Can multipartite entanglement be characterized by two-point connected correlation functions ?

TL;DR

This paper investigates whether multipartite entanglement in mixed quantum states can be fully characterized by two-point connected correlation functions, identifying specific conditions where this is possible.

Contribution

It establishes conditions under which multipartite entanglement in mixed states can be characterized solely by two-point correlations, extending understanding from pure to mixed states.

Findings

Two-point connected correlations can characterize multipartite entanglement under specific conditions.

Point-independence of one-point correlations in all decompositions is a key criterion.

Operators with (semi-)positive/negative definiteness facilitate this characterization.

Abstract

We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.