Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence

TL;DR

This paper introduces a practical method for determining canonical forms of multipartite entangled states, enabling efficient verification of local unitary equivalence for pure and mixed states in arbitrary dimensions.

Contribution

It extends previous techniques to construct canonical forms for mixed multipartite states, incorporating local symmetries inherited from pure state counterparts.

Findings

Canonical forms for mixed N-partite entangled states are constructed.

A systematic scheme for expressing local symmetries is developed.

The method facilitates verifying local unitary equivalence between states.

Abstract

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states.