We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations.
@article{arxiv.1307.6037,
title = {A Note on State Decomposition Independent Local Invariants},
author = {Ting-Gui Zhang and Naihuan Jing and Xianqing Li-Jost and Ming-Jing Zhao and Shao-Ming Fei},
journal= {arXiv preprint arXiv:1307.6037},
year = {2013}
}