报告题目：Multipartite entanglement measure and complete monogamy relation
报告人：郭钰
报告时间：2020-11-07 9:30-10:30
腾讯会议ID：389 680 353
报告摘要：Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in the literature being not complete. We establish here a strict framework for defining the multipartite entanglement measure (MEM): apart from the postulates of the bipartite measure, i.e., vanishing on separable measures and nonincreasing under local operations and classical communication, a complete MEM should additionally satisfy the unification condition and the hierarchy condition. We then come up with a complete monogamy formula for the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition) and a tightly complete monogamy relation for the complete MEM (an MEM is called a complete MEM if it satisfies both the unification condition and the hierarchy condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, Tsallis q entropy of entanglement, Rényi α entropy of entanglement, the convex-roof extension of negativity, and negativity. We show that (i) the extensions of EoF, concurrence, tangle, and Tsallis q entropy of entanglement are complete MEMs; (ii) multipartite extensions of Rényi α entropy of entanglement, negativity, and the convex-roof extension of negativity are unified MEMs but not complete MEMs; and (iii) all these multipartite extensions are completely monogamous, and the ones which are defined by the convex-roof structure (except for the Rényi α entropy of entanglement and the convex-roof extension of negativity) are not only completely monogamous but also tightly completely monogamous. In addition, as a byproduct, we find a class of states that satisfy the additivity of EoF. We also find a class of tripartite states one part of which can be maximally entangled with the other two parts simultaneously according to the definition of mixed maximally entangled state (MMES) in Li et al. [Z. Li, M. Zhao, S. Fei, H. Fan, and W. Liu, Quantum Inf. Comput. 12, 0063 (2012)]. Consequently, we improve the definition of maximally entangled state (MES) and prove that the only MES is the pure MES.
参考文献：Phys. Rev. A 101, 032301 (2020).
报告人简介：郭钰，男，山西大同大学数学与统计学院教授、副经理，大同市学术技术带头人，山西省高校学校优秀青年学术带头人，山西省“三晋英才”支持计划2018年度青年优秀人才，山西省学术技术带头人，山西师范大学、太原师范学院和太原科技大学硕士生导师。2011年6于山西大学获基础数学专业理学博士学位。2011年7月份进入太原理工大学博士后流动站工作，2013年6月份出站。2016年8月-2017年8月19日在加拿大卡尔加里大学量子科学技术研究所访问。主要从事量子信息理论研究。在量子关联理论方面，用算子理论、算子代数方法得到了关于量子纠缠态、量子关联态的探测方案、纠缠度量、量子关联演化、构造新的量子关联、不可扩张纠缠基、量子相干性以及量子纠缠单配性等一系列结果。在量子信息领域SCI核心期刊发表论文35篇，出版专著一部。作为主持人已结题中国博士后科学基金第52批面上项目一项，结题国家自然科学基金青年科学基金项目一项，结题山西省基础研究计划项目一项，结题山西省应用基础研究计划项目一项，在研国家自然科学基金面上项目一项。参与的项目“基于算子理论的量子态纠缠性及相关问题研究”获2014年度山西省科学技术奖自然科学类二等奖；项目“量子关联的数学刻画”获2019 年度山西省高等学校优秀科研成果自然科学类二等奖。
