We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be extended to multipartite high dimensional system.
@article{arxiv.2003.10627,
title = {Local Unitary Invariants of Quantum States},
author = {Meiyu Cui and Jingmei Chang and Ming-Jing Zhao and Xiaofen Huang and Tinggui Zhang},
journal= {arXiv preprint arXiv:2003.10627},
year = {2020}
}