日期:2023-08-23 出版日期:2023-11-14 发布日期:2023-11-27
通讯作者: Zhong-Xi Shen, Ke-Ke Wang, Shao-Ming Fei E-mail:18738951378@163.com;wangkk@cnu.edu.cn;feishm@cnu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos.12075159 and 12171044), the Beijing Natural Science Foundation (Grant No.Z190005), and the Academician Innovation Platform of Hainan Province.

Parameterized monogamy and polygamy relations of multipartite entanglement

Zhong-Xi Shen(沈中喜)^1,†, Ke-Ke Wang(王珂珂)^1,‡, and Shao-Ming Fei(费少明)^1,2,§

1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2 Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany

Received:2023-06-12 Revised:2023-08-08 Accepted:2023-08-23 Online:2023-11-14 Published:2023-11-27
Contact: Zhong-Xi Shen, Ke-Ke Wang, Shao-Ming Fei E-mail:18738951378@163.com;wangkk@cnu.edu.cn;feishm@cnu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos.12075159 and 12171044), the Beijing Natural Science Foundation (Grant No.Z190005), and the Academician Innovation Platform of Hainan Province.

摘要/Abstract

摘要： Monogamy and polygamy relations are important properties of entanglement, which characterize the entanglement distribution of multipartite systems. We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities, and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation. We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

关键词: monogamy, polygamy, concurrence, entanglement of formation

Abstract: Monogamy and polygamy relations are important properties of entanglement, which characterize the entanglement distribution of multipartite systems. We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities, and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation. We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

Key words: monogamy, polygamy, concurrence, entanglement of formation

中图分类号: (Entanglement measures, witnesses, and other characterizations)

03.67.Mn

03.65.Ud (Entanglement and quantum nonlocality) 03.67.-a (Quantum information)

Zhong-Xi Shen(沈中喜), Ke-Ke Wang(王珂珂), and Shao-Ming Fei(费少明). Parameterized monogamy and polygamy relations of multipartite entanglement[J]. 中国物理B, 2023, 32(12): 120303-120303.

Zhong-Xi Shen(沈中喜), Ke-Ke Wang(王珂珂), and Shao-Ming Fei(费少明). Parameterized monogamy and polygamy relations of multipartite entanglement[J]. Chin. Phys. B, 2023, 32(12): 120303-120303.

参考文献

[1] Jafarpour M, Hasanvand F K and Afshar D 2017 Commun. Theor. Phys. 67 27
[2] Wang M Y, Xu J Z, Yan F L and Gao T 2018 Europhys. Lett. 123 60002
[3] Huang H L, Goswami A K, Bao W S and Panigrahi P K 2018 Sci. China Phys. Mech. Astron. 61 060311
[4] Deng F G, Ren B C and Li X H 2017 Sci. Bull. 62 46
[5] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[6] Boyer M, Ran G, Dan K and Mor T 2009 Phys. Rev. A 79 032341
[7] Raussendorf R and Briegel H J 2001 Phys. Rev. Lett. 86 5188
[8] Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
[9] Terhal B M 2004 IBM J. Res. Dev. 48 71
[10] Kim J S, Gour G and Sanders B C 2012 Contemp. Phys. 53 417
[11] Guo Y and Gour G 2019 Phys. Rev. A 99 042305
[12] Pawlowski M 2010 Phys. Rev. A 82 032313
[13] Tomamichel M, Fehr S, Kaniewski J and Wehner S 2013 New J. Phys. 15 103002
[14] Seevinck M P 2010 Quantum Inf. Process. 9 273
[15] Ma X S, Dakic B, Naylor W, Zeilinger A and Walther P 2011 Nat. Phys. 7 399
[16] Verlinde E and Verlinde H 2013 J. High Energy Phys. 10 107
[17] Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[18] Osborne T J and Verstraete F 2006 Phys. Rev. Lett. 96 220503
[19] Bai Y K, Zhang N, Ye M Y and Wang Z D 2013 Phys. Rev. A 88 012123
[20] Bai Y K, Xu Y F and Wang Z D 2014 Phys. Rev. Lett. 113 100503
[21] Ou Y C and Fan H 2007 Phys. Rev. A 75 062308
[22] Kim J S, Das A and Sanders B C 2009 Phys. Rev. A 79 012329
[23] He H and Vida G 2015 Phys. Rev. A 91 012339
[24] Kim J S 2010 Phys. Rev. A 81 062328
[25] Kim J S 2016 Ann. Phys. 373 197
[26] Luo Y, Tian T, Shao L H and Li Y M 2016 Phys. Rev. A 93 062340
[27] Kim J S and Sanders B C 2010 J. Phys. A: Math. Theor. 43 445305
[28] Wang Y X, Mu L Z, Vedral V and Fan H 2016 Phys. Rev. A 93 022324
[29] Kim J S and Sanders B C 2011 J. Phys. A: Math. Theor. 44 295303
[30] Khan A, Rehman J, Wang K and Shin H 2019 Sci. Rep. 9 16419
[31] Gao L M, Yan F L and Gao T 2020 Int. J. Theor. Phys. 59 3098
[32] Gao L M, Yan F L and Gao T 2021 Quantum Inf. Process. 20 332
[33] Gour G, Bandyopadhay S and Sanders B C 2007 Math. Phys. 48 012108
[34] Buscemi F, Gour G and Kim J S 2009 Phys. Rev. A 80 012324
[35] Kim J S 2012 Phys. Rev. A 85 062302
[36] Kim J S 2016 Phys. Rev. A 94 062338
[37] Guo Y 2018 Quantum Inf. Process. 17 222
[38] Zhu X N and Fei S M 2014 Phys. Rev. A 90 024304
[39] Jin Z X and Fei S M 2017 Quantum Inf. Process. 16 77
[40] Jin Z X, Li J, Li T and Fei S M 2018 Phys. Rev A 97 032336
[41] Luo Y and Li Y M 2018 Commun. Theor. Phys. 69 532
[42] Yang L M, Chen B, Fei S M and Wang Z X 2019 Commun. Theor. Phys. 71 545
[43] Liu W W, Yang Z F and Fei S M 2021 Int. J. Theor. Phys. 60 4177
[44] Uhlmann A 2000 Phys. Rev. A 62 032307
[45] Rungta P, Buzek V, Caves C M, Hillery M and Milburn G J 2001 Phys. Rev. A 64 042315
[46] Albeverio S and Fei S M 2001 J. Opt. B: Quantum Semiclass. Opt. 3 223
[47] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[48] Acin A, Andrianov A, Costa L, Jané E, Latorre J I and Tarrach R 2000 Phys. Rev.Lett. 85 1560
[49] Gao X H and Fei S M 2008 Eur. Phys. J. Spec. Top. 159 71
[50] Laustsen T, Verstraete F and Van Enk S J 2003 Quantum Inf. Comput. 3 64
[51] Yu C S and Song H S 2008 Phys. Lett. A 373 727
[52] Gour G, Meyer D A and Sanders B C 2005 Phys. Rev. A 72 042329
[53] Bennett C H, Bernstein H J, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
[54] Bennett C H, Divincenzo D P, Smolin J A and Wootters W K 1996 Phys. Rev. A 54 3824
[55] Cohen O 1998 Phys. Rev. Lett. 80 2493

Parameterized monogamy and polygamy relations of multipartite entanglement

Parameterized monogamy and polygamy relations of multipartite entanglement

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Qi Sun(孙琪), Tao Li(李陶), Zhi-Xiang Jin(靳志祥), and Deng-Feng Liang(梁登峰). Unified entropy entanglement with tighter constraints on multipartite systems[J]. 中国物理B, 2023, 32(3): 30304-030304.
[2]	Qing-Yun Zhou(周晴云), Xiao-Gang Fan(范小刚), Fa Zhao(赵发), Dong Wang(王栋), and Liu Ye(叶柳). Transformation relation between coherence and entanglement for two-qubit states[J]. 中国物理B, 2023, 32(1): 10304-010304.
[3]	Zhan-Yun Wang(王展云), Feng-Lin Wu(吴风霖), Zhen-Yu Peng(彭振宇), and Si-Yuan Liu(刘思远). Robustness of two-qubit and three-qubit states in correlated quantum channels[J]. 中国物理B, 2022, 31(7): 70302-070302.
[4]	Jing Li(李静), Lijuan Hu(胡丽娟), Jing Lu(卢竞), and Lan Zhou(周兰). Entanglement of two distinguishable atoms in a rectangular waveguide: Linear approximation with single excitation[J]. 中国物理B, 2021, 30(9): 90307-090307.
[5]	Jia-Bin Zhang(张嘉斌), Zhi-Xiang Jin(靳志祥), Shao-Ming Fei(费少明), and Zhi-Xi Wang(王志玺). Optimized monogamy and polygamy inequalities for multipartite qubit entanglement[J]. 中国物理B, 2021, 30(10): 100310-100310.
[6]	郭梦丽, 李波, 王志玺, 费少明. Tighter constraints of multiqubit entanglementin terms of Rényi-α entropy[J]. 中国物理B, 2020, 29(7): 70304-070304.
[7]	靳志祥, 乔从丰. Monogamy and polygamy relations of multiqubit entanglement based on unified entropy[J]. 中国物理B, 2020, 29(2): 20305-020305.
[8]	郑一丹, 毛竹, 周斌. Entanglement teleportation via a couple of quantum channels in Ising-Heisenberg spin chain model of a heterotrimetallic Fe-Mn-Cu coordination polymer[J]. 中国物理B, 2019, 28(12): 120307-120307.
[9]	张曼, 周澜, 钟伟, 盛宇波. Direct measurement of the concurrence of hybrid entangled state based on parity check measurements[J]. 中国物理B, 2019, 28(1): 10301-010301.
[10]	秦猛, 任中洲, 张欣. Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems[J]. 中国物理B, 2018, 27(6): 60301-060301.
[11]	S Golkar,M K Tavassoly. Dynamics of entanglement protection of two qubits using a driven laser field and detunings: Independent and common, Markovian and/or non-Markovian regimes[J]. 中国物理B, 2018, 27(4): 40303-040303.
[12]	T M El-Shahat, M Kh Ismail. Some studies of the interaction between two two-level atoms and SU(1, 1) quantum systems[J]. 中国物理B, 2018, 27(10): 100201-100201.
[13]	P J Geetha,Sudha,K S Mallesh. Comparative analysis of entanglement measures based on monogamy inequality[J]. 中国物理B, 2017, 26(5): 50301-050301.
[14]	石现. Monogamy relations of quantum entanglement for partially coherently superposed states[J]. 中国物理B, 2017, 26(12): 120303-120303.
[15]	林秦, 白彦魁, 叶明勇, 林秀敏. Measurement-induced nonlocality in the W and Greenberger-Horne-Zeilinger superposition states[J]. 中国物理B, 2015, 24(3): 30304-030304.