© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1811.08066 · Journal of Physics B Atomic Molecular and Optical Physics

Gaussian multipartite quantum discord from classical mutual information

Mark Bradshaw, Ping Koy Lam, Syed M. Assad

Published Sep 13, 2019• 2 citations

Abstract

Abstract Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be defined by the mutual information of the multipartite measurement outcomes. In general the quantum discord of an arbitrary quantum state involves an optimisation of over the classical measurements which is hard to compute. In this paper, we examine the quantum discord in the experimentally relevant case when the quantum states are Gaussian and the measurements are restricted to Gaussian measurements. We perform the optimisation over the measurements to find the Gaussian discord of the bipartite EPR state and tripartite GHZ state in the presence of different types of noise: uncorrelated noise, multiplicative noise and correlated noise. We find that by adding uncorrelated noise and multiplicative noise, the quantum discord always decreases. However, correlated noise can either increase or decrease the quantum discord. We also find that for low noise, the measurements that maximise the classically accessible correlations are single quadrature measurements. As the noise increases, a dual quadrature measurement becomes optimal.

DOI: 10.1088/1361-6455/ab443c

Related papers

Multipartite Generalization of Quantum Discord

Chandrashekar Radhakrishnan, Mathieu Laurière, Tim Byrnes

A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.

arXiv:1909.08194•Physical Review Letters•Mar 16, 2020•60 citations

Quantum discord for Gaussian states with non-Gaussian measurements

Paolo Giorda, Michele Allegra, Matteo G. A. Paris

In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous-variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states and mixed thermal states, and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.

arXiv:1206.1807•Physical Review A•Nov 27, 2012•31 citations

Experimental determination of tripartite quantum discord

Vaishali Gulati, Shaileyee Bhowmick, Tim Byrnes +2 more

Quantum discord is a measure of nonclassical correlations in quantum systems. While the bipartite version of quantum discord is experimentally well-studied, the multipartite version has never been convincingly measured. In this study, we experimentally investigate tripartite quantum discord using an NMR quantum information processor. Building on a theoretical framework for conditional projective measurements and quantum conditional mutual information, we quantify the tripartite quantum discord and its contributions in different three-qubit states such as the Greenberger-Horne-Zeilinger (GHZ) and Werner (W) states as well as classical mixtures of biseparable Bell states, and classical mixtures of product states. The experiments employed full quantum state tomography and temporal averaging to prepare mixed states, achieving fidelities exceeding 95%. Our results confirm that quantum discord persists even in the absence of entanglement, highlighting its utility as a broader indicator of quantum correlations. Furthermore, we validate the nonconvexity of discord, confirming that classical mixtures of zero-discord states can exhibit nonzero discord. This experimentally confirms that quantum discord does not fit into the framework of resource theory. This work establishes a robust methodology for measuring quantum discord, illuminating the structure and distribution of quantum correlations in multipartite systems.

Proceedings of the National Academy of Sciences•Jul 2, 2025•3 citations

Experimental verification of quantum discord in continuous-variable states and operational significance of discord consumption

Sara Hosseini, Saleh Rahimi-Keshari, Jing Yan Haw +9 more

We introduce a simple and efficient technique to verify quantum discord in unknown Gaussian states and certain class of non-Gaussian states. We show that any separation in the peaks of the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurements performed on the other subsystem indicates correlation between the corresponding quadratures and hence nonzero quantum discord. We also demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interaction.

•Jan 1, 2014•2 citations

Quantum discord for two-qubit X states

Mazhar Ali, A. R. P. Rau, G. Alber

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called $X$ states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.

arXiv:1002.3429•Physical Review A•Apr 12, 2010•835 citations

Experimental Investigation of the Evolution of Gaussian Quantum Discord in an Open System

Lars S. Madsen, Adriano Berni, Mikael Lassen +1 more

Gaussian quantum discord is a measure of quantum correlations in gaussian systems. Using gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipation on gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation.

arXiv:1204.2738•Physical Review Letters•Jul 17, 2012•65 citations

Abstract Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be defined by the mutual information of the multipartite measurement outcomes. In general the quantum discord of an arbitrary quantum state involves an optimisation of over the classical measurements which is hard to compute. In this paper, we examine the quantum discord in the experimentally relevant case when the quantum states are Gaussian and the measurements are restricted to Gaussian measurements. We perform the optimisation over the measurements to find the Gaussian discord of the bipartite EPR state and tripartite GHZ state in the presence of different types of noise: uncorrelated noise, multiplicative noise and correlated noise. We find that by adding uncorrelated noise and multiplicative noise, the quantum discord always decreases. However, correlated noise can either increase or decrease the quantum discord. We also find that for low noise, the measurements that maximise the classically accessible correlations are single quadrature measurements. As the noise increases, a dual quadrature measurement becomes optimal.

A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.

In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous-variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states and mixed thermal states, and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.

Quantum discord is a measure of nonclassical correlations in quantum systems. While the bipartite version of quantum discord is experimentally well-studied, the multipartite version has never been convincingly measured. In this study, we experimentally investigate tripartite quantum discord using an NMR quantum information processor. Building on a theoretical framework for conditional projective measurements and quantum conditional mutual information, we quantify the tripartite quantum discord and its contributions in different three-qubit states such as the Greenberger-Horne-Zeilinger (GHZ) and Werner (W) states as well as classical mixtures of biseparable Bell states, and classical mixtures of product states. The experiments employed full quantum state tomography and temporal averaging to prepare mixed states, achieving fidelities exceeding 95%. Our results confirm that quantum discord persists even in the absence of entanglement, highlighting its utility as a broader indicator of quantum correlations. Furthermore, we validate the nonconvexity of discord, confirming that classical mixtures of zero-discord states can exhibit nonzero discord. This experimentally confirms that quantum discord does not fit into the framework of resource theory. This work establishes a robust methodology for measuring quantum discord, illuminating the structure and distribution of quantum correlations in multipartite systems.

We introduce a simple and efficient technique to verify quantum discord in unknown Gaussian states and certain class of non-Gaussian states. We show that any separation in the peaks of the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurements performed on the other subsystem indicates correlation between the corresponding quadratures and hence nonzero quantum discord. We also demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interaction.

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called

X

states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.

Gaussian quantum discord is a measure of quantum correlations in gaussian systems. Using gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipation on gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation.