Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States

TL;DR

This paper introduces a practical method for classifying multipartite pure states in arbitrary dimensions under local unitary transformations, extending existing qubit-focused techniques to more complex systems using high order singular value decomposition.

Contribution

It develops a new classification scheme leveraging high order SVD and local symmetries, applicable to arbitrary dimensional multipartite states, expanding prior qubit-specific methods.

Findings

Provides a systematic classification framework for multipartite states.

Extends existing qubit-based methods to higher dimensions.

Utilizes high order singular value decomposition for state analysis.

Abstract

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states.