Coherent and incoherent contents of correlations

TL;DR

This paper explores the structure of quantum correlations within unitary orbits, distinguishing between coherent and incoherent correlations, and analyzes their implications for entanglement in bipartite systems.

Contribution

It introduces the concepts of coherent and incoherent correlations within unitary orbits and provides a framework to quantify classical correlations based on probability distributions.

Findings

Product states form a negligible subset of all states

All unitary orbits contain classically correlated states

Entanglement is analyzed within this correlation framework for two-qubit systems

Abstract

We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated states. Using this we give meaning to degeneration of quantum correlations due to a unitary interactions, which we call coherent correlations. The remaining classical correlations are called incoherent correlations and quantified in terms of the distance of the joint probability distributions to its marginals. Finally, we look at how entanglement looks in this picture for the two-qubit case.