Local Invariants for a Class of Mixed States
  We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are locally equivalent if and only if all these invariants have equal values for them. 
Sergio Albeverio, Shao-Ming Fei, Debashish Goswami