Criterion of local unitary equivalence for multipartite states
Ting-Gui Zhang, Ming‐Jing Zhao, Ming Li, Shao-Ming Fei, Xianqing Li‐Jost · Physical Review A · 2013
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. In addition, explicit expressions of the local unitary operators are constructed for locally equivalent states. Complementary to the criterion, an alternative approach based on the partial transposition of matrices is also given, which makes the criterion more effective in dealing with generally degenerated mixed states.