学术报告报告主题: Jordan Negativity and Quantum Incompatibility
报 告 人: 骆顺龙研究员
报告时间：2025年5月27日（星期二）上午10:00-11：00
报告地点：清清文理楼3A01
邀 请 人: 郑驻军 教授
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数学学院
2025年5月22日
报告摘要：
A fundamental feature of quantum mechanics is the incompatibility between quantum measurements, which leads to the Heisenberg uncertainty relations and is intrinsically related to detection of many other quantum features such as nonlocality and steering. Given the significance and ubiquity of incompatibility, it is desirable to quantify the degree of incompatibility between two quantum measurements which are mathematically described by positive operator valued measures (POVMs). The commutator (Lie product) between operators has widely been used in quantifying incompatibility (non-commutativity) and plays a crucial role in quantum mechanics. In contrast, the anti-commutator (Jordan product) between operators has been relatively less employed in the study of quantum mechanics. In this work, we explore the role of the Jordan product in characterizing measurement incompatibility. The key observation lies in that while the product of two non-negative classical observables is automatically non-negative, this is not the case for quantum observables. Indeed the Jordan product of two non-negative observables is not necessarily non-negative. This negativity of the Jordan product is a purely quantum phenomenon and is here exploited to quantify a kind of measurement incompatibility, which interpolates between non-commutativity and joint measurability. We reveal basic features of this approach, make some comparisons with existing quantifiers of incompatibility.