We study the local unitary equivalence for two and three-qubit mixed states by investigating the invariants under local unitary transformations. For two-qubit system, we prove that the determination of the local unitary equivalence of 2-qubits states only needs 14 or less invariants for arbitrary two-qubit states. Using the same method, we construct invariants for three-qubit mixed states. We prove that these invariants are sufficient to guarantee the LU equivalence of certain kind of three-qubit states. Also, we make a comparison with earlier works.
@article{arxiv.1707.03934,
title = {On Local Unitary Equivalence of Two and Three-qubit States},
author = {Bao-zhi Sun and Shao-Ming Fei and Zhi-xi Wang},
journal= {arXiv preprint arXiv:1707.03934},
year = {2017}
}