Equivalence of Quantum States under Local Unitary Transformations
  In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented. 
Shao-Ming Fei and Naihuan Jing