​报告题目：von Neumann entropy, sandwiched Renyi relative entropy and related preservers

报  告  人：齐霄霏

报告时间：2020年12月6日（周日）10:00-11:30 

腾讯会议 ID：311 832 533

摘要：The von Neumann entropy and the relative entropy are powerful tools and play important roles in quantum information theory. Assume that H is an infinite dimensional complex Hilbert space. Denote by T(H)⁺ the cone of positive trace-class operators on H and S(H) the set of all quantum states on H. In this talk, we first give a necessary and sufficient condition for two quantum states being equal by von Neumann entropy and Tsallis p-entropy, and then the maps on S(H) preserving the von Neumann entropy and Tsallis p-entropy of a convex combination are characterized. On the other hand, we give the definition of sandwiched Renyi relative entropy for on T(H)⁺ and then characterize all surjective maps preserving the sandwiched Renyi relative entropy on T(H)⁺. Particularly, the definition of sandwiched Renyi relative entropy on S(H) is given and all surjective maps preserving sandwiched Renyi relative entropy on S(H) are necessarily implemented by either a unitary or an anti-unitary operator.

 报告人简介：齐霄霏，理学博士，山西大学数学科学学院教授，博士生导师。长期以来从事算子理论与算子代数上各类映射的结构性质，以及量子信息科学中量子关联、纠缠刻画等问题的应用研究。目前为止，已出版学术专著1部，在《Journal of Functional Analysis》、《Science in China:Mathematics》、《Physical Review A》、《Science in China:Physics, Mechanics&Astronomy》、《Chinese Science Bulletin》等知名学术刊物上发表论文90余篇。主持或完成国家自然科学基金项目3项、山西省优秀青年基金项目1项、其它省级项目2项，获山西省科学技术奖自然科学类二等奖1项。

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报告题目：Probability Distribution Densityof Uncertainty, Uncertainty Region and Uncertainty Relation 

报  告  人：张林

报告时间：2020年12月6日（周日）15:00-16:30 

腾讯会议 ID：396 873 334

摘要：We study the distribution behaviors of uncertainties, as quantifiedby the standard deviation (square root of variance), of quantumobservables in random quantum states (in general mixed) induced fromthe uniform Haar measure on the pure states of the purified system.The joint probability distribution densities of uncertainties ofqubit quantum observables are derived analytically. This opens a newvista for studying uncertainty relations in a more detailed andanalytical way. The results maybe be generalized to multipleobservables in higher dimensional spaces.

 报告人简介：张林，2012年毕业于浙江大学，获得理学博士学位，2012年开始至今在杭州电子科技大学理学院工作。主要从事量子信息的研究。2019年6月-2020年6月期间访问德国马克斯普朗克数学研究所(莱比锡)，主题是随机联合测量和非局域性、不确定性关系。近年来以第一作者身份发表SCI学术论文30余篇，目前主持国家自然科学基金面上项目1项。