标题： 纠缠观测器和状态的局部单元等价性可判定性 显示英文标题

标题： Decidabilities of local unitary equivalence for entanglement witnesses and states

摘要： 通过局部幺正(LU)操作确定两个状态是否等价的问题对于量子信息处理非常重要。在本文中，我们提出了一种替代视角来研究这个问题，即通过比较纠缠观测器和状态之间的LU等价性可判定性（简称LU可判定性）。我们引入了厄米特算子集之间的关系，基于LU可判定性。然后我们将纠缠观测器集的LU可判定性与几个状态集的可判定性进行比较，并建立了这些集之间LU可判定性的层次结构。此外，我们意识到多个相互正交投影算子之间的同时LU(SLU)等价性对于LU等价算子至关重要。我们通过例子揭示了对于两个投影算子元组，部分SLU等价性不能保证整体SLU等价性。一般来说，我们提出了两个状态元组为SLU等价的充分必要条件。 显示英文摘要

摘要： The problem of determining whether two states are equivalent by local unitary (LU) operations is important for quantum information processing. In this paper we propose an alternative perspective to study this problem by comparing the decidabilities of LU equivalence (also known as LU decidabilities for short) between entanglement witnesses and states. We introduce a relation between sets of Hermitian operators in terms of the LU decidability. Then we compare the LU decidability for the set of entanglement witness to those decidabilities for several sets of states, and establish a hierarchy on LU decidabilities for these sets. Moreover, we realize that the simultaneous LU (SLU) equivalence between tuples of mutually orthogonal projectors is crucial to LU equivalent operators. We reveal by examples that for two tuples of projectors, the partial SLU equivalence cannot ensure the overall SLU equivalence. Generally, we present a necessary and sufficient condition such that two tuples of states are SLU equivalent.