Hierarchy of correlation quantifiers comparable to negativity

TL;DR

This paper introduces a family of correlation measures based on a new distance approach, positioning negativity within this framework, and compares these measures to existing entropy-based quantifiers to enhance computability and comparability.

Contribution

It develops a new distance-based framework for correlation measures, integrating negativity and enabling direct comparison with entropy-based quantifiers.

Findings

Negativity is incorporated into a new family of correlation measures.

The new measures are shown to be more computable than traditional ones.

Comparison with entropy-based measures highlights advantages and limitations.

Abstract

Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different sets of states. However, these quantifiers are usually hard to compute as their definition involves optimization aiming to find the closest states within the set. On the other hand, negativity is one of the few computable entanglement monotones, but its comparison with other correlations required further justification. Here we place negativity as part of a family of correlation measures that has a distance-based construction. We introduce a suitable distance, discuss the emerging measures and their applications, and compare them to relative entropy-based correlation quantifiers. This work is a step towards correlation measures that are simultaneously comparable and computable.