Postulates for measures of genuine multipartite correlations

A lot of research has been done on multipartite correlations, but the problem of satisfactorily defining genuine multipartite correlations-those not trivially reducible to lower partite correlations-remains unsolved. 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 the concept of 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 a candidate for a measure of genuine multipartite correlations based on the work that can be drawn from a local heat bath by means of a multipartite state.