Entanglement properties of GHZ and W superposition state and its decayed states

doi:10.1088/1674-1056/abd74e

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/abd74e

Entanglement properties of GHZ and W superposition state and its decayed states

Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余)^†

College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

收稿日期:2020-09-26 修回日期:2020-11-23 接受日期:2020-12-30 出版日期:2021-05-18 发布日期:2021-05-18
通讯作者: Xiao-Yu Chen E-mail:xychen@zjgsu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61871347).

Entanglement properties of GHZ and W superposition state and its decayed states

Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余)^†

College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

Received:2020-09-26 Revised:2020-11-23 Accepted:2020-12-30 Online:2021-05-18 Published:2021-05-18
Contact: Xiao-Yu Chen E-mail:xychen@zjgsu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61871347).

摘要/Abstract

摘要： We use the generalized Wootters formula, the positive partial transpose (PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. It shows that the results of the generalized Wootters formula in the part near the W state are tight. In the other parts, the PPT criterion is superior to the generalized Wootters formula. Furthermore, we investigate the relationship between entanglement and coherence.

关键词: quantum entanglement, Wootters formula, matched entanglement witness, coherence

Abstract: We use the generalized Wootters formula, the positive partial transpose (PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. It shows that the results of the generalized Wootters formula in the part near the W state are tight. In the other parts, the PPT criterion is superior to the generalized Wootters formula. Furthermore, we investigate the relationship between entanglement and coherence.

Key words: quantum entanglement, Wootters formula, matched entanglement witness, coherence

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)

Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余). Entanglement properties of GHZ and W superposition state and its decayed states[J]. 中国物理B, 2021, 30(6): 60301-060301.

Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余). Entanglement properties of GHZ and W superposition state and its decayed states[J]. Chin. Phys. B, 2021, 30(6): 60301-060301.

参考文献

[1] Chen X Y and Jiang L Z 2020 IEEE J. Sel. Areas Commun. 38 557
[2] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[3] Peres A 1996 Phys. Rev. Lett. 77 1413
[4] Gühne O and Tóth G 2009 Phys. Rep. 474 1
[5] Rudolph O 2004 Lett. Math. Phys. 70 57
[6] Chen K and Wu L A 2003 Quant. Inf. Comput. 3 193
[7] Horodecki P 1997 Phys. Lett. A 232 333
[8] Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
[9] Gühne O and Seevinck M 2010 New. J. Phys. 12 053002
[10] Chen X Y, Jiang L Z and Xu Z A 2018 Front. Phys. 13 130317
[11] Hu X M, Zhang C, Zhang C J, Liu B H, Huang Y F, Han Y J, Li C F and Guo G C 2019 Quantum Eng. 1 e13
[12] Li M, Wang J, Fei S M and Li-Jost X 2014 Phys. Rev. A 89 022325
[13] Liu L, Gao T and Yan F 2018 Chin. Phys. B 27 020306
[14] Chen X Y, Jiang L Z and Xu Z A 2017 Quant. Inf. Process. 16 95
[15] Chen X Y, Jiang L Z and Xu Z A 2019 Quant. Inf. Process. 18 262
[16] Sperling J and Vogel W 2013 Phys. Rev. Lett. 111 110503
[17] Chen X Y and Jiang L Z 2020 Phys. Rev. A 101 012308
[18] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[19] Liu F, Gao D M and Cai X Q 2019 Acta Phys. Sin. 68 230301 (in Chinese)
[20] Yang H, Qin L G, Tian L J and Ma H Y 2020 Chin. Phys. B 29 040303
[21] Tan K C, Kwon H, Park C Y and Jeong H 2016 Phys. Rev. A 84 012302
[22] Lee S Y, Ji S W, Kim H J and Nha H 2011 Phys. Rev. A 84 012302
[23] Chitambar E and Hsieh M H 2016 Phys. Rev. Lett. 117 020402
[24] Yang L W and Xia Y J 2017 Chin. Phys. B 26 080302
[25] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[26] Bennett C H, Bernstein H J, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
[27] Hill S and Wootters W K 1997 Phys. Rev. Lett. 78 5022
[28] Chen Z H, Ma Z H, Gühne O and Severini S 2012 Phys. Rev. Lett. 109 200503
[29] Størmer E 1963 Acta Math. 110 223
[30] Rana S, Parashar P, Winter A and Lewenstein M 2017 Phys. Rev. A 96 052336

Entanglement properties of GHZ and W superposition state and its decayed states

Entanglement properties of GHZ and W superposition state and its decayed states

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 15

Metrics

本文评价

推荐阅读 0

[1]	Si-Ren Yang(杨思忍) and Chang-Shui Yu(于长水). Quantum dynamical resource theory under resource non-increasing framework[J]. 中国物理B, 2023, 32(4): 40305-040305.
[2]	Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis[J]. 中国物理B, 2023, 32(2): 20506-020506.
[3]	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.
[4]	Wen-Li Yu(于文莉), Yun Zhang(张允), Hai Li(李海), Guang-Fen Wei(魏广芬), Li-Ping Han(韩丽萍), Feng Tian(田峰), and Jian Zou(邹建). Enhancement of charging performance of quantum battery via quantum coherence of bath[J]. 中国物理B, 2023, 32(1): 10302-010302.
[5]	Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system[J]. 中国物理B, 2022, 31(9): 94203-094203.
[6]	Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators[J]. 中国物理B, 2022, 31(9): 90301-090301.
[7]	Huan Yang(杨欢), Ling-Ling Xing(邢玲玲), Zhi-Yong Ding(丁智勇), Gang Zhang(张刚), and Liu Ye(叶柳). Steering quantum nonlocalities of quantum dot system suffering from decoherence[J]. 中国物理B, 2022, 31(9): 90302-090302.
[8]	Zhi-Yong Ding(丁智勇), Pan-Feng Zhou(周攀峰), Xiao-Gang Fan(范小刚),Cheng-Cheng Liu(刘程程), Juan He(何娟), and Liu Ye(叶柳). Coherence migration in high-dimensional bipartite systems[J]. 中国物理B, 2022, 31(6): 60308-060308.
[9]	Yun-Chen Zhu(朱云晨), Ping-Xue Li(李平雪), Chuan-Fei Yao(姚传飞), Chun-Yong Li(李春勇),Wen-Hao Xiong(熊文豪), and Shun Li(李舜). Influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system[J]. 中国物理B, 2022, 31(6): 64201-064201.
[10]	Jing-Jing Xia(夏京京), Xiao-Tong Lu(卢晓同), and Hong Chang(常宏). Interrogation of optical Ramsey spectrum and stability study of an ⁸⁷Sr optical lattice clock[J]. 中国物理B, 2022, 31(3): 34209-034209.
[11]	Qilin Zheng(郑骑林), Jiacheng Liu(刘嘉成), Chao Wu(吴超), Shichuan Xue(薛诗川), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Xinyao Yu(于馨瑶), Miaomiao Yu(余苗苗), Mingtang Deng(邓明堂), Junjie Wu(吴俊杰), and Ping Xu(徐平). Bright 547-dimensional Hilbert-space entangled resource in 28-pair modes biphoton frequency comb from a reconfigurable silicon microring resonator[J]. 中国物理B, 2022, 31(2): 24206-024206.
[12]	Fei Gao(高飞), Fang-Hua Xu(徐芳华), and Zheng-Lin Li(李整林). Effects of mesoscale eddies on the spatial coherence of a middle range sound field in deep water[J]. 中国物理B, 2022, 31(11): 114302-114302.
[13]	Xue-Yan Cui(崔雪燕), Yi-Jing Yan(严以京), and Jian-Hua Wei(魏建华). Theoretical study on the exciton dynamics of coherent excitation energy transfer in the phycoerythrin 545 light-harvesting complex[J]. 中国物理B, 2022, 31(1): 18201-018201.
[14]	M Bagheri Harouni. Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots[J]. 中国物理B, 2021, 30(9): 90301-090301.
[15]	Xingbing Chao(潮兴兵), Yuan Gao(高源), Jianping Ding(丁剑平), and Hui-Tian Wang(王慧田). Impact of the spatial coherence on self-interference digital holography[J]. 中国物理B, 2021, 30(8): 84212-084212.