The problem with the geometric discord

We argue that the geometric discord introduced in [B. Dakic, V. Vedral, and C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality/non-classicality is not tested. On the other hand it is known that the standard, mutual-information based discord does not suffer this problem; a simplified proof of such a fact is given.Comment: 5 pages. Changes in ver 2: typos corrected, added short proof of monotonicity of standard quantum discord under one-side action. This note is meant to stimulate discussion in the community: comments are welcom

Quantum Correlations in Multipartite Quantum Systems

We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlationsComment: to be published as a chapter of the book "Lectures on general quantum correlations and their applications" edited by F. Fanchini, D. Soares-Pinto, and G. Adesso (Springer, 2017

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

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.Comment: Close to the published versio

Diagonal quantum discord

Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement. This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices. In contrast to the optimized discord, diagonal discord is easily computable; it also finds connections to thermodynamics and resource theory. Here we further show that, for the generic case of non-degenerate local density matrices, diagonal discord exhibits desirable properties as a preferable discord measure. We employ the theory of resource destroying maps [Liu/Hu/Lloyd, PRL 118, 060502 (2017)] to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels, $d>2$, and provide numerical evidence that such monotonicity holds for qubit channels as well. We also show that it is continuous, and derive a Fannes-like continuity bound. Our results hold for a variety of simple discord measures generalized from diagonal discord.Comment: 15 pages, 3 figures; published versio

Quantum discord and multipartite correlations

Recently, it was realized that quantum discord can be seen as the minimal amount of correlations which are lost when some local quantum operations are performed. Based on this formulation of quantum discord, we provide a systematical analysis of quantum and classical correlations present in both bipartite and multipartite quantum systems. As a natural result of this analysis, we introduce a new measure of the overall quantum correlations which is lower bounded by quantum discord.Comment: 7 page