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

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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. 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. 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).

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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)