酉操作的局域区分性研究

Local distinguishability of unitary operations is one of burning problems in quantum information theory. The aim of this project will solve some key theoretical problems in the local distinguishability of unitary operations. The project mainly focuses on three parts. Firstly, we study the necessary and sufficient condition for the local numerical range of unitary operator in low dimension being a convex set and give an effective way to determine whether unitary operations can be locally distinguished in the single-run scenario. Secondly, we design a distinguishability scheme for unitary operations which can be locally distinguished with a single run. Finally, we explore the minimal number of runs and the sequential scheme needed for realizing the local distinguishability of unitary operations. The project will enrich the theory of local distinguishability of unitary operations and promote the development of quantum information theory.

酉操作的局域区分性是量子信息理论中的研究热点之一。本项目拟解决酉操作的局域区分性中的若干关键理论问题，主要研究内容包括以下三个方面：研究低维系统中的酉算子的局域数值域是凸集的充要条件，给出有效方法来确定酉操作在单轮情况下可局域完美区分；设计在单轮应用下可局域区分的酉操作的区分方案；探讨酉操作实现局域完美区分所需要的最少轮数和串行方案。本项目的研究成果将丰富酉操作的局域区分理论，促进量子信息理论的发展。

酉操作的局域区分性是量子信息理论中的研究热点之一。本项目研究了如何判定低维系统上的两个不同酉操作的局域区分性，以及对于可局域完美区分的两个酉操作如何设计相应的局域区分协议。此外，我们还研究了Hopf旋模型中的Jones型基本构造、具有某些特殊性质的四元序列的线性复杂度和多体量子系统中的强量子非定域性。这些结果可使我们更好的理解量子纠缠和量子非定域性之间的关系。