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

TLDR

Nonclassicality in quantum systems is often signaled by correlations lacking classical counterparts, and while entanglement is the most prominent such correlation, many unentangled states also display nonclassical behavior, making the quantification of quantum versus classical correlations a key topic in quantum‑information theory. The study aims to distinguish quantum correlations beyond entanglement to better separate quantum from classical behavior, particularly for mixed states. The authors review the mathematical properties of quantum‑discord–based measures, their interrelations, and the common classical‑quantum division, then demonstrate how these measures quantify deviations from classicality across quantum‑information tasks, thermodynamics, open‑system dynamics, and many‑body physics. The review shows that quantum correlations often confer advantages to quantum methods over classical ones.

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 among 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 different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown 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. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.