报告题目：The Schmidt rank in the commuting operator framework
主讲人：René Schwonnek 德国汉诺威大学 研究员
时 间：2024年9月26日8:30
地 点：安徽大学磬苑校区理工E楼E400
主办单位：物理与光电工程学院
欢迎各位老师、同学届时前往！
报告摘要：
A fundamental question in quantum theory is: When can a quantum system be considered effectively finite-dimensional? A natural ansatz for approaching this question is to consider the Schmidt rank, which gives a fundamental measure for the entanglement dimension of a pure bipartite state. Its usual definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces. Unfortunately, this definition has limitations since these local Hilbert spaces do not exist (or are at least not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In our work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: the vacuum in quantum field theory, Araki–Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework.
报告人简介：
René Schwonnek，2018年毕业于德国汉诺威大学物理系，2018-2020年为新加坡国立大学研究员，2020-2022年为德国锡根大学博士后，2022年起为汉诺威大学量子信息组研究员。主要从事量子信息理论及其应用，在不确定性关系、量子密钥分配、量子随机数产生以及非对易多项式优化等研究方面取得一系列具有国际影响力的成果。在NATURE上发表论文1篇，NATURE COMMUNICATIONS和PHYS. REV. LETT.等重要学术期刊上发表SCI论文4篇，受邀多次在KQCBW 2022、QCrypt 2022等国际会议上做特邀报告。