Geometric discord of tripartite quantum systems

doi:10.1088/1674-1056/acdc11

中国物理B ›› 2023, Vol. 32 ›› Issue (10): 100301-100301.doi: 10.1088/1674-1056/acdc11

Geometric discord of tripartite quantum systems

Chunhe Xiong(熊春河)^1,2,†, Wentao Qi(齐文韬)³, Maoke Miao(缪茂可)⁴, and Minghui Wu(吴明晖)²

1 Interdisciplinary Center for Quantum Information, School of Physics, Zhejiang University, Hangzhou 310027, China;
2 School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China;
3 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
4 School of information and electrical engineering, Hangzhou City University, Hangzhou 310015, China

收稿日期:2023-04-19 修回日期:2023-05-25 接受日期:2023-06-07 出版日期:2023-09-21 发布日期:2023-10-09
通讯作者: Chunhe Xiong E-mail:xiongchunhe@zju.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12201555) and China Postdoctoral Science Foundation (Grant No. 2021M702864).

Geometric discord of tripartite quantum systems

Chunhe Xiong(熊春河)^1,2,†, Wentao Qi(齐文韬)³, Maoke Miao(缪茂可)⁴, and Minghui Wu(吴明晖)²

1 Interdisciplinary Center for Quantum Information, School of Physics, Zhejiang University, Hangzhou 310027, China;
2 School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China;
3 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
4 School of information and electrical engineering, Hangzhou City University, Hangzhou 310015, China

Received:2023-04-19 Revised:2023-05-25 Accepted:2023-06-07 Online:2023-09-21 Published:2023-10-09
Contact: Chunhe Xiong E-mail:xiongchunhe@zju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12201555) and China Postdoctoral Science Foundation (Grant No. 2021M702864).

摘要/Abstract

摘要： We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

关键词: geometric discord, tripartite quantum systems, quantum state discriminations, frozen discord

Abstract: We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

Key words: geometric discord, tripartite quantum systems, quantum state discriminations, frozen discord

中图分类号: (Quantum systems with finite Hilbert space)

03.65.Aa

03.67.-a (Quantum information) 03.67.Mn (Entanglement measures, witnesses, and other characterizations) 03.65.Yz (Decoherence; open systems; quantum statistical methods)

Chunhe Xiong(熊春河), Wentao Qi(齐文韬), Maoke Miao(缪茂可), and Minghui Wu(吴明晖). Geometric discord of tripartite quantum systems[J]. 中国物理B, 2023, 32(10): 100301-100301.

Chunhe Xiong(熊春河), Wentao Qi(齐文韬), Maoke Miao(缪茂可), and Minghui Wu(吴明晖). Geometric discord of tripartite quantum systems[J]. Chin. Phys. B, 2023, 32(10): 100301-100301.

参考文献

[1] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[2] Brunner N, Cavalcanti D, Pironio S, Scarani V and Wehner S 2014 Rev. Mod. Phys. 86 419
[3] Li Y and Ye X J and Chen J L 2016 Chin. Phys. Lett. 33 080301
[4] Modi K, Brodutch A, Cable H, Paterek T and Vedral V 2012 Rev. Mod. Phys. 84 1655
[5] Streltsov A, Adesso G and Plenio M B 2017 Rev. Mod. Phys. 89 041003
[6] Ekert A K 1991 Phys. Rev. Lett. 67 661
[7] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[8] Bennett C H and Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[9] Shor P W 1994 Proc. 35th Annual IEEE Symposium on Foundatins of Computer Science, November 20-22, 1994, Santa Fe, USA, p. 124
[10] Datta A, Flammia S T and Caves C M 2005 Phys. Rev. A 72 042316
[11] Datta A, Shaji A and Caves C M 2008 Phys. Rev. Lett. 100 050502
[12] Ahnefeld F, Theurer T, Egloff D, Matera J M and Plenio M B 2022 Phys. Rev. Lett. 129 120501
[13] Yin Q, Xiang G Y, Li C F and Guo G C 2017 Chin. Phys. Lett. 34 030301
[14] Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
[15] Henderson L and Vedral V 2001 J. Phys. A: Math. Gen. 34 6899
[16] Okrasa M and Walczak Z 2011 Europhys. Lett. 96 60003
[17] Giorgi G L, Bellomo B, Galve F and Zambrini R 2011 Phys. Rev. Lett. 107 190501
[18] Modi K, Paterek T, Son W, Vedral V and Williamson M 2010 Phys. Rev. Lett. 104 080501
[19] Hu M L, Hu X, Wang J, Peng Y, Zhang Y R and Fan H 2018 Phys. Rep. 762-764 1
[20] Bera A, Das T, Sadhukhan D, Roy S S, Sen(De) A and Sen U 2018 Rep. Prog. Phys. 81 024001
[21] Radhakrishnan C, Laurière M and Byrnes T 2020 Phys. Rev. Lett. 124 110401
[22] Li B, Zhu C L, Liang X B, Ye B L and Fei S M 2021 Phys. Rev. A 104 012428
[23] Zhou J, Hu H and Jing N 2022 Quantum. Inf. Process. 21 147
[24] Zhu C L, Hu B, Li B, Wang Z X and Fei S M 2022 Quantum. Inf. Process. 21 264
[25] Wei J N, Duan Z B and Zhang J 2022 Int. J. Theor. Phys. 61 257
[26] Zhou X and Zheng Z J 2022 Eur. Phys. J. Plus 137 625
[27] Datta A 2016 arXiv: 1003.5256 [quant-ph]
[28] Dakic B, Vedral V and Brukner C 2010 Phys. Rev. Lett. 105 190502
[29] Spehner D and Orszag M 2013 New J. Phys. 15 103001
[30] Spehner D and Orszag M 2013 J. Phys. A: Math. Theor. 47 035302
[31] Roga W, Spehner D and Illuminati F 2015 J. Phys. A: Math. Theor. 49 235301
[32] Wei T C and Goldbart P M 2003 Phys. Rev. A 68 042307
[33] Streltsov A, Singh U, Dhar H S, Bera M and Adesso G 2015 Phys. Rev. Lett. 115 020403
[34] Nielsen M and Chuang I 2000 Quantum computation and quantum information (Cambridge: Cambridge University Press) p. 409
[35] Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
[36] Aaronson B, Franco R Lo and Adesso G 2013 Phys. Rev. A 88 012120
[37] Eldar Y C 2003 Phys. Rev. A 68 052303
[38] Bhatia R 1996 Matrix Analysis: Graduate Texts in Mathematics 169 (Berlin: Springer) p. 58
[39] Mazzola L, Piilo J and Maniscalco S 2010 Phys. Rev. Lett. 104 200401

Geometric discord of tripartite quantum systems

Geometric discord of tripartite quantum systems

RichHTML

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 3

Metrics

本文评价

推荐阅读 0

[1]	Mohamed Amazioug, Larbi Jebli, Mostafa Nassik, Nabil Habiballah. Quantifying non-classical correlations under thermal effects in a double cavity optomechanical system[J]. 中国物理B, 2020, 29(2): 20304-020304.
[2]	刘辰, 董裕力, 朱士群. Geometric discord for non-X states[J]. 中国物理B, 2014, 23(6): 60307-060307.
[3]	吴韬, 宋学科, 叶柳. Relative ordering of square-norm distance correlations in open quantum systems[J]. , 2014, 23(10): 100302-100302.