Postulates for measures of genuine multipartite correlations

TL;DR

This paper establishes foundational postulates for measuring genuine multipartite correlations, critiques existing measures like covariance, and proposes a new candidate measure based on local bath work extraction.

Contribution

It introduces three postulates for genuine multipartite correlation measures, analyzes covariance's inadequacy, and proposes a novel measure based on local bath work extraction.

Findings

Covariance fails two postulates for genuine correlations

Proposed a new measure based on local bath work extraction

Degree of correlations offers partial characterization

Abstract

A lot of research has been done on multipartite correlations. However, it seems strange that there is no definition of so called genuine multipartite correlations. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce degree of correlations which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence, it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose candidate for a measure of genuine multipartite correlations based on the work that can be drawn from local bath by means of a multipartite state.