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arXiv:1609.05985 · Chinese Physics B

A note on local unitary equivalence of isotropic-like states

Tinggui Zhang, Bobo Hua, Ming Li, Ming‐Jing Zhao, Hong Wei Yang

Published Dec 1, 2015• 6 citations
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Abstract

We consider the local unitary equivalence of a class of quantum states in bipartite case and 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.

DOI
10.1088/1674-1056/24/12/120305

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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.