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Criterion of Local Unitary Equivalence for Multipartite States
Ting-Gui Zhang, Ming-Jing Zhao, Ming Li, Shao-Ming Fei and Xianqing Li-Jost
We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment. The criterion is shown to be operational even for particularly degenerated states by detailed examples. Besides, explicit expressions of the local unitary operators are constructed for locally equivalent states. In complement to the criterion, an alternative approach based on partial transposition of matrices are also given, which makes the criterion more effective in dealing with generally degenerated mixed states.