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.
Cite
@article{arxiv.quant-ph/0603104,
title = {A Note on Equivalence of Bipartite States under Local Unitary Transformations},
author = {Bao-Zhi Sun and Shao-Ming Fei and Xianqing Li-Jost and Zhi-Xi Wang},
journal= {arXiv preprint arXiv:quant-ph/0603104},
year = {2009}
}