Genuine Correlations of Tripartite System

TL;DR

This paper introduces a measure for genuine tripartite correlations in quantum systems, distinguishing between total, classical, and quantum correlations, and provides analytical expressions for specific states.

Contribution

It proposes a new measure for genuine tripartite correlations based on bipartition analysis and derives analytical formulas for pure and rank-2 symmetrical states.

Findings

Genuine tripartite total and classical correlations are at least as large as pairwise correlations.

Genuine quantum tripartite correlation can be less than pairwise quantum correlations.

Analytical expressions are obtained for pure and rank-2 symmetrical states.

Abstract

We define genuine total, classical and quantum correlations in tripartite systems. The measure we propose is based on the idea that genuine tripartite correlation exists if and only if the correlation between any bipartition does not vanish. We find in a symmetrical tripartite state, for total correlation and classical correlation, the genuine tripartite correlations are no less than pair-wise correlations. However, the genuine quantum tripartite correlation can be surpassed by the pair-wise quantum correlations. Analytical expressions for genuine tripartite correlations are obtained for pure states and rank-2 symmetrical states. The genuine correlations in both entangled and separable states are calculated.