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发布时间:2025-07-02文章来源:华南理工大学数学学院浏览次数:10

报告主题: Entanglement and Separation of Orbits

报 告 人: 张林教授

报告时间:2025年7月4日(星期五)下午4:00-5:00

报告地点:清清文理楼3A02  

邀 请 人: 郑驻军 教授

 

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                       数学学院


                       2025年7月2日

摘    要:

The problem of locally unitary equivalence of multipartite quantum states is a well-studied topic in quantum information theory. It involves characterizing the full invariants of local unitary orbits of multipartite states, which generate al- polynomial invariants and can be used to describe any physical function that is invariant under local unitary transformations. For two-qubit states, a complete set of 18 local unitary invariants was found by Makhlin. In this work, we present a necessary and sufficient condition for entangled two-qubit states in terms of 9 of the 18 Makhlin invariants. We also find analytical relations between Makhlin‘s fundamental invariants and the locally unitary Bargmann invariants, which are related to the traces of products of density operators with marginals. Since Bargmann invariants can be measured using a quantum circuit known as the cycle test, a generalization of SWAP test, our results provide a physical and operational criterion for entanglement detection.