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:1502.02331 · New Journal of Physics

Operational discord measure for Gaussian states with Gaussian measurements

Saleh Rahimi-Keshari, Timothy C. Ralph, Carlton M. Caves

Published Jun 29, 2015• 4 citations
arXivHTMLPDF

Abstract

We introduce an operational discord-type measure for quantifying nonclassical correlations in bipartite Gaussian states based on using Gaussian measurements. We refer to this measure as operational Gaussian discord (OGD). It is defined as the difference between the entropies of two conditional probability distributions associated to one subsystem, which are obtained by performing optimal local and joint Gaussian measurements. We demonstrate the operational significance of this measure in terms of a Gaussian quantum protocol for extracting maximal information about an encoded classical signal. As examples, we calculate OGD for several Gaussian states in the standard form.

DOI
10.1088/1367-2630/17/6/063037

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

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

Quantumness of bipartite states in terms of conditional entropies

Nan Li, Shunlong Luo, Zhengmin Zhang

Quantum discord, as defined by Olliver and Zurek (2002 Phys. Rev. Lett. 88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver–Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples.

Journal of Physics A Mathematical and Theoretical•Aug 29, 2007•10 citations

Discrimination of discord in separable Gaussian states

Gaetana Spedalieri, Stefano Pirandola, Samuel L. Braunstein

Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.

arXiv:1807.01992•Quantum Communications and Quantum Imaging•Sep 18, 2018•0 citations

Measurement-based method for verifying quantum discord

Saleh Rahimi-Keshari, Carlton M. Caves, Timothy C. Ralph

We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete positive operator valued measurement (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVM's are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.

arXiv:1209.2221•Physical Review A•Jan 17, 2013•25 citations

Nonclassicality by Local Gaussian Unitary Operations for Gaussian States

Yangyang Wang, Xiaofei Qi, Jinchuan Hou

A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B ) < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 ) -mode Gaussian states and an estimate of N for ( n + m ) -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.

Entropy•Apr 11, 2018•6 citations
We introduce an operational discord-type measure for quantifying nonclassical correlations in bipartite Gaussian states based on using Gaussian measurements. We refer to this measure as operational Gaussian discord (OGD). It is defined as the difference between the entropies of two conditional probability distributions associated to one subsystem, which are obtained by performing optimal local and joint Gaussian measurements. We demonstrate the operational significance of this measure in terms of a Gaussian quantum protocol for extracting maximal information about an encoded classical signal. As examples, we calculate OGD for several Gaussian states in the standard form.
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.
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, as defined by Olliver and Zurek (2002 Phys. Rev. Lett. 88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver–Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples.
Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.
We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete positive operator valued measurement (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVM's are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.
A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B ) < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 ) -mode Gaussian states and an estimate of N for ( n + m ) -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.