Multiparticle entanglement classification with ergotropic gap

TL;DR

This paper links quantum multipartite entanglement to thermodynamic ergotropic gaps, introducing a classification method based on ergotropic gap indicators and geometric measures.

Contribution

It establishes a relation between entanglement measures and ergotropic gaps, and introduces a new classification criterion for multipartite entanglement using ergotropic gap indicators.

Findings

Marginal ergotropic gaps form a convex polytope for each SLOCC class

A refined criterion for entanglement classification under SLOCC is proposed

Relation between geometric entanglement measure and ergotropic gaps is established

Abstract

The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We establish a direct relation between the geometric measure of entanglement and the ergotropic gaps. We show that all the marginal ergotropic gaps form a convex polytope for each class of quantum states that are equivalent under stochastic local operations and classical communication (SLOCC). We finally introduce the concept of multipartite ergotropic gap indicators and use them to present a refined criterion for classifying entanglement under SLOCC.