Genuine quantum and classical correlations in multipartite systems

TL;DR

This paper introduces a framework for quantifying genuine total, quantum, and classical correlations in multipartite quantum systems using relative entropy, and explores their properties in three-qubit pure states.

Contribution

It generalizes correlation measures from bipartite to multipartite systems and establishes a ladder ordering law for correlations in three-qubit pure states.

Findings

Genuine correlations are quantified using relative entropy.

Quantum and classical bipartite correlations follow a ladder ordering law.

The law is determined by two-body mutual informations or one-qubit entropies.

Abstract

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the "distance" between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.