Speaker: 朱黄俊教授，复旦大学

Inviter: 骆顺龙研究员

Title: Optimal Quantum Measurements with Respect to the Fidelity

Language: Chinese

Time & Venue: 2025.11.14 14:30-15:30 南楼N613

Abstract: Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two states. Despite being known for over thirty years, the structure of optimal quantum measurements with respect to the fidelity remains elusive. Here we clarify this problem, with a focus on minimal optimal measurements, which admit no nontrivial coarse graining that is still optimal. We show that there exists either a unique minimal optimal measurement or infinitely many inequivalent minimal optimal measurements. Moreover, the first case holds if and only if the two density operators satisfy a weak commutativity condition. In addition, we provide a complete characterization of all minimal optimal measurements when one state is pure. The connections with quantum incompatibility, operator pencils, and geometric means are highlighted.