Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1112.2767 · Journal of Physics A Mathematical and Theoretical

Quantum discord: ‘discord’ between the whole and its constituent

Xi-Jun Ren, Heng Fan

Published Oct 9, 2012• 0 citations
arXivHTMLPDF

Abstract

Quantum discord, a measure of quantum correlation beyond entanglement, is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information. In this paper, we report some new interpretations of discord which rely on the differences between measurement-induced effects on the local measured system and the whole system. Specifically, with proper quantitative definitions introduced in Buscemi et al (2008 Phys. Rev. Lett. 100 210504), we find that quantum discord can be interpreted as the differences of measurement-induced disturbance or information gain on the local measured system and on the whole system. Combined with previous similar results based on measurement-induced entanglement and decoherence, our results provide a unified view on quantum discord.

DOI
10.1088/1751-8113/45/42/425304

Related papers

Nonzero Classical Discord

Vlad Gheorghiu, M. C. de Oliveira, Barry C. Sanders

Quantum discord is the quantitative difference between two alternative expressions for bipartite mutual information, given respectively in terms of two distinct definitions for the conditional entropy. By constructing a stochastic model of shared states, classical discord can be similarly defined, quantifying the presence of some stochasticity in the measurement process. Therefore, discord can generally be understood as a quantification of the system's state disturbance due to local measurements, be it quantum or classical. We establish an operational meaning of classical discord in the context of state merging with noisy measurement and thereby show the quantum-classical separation in terms of a negative conditional entropy.

arXiv:1407.5507•Physical Review Letters•Jul 14, 2015•9 citations

Quantum discord for two-qubit systems

Shunlong Luo

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.

Physical Review A•Apr 3, 2008•1,060 citations

Unification of different views of decoherence and discord

Patrick J. Coles

Macroscopic behavior such as the lack of interference patterns has been attributed to ``decoherence,'' a word with several possible definitions such as (1) the loss of off-diagonal density matrix elements, (2) the flow of information to the environment, (3) the loss of complementary information, and (4) the loss of the ability to create entanglement in a measurement. In this article, we attempt to unify these distinct definitions by providing general quantitative connections between them, valid for all finite-dimensional quantum systems or quantum processes. The most important application of our results is to the understanding of quantum discord, a measure of the nonclassicality of the correlations between quantum systems. We show that some popular measures of discord measure the information missing from the purifying system and hence quantify security, which can be stated operationally in terms of distillable secure bits. The results also give some strategies for constructing discord measures.

arXiv:1110.1664•Physical Review A•Apr 3, 2012•57 citations

Revised Definitions of Quantum Dissonance and Quantum Discord

Zhanjun Zhang

We show that all the correlations defined by K. Modi et al [Phys. Rev. Lett. {\bf 104}, 080501 (2010)] except for the total mutual information should be redefined so that some physical quantities (e.g., the accessible maximal classical correlation and the resultant exact quantum discord) are right.

arXiv:1011.4333•Nov 19, 2010•3 citations

Comparison of the attempts of quantum discord and quantum entanglement to capture quantum correlations

Asma Al-Qasimi, Daniel F. V. James

Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.

Physical Review A•Mar 2, 2011•87 citations

Entanglement as minimal discord over state extensions

Shunlong Luo

The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.

Physical Review A•Sep 29, 2016•18 citations
Quantum discord, a measure of quantum correlation beyond entanglement, is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information. In this paper, we report some new interpretations of discord which rely on the differences between measurement-induced effects on the local measured system and the whole system. Specifically, with proper quantitative definitions introduced in Buscemi et al (2008 Phys. Rev. Lett. 100 210504), we find that quantum discord can be interpreted as the differences of measurement-induced disturbance or information gain on the local measured system and on the whole system. Combined with previous similar results based on measurement-induced entanglement and decoherence, our results provide a unified view on quantum discord.
Quantum discord is the quantitative difference between two alternative expressions for bipartite mutual information, given respectively in terms of two distinct definitions for the conditional entropy. By constructing a stochastic model of shared states, classical discord can be similarly defined, quantifying the presence of some stochasticity in the measurement process. Therefore, discord can generally be understood as a quantification of the system's state disturbance due to local measurements, be it quantum or classical. We establish an operational meaning of classical discord in the context of state merging with noisy measurement and thereby show the quantum-classical separation in terms of a negative conditional entropy.
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.
Macroscopic behavior such as the lack of interference patterns has been attributed to ``decoherence,'' a word with several possible definitions such as (1) the loss of off-diagonal density matrix elements, (2) the flow of information to the environment, (3) the loss of complementary information, and (4) the loss of the ability to create entanglement in a measurement. In this article, we attempt to unify these distinct definitions by providing general quantitative connections between them, valid for all finite-dimensional quantum systems or quantum processes. The most important application of our results is to the understanding of quantum discord, a measure of the nonclassicality of the correlations between quantum systems. We show that some popular measures of discord measure the information missing from the purifying system and hence quantify security, which can be stated operationally in terms of distillable secure bits. The results also give some strategies for constructing discord measures.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.