【讲座题目】Bounding the joint numerical range of Pauli strings by graph parameters
【主 讲 人】许振朋（安徽大学）
【讲座时间】2025年6月20日周五下午14：30
【讲座地点】主楼C座636
【主讲人简介】许振朋教授，2013年至2018年于南开大学陈省身数学所理论物理室攻读博士学位，毕业后在德国锡根大学从事博士后工作，并获德国洪堡基金会支持。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。近五年发表Physical Review Letters 4篇，Nature Communications、Science Advances、PRX Quantum各1篇，并荣获奥地利科学院颁发的2021年度埃伦费斯特量子基础最佳论文奖。
【讲座内容简介】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, 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 [C. de Gois, K. Hansenne and O. Gühne, PRA 107, 062211 (2023)], and answer an open question in [M. B. Hastings and R. O'Donnell, Proc. STOC 2022, pp. 776-789], which implies a new graph parameter that we call beta(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.
