报告题目：Bounding the Joint Numerical Range of Pauli Strings by Graph Parameters

报  告 人：许振朋 教授，安徽大学

研究方向：量子关联、量子网络系统

报告时间：2025年1月6日（星期一）上午10:30

报告地点：量子楼410报告厅

报告摘要：

The relations among a given set of observables on a quantum system are effectively captured by their so-called joint numerical range, which is the set of tuples of jointly attainable expectation values. Here we explore geometric properties of this construct for Pauli strings, whose pairwise commutation and anticommutation relations determine a graph G. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range, and we develop this approach in different directions. As a consequence, we find counterexamples to a conjecture by de Gois et al. [Phys. Rev. A 107, 062211 (2023)], and answer an open question raised by Hastings and O’Donnell [STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 776–789], which implies a new graph parameter that we call “B(G)” Furthermore, we provide new insights into the perennial problem of estimating the ground-state energy of a many-body Hamiltonian. Our methods give lower bounds on the ground-state energy, which are typically hard to come by, and might therefore be useful in a variety of related fields.

报告人简介：

许振朋，博士，现任安徽大学教授。他本科毕业于吉林大学数学专业，博士毕业于南开大学陈省身数学研究所理论物理方向，之后在德国洪堡基金会的支持下，在德国Siegen大学担任博士后研究员。他的研究兴趣集中在不同系统中的量子关联，包括单粒子系统、多粒子系统以及最近的量子网络系统。在过去的几年里，他作为(共同)第一作者或通讯作者发表了22篇SCI论文，含5篇PRL和1篇NC。基于以往工作，他获得了2021年奥地利科学院量子基础Ehrenfest最佳论文奖。