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A Complete Set of Local Invariants for a Family of Multipartite Mixed States
Xiao-Hong Wang, Shao-Ming Fei and Ke Wu
We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed states in KxMxN composite systems. Two density matrices in the same class are equivalent under local unitary transformations if and only if all these invariants have equal values for these density matrices.