The classical-quantum boundary for correlations: discord and related measures

TL;DR

This paper reviews how quantum discord and related measures quantify nonclassical correlations in quantum systems, highlighting their mathematical properties and their role in quantum information processing, thermodynamics, and many-body physics.

Contribution

It provides a comprehensive review of quantum discord and related measures, clarifying their properties, relationships, and significance in various quantum phenomena.

Findings

Quantum correlations often indicate advantages in quantum information tasks.

Measures of quantum discord reveal nonclassicality beyond entanglement.

Quantum correlations are relevant in thermodynamics and many-body physics.

Abstract

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.