中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30305-030305.doi: 10.1088/1674-1056/ad1748

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Complementary monogamy and polygamy properties among multipartite systems

Tao Li(李陶)1, Jing-Yi Zhou(周静怡)1, Qi Sun(孙琪)1,†, Zhi-Xiang Jin(靳志祥)2, Deng-Feng Liang(梁登峰)1, and Ting Luo(罗婷)3   

  1. 1 School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China;
    2 School of Computer Science and Techonology, Dongguan University of Technology, Dongguan 523808, China;
    3 People's Public Security University of China, Academy of Information Network Security, Beijing 100038, China
  • 收稿日期:2023-10-07 修回日期:2023-12-01 接受日期:2023-12-20 出版日期:2024-02-22 发布日期:2024-03-06
  • 通讯作者: Qi Sun E-mail:Sunqi_916@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12175147), the Disciplinary Funding of Beijing Technology and Business University, the Fundamental Research Funds for the Central Universities (Grant No. 2022JKF02015), and the Research and Development Program of Beijing Municipal Education Commission (Grant No. KM202310011012).

Complementary monogamy and polygamy properties among multipartite systems

Tao Li(李陶)1, Jing-Yi Zhou(周静怡)1, Qi Sun(孙琪)1,†, Zhi-Xiang Jin(靳志祥)2, Deng-Feng Liang(梁登峰)1, and Ting Luo(罗婷)3   

  1. 1 School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China;
    2 School of Computer Science and Techonology, Dongguan University of Technology, Dongguan 523808, China;
    3 People's Public Security University of China, Academy of Information Network Security, Beijing 100038, China
  • Received:2023-10-07 Revised:2023-12-01 Accepted:2023-12-20 Online:2024-02-22 Published:2024-03-06
  • Contact: Qi Sun E-mail:Sunqi_916@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12175147), the Disciplinary Funding of Beijing Technology and Business University, the Fundamental Research Funds for the Central Universities (Grant No. 2022JKF02015), and the Research and Development Program of Beijing Municipal Education Commission (Grant No. KM202310011012).

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摘要： Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th (0≤γ ≤α, α≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-th (δ≥ β, 0≤β≤1) power of entanglement of assistance based on unified-(q,s) entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of γ and δ. These results are then applied to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.

关键词: monogamy relation, polygramy relation

Abstract: Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th (0≤γ ≤α, α≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-th (δ≥ β, 0≤β≤1) power of entanglement of assistance based on unified-(q,s) entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of γ and δ. These results are then applied to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.

Key words: monogamy relation, polygramy relation

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

  • 03.67.Mn
03.65.Ud (Entanglement and quantum nonlocality)