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.
@article{arxiv.0801.1704,
title = {Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations},
author = {Zu-Huan Yu and Xian-Qing Li-Jost and Shao-Ming Fei},
journal= {arXiv preprint arXiv:0801.1704},
year = {2008}
}