报告人：许振朋（安徽大学 教授）
报告时间：2024年11月24日下午4：30
报告地点：杏林湾酒店203会议室
联系人：陈芝花教授
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报告摘要：The interplay between the quantum state space and a specific set of measurements can be effectively captured by examining the set of jointly attainable expectation values. This set is commonly referred to as the (convex) joint numerical range. In this work, we explore geometric properties of this construct for measurements represented by tensor products of Pauli observables, also known as Pauli strings. The structure of pairwise commutation and anticommutation relations among a set of Pauli strings determines a graph G, sometimes also called the frustration graph. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range. Such an outer approximation can be very practical since ellipsoids can be handled analytically even in high dimensions. We find counterexamples to a conjecture from [arXiv:2207.02197], and answer an open question in [Proc. STOC 2022, pp. 776-789], which implies a new graph parameter that we call β(G). Besides, we develop this approach in different directions, such as comparison with graph-theoretic approaches in other fields, applications in quantum information theory, numerical methods, properties of the new graph parameter, etc. Our approach suggests many open questions that we discuss briefly at the end.
报告人简介：许振朋博士现就职于安徽大学，教授，博士生导师，毕业于南开大学陈省身数学研究所，毕业后在德国锡根大学从事博士后工作，期间获德国洪堡基金会支持。许博士的研究方向为量子力学基础问题和量子信息，专注于不同系统中的量子关联，从单体系统、少体系统到近期的网络系统。近五年来，以独立第一作者或通讯作者身份在PRL ，Nature Communications、Optica等顶尖期刊发表多篇。基于以往工作，申请人荣获2021年度奥地利科学院颁发的埃伦费斯特量子基础最佳论文奖。
