Representation Class and Geometrical Invariants of Quantum States under   Local Unitary Transformations
  We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes. 
Zu-Huan Yu, Xian-Qing Li-Jost and Shao-Ming Fei