Chiral Symmetries and Multiparticle Entanglement

TL;DR

This paper explores how chiral symmetries in multiparticle quantum systems lead to highly entangled states, providing new methods for entanglement characterization and identifying genuinely multipartite entangled states.

Contribution

It demonstrates that chiral symmetries induce extremal entanglement, develops a method for analyzing multiparticle entanglement in symmetric states, and discusses broader implications.

Findings

Chiral symmetric states are highly entangled according to the geometric measure.

A simple method for genuine multiparticle entanglement in three-particle states is introduced.

Identifies multipartite entangled states with positive partial transposes across all bipartitions.

Abstract

Bosons and fermions are defined by their exchange properties and the underlying symmetries determine the structure of the corresponding state spaces. For two particles there are two possible exchange symmetries, resulting in symmetric or antisymmetric behaviour, but when exploring multiparticle systems also quantum states with chiral symmetries appear. In this work we demonstrate that chiral symmetries lead to extremal forms of quantum entanglement. More precisely, we show that subspaces with this symmetry are highly entangled with respect to the geometric measure of entanglement, leading to observables which can be useful for entanglement characterization. Along the way, we develop a simple method to solve the problem of genuine multiparticle entanglement for unitarily invariant three-particle states and use it to identify genuine multipartite entangled states whose partial transposes with respect to all bipartitions are positive. Finally, we consider generalizations with less symmetry and discuss potential applications.