Unified entropy entanglement with tighter constraints on multipartite systems

doi:10.1088/1674-1056/aca399

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30304-030304.doi: 10.1088/1674-1056/aca399

Unified entropy entanglement with tighter constraints on multipartite systems

Qi Sun(孙琪)¹, Tao Li(李陶)^1,†, Zhi-Xiang Jin(靳志祥)^2,‡, and Deng-Feng Liang(梁登峰)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

收稿日期:2022-09-22 修回日期:2022-11-15 接受日期:2022-11-17 出版日期:2023-02-14 发布日期:2023-02-21
通讯作者: Tao Li, Zhi-Xiang Jin E-mail:litao@btbu.edu.cn;jzxjinzhixiang@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12175147, 11847209, and 11675113), the Natural Science Foundation of Beijing (Grant No. KZ201810028042), and Beijing Natural Science Foundation (Grant No. Z190005).

Unified entropy entanglement with tighter constraints on multipartite systems

Qi Sun(孙琪)¹, Tao Li(李陶)^1,†, Zhi-Xiang Jin(靳志祥)^2,‡, and Deng-Feng Liang(梁登峰)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

Received:2022-09-22 Revised:2022-11-15 Accepted:2022-11-17 Online:2023-02-14 Published:2023-02-21
Contact: Tao Li, Zhi-Xiang Jin E-mail:litao@btbu.edu.cn;jzxjinzhixiang@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12175147, 11847209, and 11675113), the Natural Science Foundation of Beijing (Grant No. KZ201810028042), and Beijing Natural Science Foundation (Grant No. Z190005).

摘要/Abstract

摘要： Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide a characterization of multiqubit entanglement constraints in terms of unified-$(q,s)$ entropy. A class of tighter monogamy inequalities of multiqubit entanglement based on the $\alpha$-th power of unified-$(q,s)$ entanglement for $\alpha\geq 1$ and a class of polygamy inequalities in terms of the $\beta$-th power of unified-$(q,s)$ entanglement of assistance are established in this paper. Our results present a general class of the monogamy and polygamy relations for bipartite entanglement measures based on unified-$(q,s)$ entropy, which are tighter than the existing ones. What is more, some usual monogamy and polygamy relations, such as monogamy and polygamy relations based on entanglement of formation, Renyi-$q$ entanglement of assistance and Tsallis-$q$ entanglement of assistance, can be obtained from these results by choosing appropriate parameters $(q,s)$ in unified-$(q,s)$ entropy entanglement. Typical examples are also presented for illustration.

关键词: entanglement, monogamy relations, polygamy relations

Abstract: Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide a characterization of multiqubit entanglement constraints in terms of unified-$(q,s)$ entropy. A class of tighter monogamy inequalities of multiqubit entanglement based on the $\alpha$-th power of unified-$(q,s)$ entanglement for $\alpha\geq 1$ and a class of polygamy inequalities in terms of the $\beta$-th power of unified-$(q,s)$ entanglement of assistance are established in this paper. Our results present a general class of the monogamy and polygamy relations for bipartite entanglement measures based on unified-$(q,s)$ entropy, which are tighter than the existing ones. What is more, some usual monogamy and polygamy relations, such as monogamy and polygamy relations based on entanglement of formation, Renyi-$q$ entanglement of assistance and Tsallis-$q$ entanglement of assistance, can be obtained from these results by choosing appropriate parameters $(q,s)$ in unified-$(q,s)$ entropy entanglement. Typical examples are also presented for illustration.

Key words: entanglement, monogamy relations, polygamy relations

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

03.67.Mn

03.65.Ud (Entanglement and quantum nonlocality)

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.

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]. Chin. Phys. B, 2023, 32(3): 30304-030304.

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Unified entropy entanglement with tighter constraints on multipartite systems

Unified entropy entanglement with tighter constraints on multipartite systems

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