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中国物理B：英文版

A note on local unitary equivalence of isotropic-like states

张廷桂, 华波波, Li Zhi ming, 赵明镜, 杨红

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.

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We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.
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The necessary and sufficient conditions for the equivalence of arbitrary nnn-qubit pure quantum states under local unitary (LU) operations derived in [B. Kraus, Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two nnn-qubit states (with n>2n>2n>2 arbitrary) which have the properties that all the entropies of any subsystem coincide; however, the states are neither LU equivalent nor can be mapped into each other by general local operations and classical communication.
Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.