学术报告20250604: Geometry of sets of Bargmann invariants

报告题目：Geometry of sets of Bargmann invariants

报告人：张林教授 杭州电子科技大学

报告时间：2025年6月4日下午15:30-16:30

报告地点：腾讯会议885-239-944

摘 要：Certain unitary invariants, known as Bargmann invariants or multivariate traces of quantum states, have recently gained attention due to their applications in quantum information theory. However, determining the boundaries of sets of Bargmann invariants remains a theoretical challenge. In this study, we address the problem by developing a unified, dimension-independent formulation that characterizes the sets of the third and fourth Bargmann invariants. In particular, our result for the set of fourth Bargmann invariants confirms the conjecture given by Fernandes et al. [Phys. Rev. Lett. 133,190201 (2024)]. Based on the obtained results, we conjecture that the unified, dimension-independent formulation of the boundaries for sets of third- and fourth-order Bargmann invariants may extend to the general case of the nth-order Bargmann invariants. These results deepen our understanding of the fundamental physical limits within quantum mechanics and pave the way for novel applications of Bargmann invariants in quantum information processing and related fields.

报告人简介：张林，杭州电子科技大学理学院教授，博士生导师。主要研究领域包括量子信息理论中的随机矩阵方法与熵不等式，以及李群表示论、几何不变量理论在量子信息科学中的交叉应用。目前致力于运用可测量的巴格曼不变量研究量子信息中的各种理论问题。

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内蒙古大学数学科学学院

2025年6月3日