Local unitary invariants for multipartite quantum systems

TL;DR

This paper introduces a method to generate local unitary invariants for multipartite quantum systems, applicable to fermions and distinguishable particles, including well-known invariants and their generalizations.

Contribution

It provides a systematic approach to construct local unitary invariants for complex quantum systems, extending to higher dimensions and unifying existing invariants.

Findings

Infinite families of invariants are organized systematically.

The method generalizes well-known invariants to higher dimensions.

Applicability to both fermions and distinguishable particles.

Abstract

A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher dimensional single particle Hilbert spaces is straightforward. Many well-known invariants and their generalizations are also included.