Unified view of correlations using the square norm distance

TL;DR

This paper explores a unified framework for quantum correlations using the square norm distance, deriving explicit formulas for total, quantum, and classical correlations, and analyzing their interrelations.

Contribution

It introduces a geometric approach to quantify correlations with the square norm, extending previous methods and analyzing their relationships for bipartite states.

Findings

Explicit formulas for geometric total, quantum, and classical correlations.

The geometric correlations do not satisfy a closed additivity relation.

The approach generalizes the geometric quantum discord concept.

Abstract

The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated in a quantum and a classical part thanks to an additive relation involving only distances between states. Here, we investigate a unified view of correlations using as distance measure the square norm, already used to define the so-called geometric quantum discord. We thus consider geometric quantifiers also for total and classical correlations finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum and classical correlations and we find that they do not satisfy anymore a closed additivity relation.