On Local Unitary Equivalence of Multipartite Quantum States

Abstract

Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. For multipartite quantum states, the verification of local unitary equivalence is still a challenging problem. With the aid of fixed point unitary subgroup and tensor decomposability of certain unitary matrices, we derive the necessary and sufficient conditions for the local unitary equivalence of multipartite quantum states. Moreover, we also present several specific examples to illustrate the operability of our criterion.