主 题：One application of Duistermaat-Heckman measure in quantum information theory
报告人：张林 杭州电子科技大学教授
摘 要：While the exact separability probability of 8/33 for two-qubit states under the Hilbert-Schmidt measure has been reported by Huong and Khoi [J.Phys.A:Math.Theor.57,445304(2024)], detailed derivations remain inaccessible for general audiences. This paper provides a comprehensive, self-contained derivation of this result, elucidating the underlying geometric and probabilistic structures. We achieve this by developing a framework centered on the computation of Hilbert-Schmidt volumes for key components: the quantum state space, relevant flag manifolds, and regular (co)adjoint orbits. Crucially, we establish and leverage the connection between these Hilbert-Schmidt volumes and the symplectic volumes of the corresponding regular co-adjoint orbits, formalized through the Duistermaat-Heckman measure. By meticulously synthesizing these volume computations—specifically, the ratios defining the relevant probability measures—we reconstruct and rigorously verify the 8/33 separability probability. Our approach offers a transparent pathway to this fundamental constant, detailing the interplay between symplectic geometry, representation theory, and quantum probability.
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。
报告时间：2025年10月31日上午9:00-10:00
报告地点：创新楼北楼512
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内蒙古大学数学科学学院
2025年10月23日
蒙ICP16002391号-1