A Note on Equivalence of Bipartite States under Local Unitary   Transformations
  The equivalence of arbitrary dimensional bipartite states under local unitary transformations (LUT) is studied. A set of invariants and ancillary invariants under LUT is presented. We show that two states are equivalent under LUT if and only if they have the same values for all of these invariants. 
Bao-Zhi Sun, Shao-Ming Fei, Xianqing Li-Jost, Zhi-Xi Wang