N-比特系统更紧的单配性不等式

doi:10.13371/j.cnki.chin.q.j.m.2024.04.007

数学季刊 ›› 2024, Vol. 39 ›› Issue (4): 407-419.doi: 10.13371/j.cnki.chin.q.j.m.2024.04.007

N-比特系统更紧的单配性不等式

1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China; 2. Research Center for Mathematics and Interdisciplinary Science and Technology, Kunming 650500, China; 3. School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China

收稿日期:2023-12-26 出版日期:2024-12-30 发布日期:2024-12-30
通讯作者: YANG Yan-min (1987-), female, native of Dali, Yunnan, lecturer of Kunming University of Science and Technology, engages in algebra and quantum computation; E-mail:ym.yang@kust.edu.cn
作者简介:ZHANG Lu-lu (1997-), female, native of Nanyang, Henan, graduate student of Kunming University of Science and Technology; YANG Yan-min (1987-), female, native of Dali, Yunnan, lecturer of Kunming University of Science and Technology, engages in algebra and quantum computation; CHEN Wei (1984-), male, native of Xinyang, Henan, associate professor of Dongguan University of Technology, engages in algebra and quantum computation.
基金资助:
Supported by Yunnan Provincial Research Foundation for Basic Research (Grant No. 202001AU070041); Natural Science Foundation of Kunming University of Science and Technology (Grant No.KKZ3202007036); Basic and Applied Basic Research Funding Program of Guangdong Province (Grant Nos. 2019A1515111097 and 2023A1515012074).

Some Tighter Monogamy Inequalities in N-Qubit Systems

1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China; 2. Research Center for Mathematics and Interdisciplinary Science and Technology, Kunming 650500, China; 3. School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China

Received:2023-12-26 Online:2024-12-30 Published:2024-12-30
Contact: YANG Yan-min (1987-), female, native of Dali, Yunnan, lecturer of Kunming University of Science and Technology, engages in algebra and quantum computation; E-mail:ym.yang@kust.edu.cn
About author:ZHANG Lu-lu (1997-), female, native of Nanyang, Henan, graduate student of Kunming University of Science and Technology; YANG Yan-min (1987-), female, native of Dali, Yunnan, lecturer of Kunming University of Science and Technology, engages in algebra and quantum computation; CHEN Wei (1984-), male, native of Xinyang, Henan, associate professor of Dongguan University of Technology, engages in algebra and quantum computation.
Supported by:
Supported by Yunnan Provincial Research Foundation for Basic Research (Grant No. 202001AU070041); Natural Science Foundation of Kunming University of Science and Technology (Grant No.KKZ3202007036); Basic and Applied Basic Research Funding Program of Guangdong Province (Grant Nos. 2019A1515111097 and 2023A1515012074).

摘要/Abstract

摘要： We construct a piecewise function to investigate some monogamy inequalities in terms of the αth power of concurrence and negativity (α≥2), entanglement of formation (α≥\sqrt{2}), and Tsallis-q entanglement (α≥1). These inequalities are tighter than the existing results with detailed examples. Particularly, it is worth highlighting some classes of quantum states which can saturate these monogamy inequalities for α= 2, 4 and 6 in terms of concurrence and negativity and for α= 1, 2 and 3 in terms of Tsallis-q entanglement.

关键词: Monogamy inequalities, Entanglement measures, N-qubit systems

Abstract: We construct a piecewise function to investigate some monogamy inequalities in terms of the αth power of concurrence and negativity (α≥2), entanglement of formation (α≥\sqrt{2}), and Tsallis-q entanglement (α≥1). These inequalities are tighter than the existing results with detailed examples. Particularly, it is worth highlighting some classes of quantum states which can saturate these monogamy inequalities for α= 2, 4 and 6 in terms of concurrence and negativity and for α= 1, 2 and 3 in terms of Tsallis-q entanglement.

Key words: Monogamy inequalities, Entanglement measures, N-qubit systems

中图分类号:

张露露, 杨彦敏, 陈伟. N-比特系统更紧的单配性不等式[J]. 数学季刊, 2024, 39(4): 407-419.

ZHANG Lu-lu, YANG Yan-min, CHEN Wei. Some Tighter Monogamy Inequalities in N-Qubit Systems[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(4): 407-419.

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N-比特系统更紧的单配性不等式

Some Tighter Monogamy Inequalities in N-Qubit Systems

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