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.
@article{arxiv.quant-ph/0506135,
title = {Equivalence of Quantum States under Local Unitary Transformations},
author = {Shao-Ming Fei and Naihuan Jing},
journal= {arXiv preprint arXiv:quant-ph/0506135},
year = {2009}
}