Multipartite entanglement includes not only the genuine entanglement but also the k-entanglement (k≥2). It is known that most bipartite entanglement measures have been shown to be monogamous, but the monogamy relation is involved in the bipartite entanglement measures rather than the multipartite ones. Therefore, how to explore the monogamy relation for k-entanglement becomes a basic open problem. In this talk, we introduced an axiomatic definition of the monogamy relation for the k-entanglement measure based on the coarser relation of the system partition. We also present the axiomatic definition of the complete k-entanglement measure and the associated complete monogamy relation according to the framework of the complete multipartite entanglement measure we established in [Phys. Rev. A 101, 032301 (2020)], which is shown to be an efficient tool for characterizing the multipartite quantum correlation as complementary to the monogamy relation associated with the bipartite measure. Consequently, the relation and the difference between monogamy, complete monogamy, and tightly complete monogamy are clearly depicted in light of the three types of coarser relation of the system partition. We then illustrate our approach with two classes of k-entanglement measures in detail. We find that all these k-entanglement measures are monogamous if the reduced function is strictly concave, and they are not completely monogamous, and in general they are not complete.

报告人简介

郭钰，内蒙古大学数学科学学院教授、博士生导师。主要从事算子理论、算子代数与量子信息交叉领域理论研究。主持在研国家自然科学基金面上项目一项，主持完成国家自然科学基金面上项目、国家自然科学基金青年科学基金项目、中国博士后科学基金项目、山西省自然科学基金面上项目、山西省自然科学基金青年基金项目、山西省留学人员科技活动择优资助项目、山西省高等学校科技创新项目优秀成果培育项目等项目8项。在科学出版社出版专著1部，在 Quantum、Quant. Sci. Tech.、Phys. Rev. A、New J. Phys.、J. Phys. A等杂志发表学术论文50余篇。

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王东升 副研究员