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:1301.1961 · Physical Review A

Comment on “Witnessed entanglement and the geometric measure of quantum discord”

Swapan Rana, Preeti Parashar

Published Jan 22, 2013• 23 citations
arXivHTMLPDF

Abstract

In a recent article [Phys. Rev. A 86, 024302 (2012)], the authors have derived some hierarchy relations between geometric discord and entanglement (measured by negativity and its square). We point out that these results are incorrect and give analytic counterexamples. We also briefly discuss the reason for such violations.
DOI
10.1103/physreva.87.016301

Related papers

Reply to “Comment on ‘Witnessed entanglement and the geometric measure of quantum discord’ ”

Tiago Debarba, Thiago O. Maciel, Reinaldo O. Vianna

We show that the mistakes pointed out by Rana and Parashar [Phys. Rev. A 87, 016301 (2013)] do not invalidate the main conclusion of our work [Phys. Rev. A 86, 024302 (2012)]. We show that the errors affected only a particular application of our general results, and present the correction.

arXiv:1304.3864•Physical Review A•Apr 9, 2013•6 citations

Witnessed entanglement and the geometric measure of quantum discord

Tiago Debarba, Thiago O. Maciel, Reinaldo O. Vianna

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which has been conjectured before [D. Girolami and G. Adesso, Phys. Rev. A 84, 052110 (2011)]. We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically for Werner states and for families of bound entangled states.

arXiv:1207.1298•Physical Review A•Aug 27, 2012•90 citations

Comment on “Sudden change in quantum discord accompanying the transition from bound to free entanglement”

Swapan Rana, Preeti Parashar

In a recent article [Phys. Rev. A 87, 022340 (2013)], Yan et al. have studied geometric discord for a well-known class of bound entangled states. Based on their calculation, they claim ``It is found that there exists a nondynamic sudden change in quantum discord'' for these states. In this Comment, we criticize their work by pointing out that what has been calculated is actually a bound and is not the exact value of discord. Since, generally, it is not possible to infer the exact value (or property) of a quantity just from its bound, we cannot conclude about (exact) discord and its change. Thus, the above-mentioned conclusion cannot be drawn from the calculations of the paper.

arXiv:1309.6890•Physical Review A•Sep 16, 2013•1 citation

Comparative study of quantum discord and geometric discord for generic bipartite states

Bao Liu, Zheng Hu, Xi-Wen Hou

The characterization of quantum discord (QD) and geometric discord (GD) has mostly concentrated on two-qubit states since the minimization in both discords is a daunting task for high-dimensional states. Numerical calculations of both discords are carried out for a generic bipartite state. When one-dimensional orthogonal projectors for a local measurement on n-dimensional Hilbert space are realized by the generators and the Euler angles of SU (n), the optimal measurements have a figure of merit that includes n(n - 1) Euler parameters. As an representative example, such projectors and two kinds of algorithms are used to estimate both discords for two-qutrit mixed states in recent literature. The generalized negativity as a measure of quantum entanglement is calculated for reference purposes. For those states with one parameter the discords and the negativity respectively display the nonlinear and the linear function of the parameter, with different turning points. However, they are positively correlated in the suitable ranges of the parameter for those states. The hierarchy of those quantities is discussed as well. Those shed new light on the understanding of QDs and quantum entanglement of mixed states in high-dimensions.

International Journal of Quantum Information•Aug 1, 2014•6 citations

Peculiarities of quantum discord’s geometric measure

Josep Amengual i Batle, Angel Ricardo Plastino, Angel Ricardo Plastino +1 more

Some properties of the quantum discord based on the geometric measure advanced by Dakic et al (2010 Phys. Rev. Lett. 105 190502 ) are discussed here by recourse to a systematic survey of the two-qubit state-space, with emphasis on Werner and MEM states. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario. Some considerations regarding the XY model are also made.

Journal of Physics A Mathematical and Theoretical•Nov 25, 2011•13 citations

Properties of a geometric measure for quantum discord

Josep Amengual i Batle, Angel Ricardo Plastino, Plastino, A. R. +1 more

We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.

arXiv:1103.0704•Mar 3, 2011•2 citations
We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which has been conjectured before [D. Girolami and G. Adesso, Phys. Rev. A 84, 052110 (2011)]. We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically for Werner states and for families of bound entangled states.
In a recent article [Phys. Rev. A 87, 022340 (2013)], Yan et al. have studied geometric discord for a well-known class of bound entangled states. Based on their calculation, they claim ``It is found that there exists a nondynamic sudden change in quantum discord'' for these states. In this Comment, we criticize their work by pointing out that what has been calculated is actually a bound and is not the exact value of discord. Since, generally, it is not possible to infer the exact value (or property) of a quantity just from its bound, we cannot conclude about (exact) discord and its change. Thus, the above-mentioned conclusion cannot be drawn from the calculations of the paper.
The characterization of quantum discord (QD) and geometric discord (GD) has mostly concentrated on two-qubit states since the minimization in both discords is a daunting task for high-dimensional states. Numerical calculations of both discords are carried out for a generic bipartite state. When one-dimensional orthogonal projectors for a local measurement on n-dimensional Hilbert space are realized by the generators and the Euler angles of SU (n), the optimal measurements have a figure of merit that includes n(n - 1) Euler parameters. As an representative example, such projectors and two kinds of algorithms are used to estimate both discords for two-qutrit mixed states in recent literature. The generalized negativity as a measure of quantum entanglement is calculated for reference purposes. For those states with one parameter the discords and the negativity respectively display the nonlinear and the linear function of the parameter, with different turning points. However, they are positively correlated in the suitable ranges of the parameter for those states. The hierarchy of those quantities is discussed as well. Those shed new light on the understanding of QDs and quantum entanglement of mixed states in high-dimensions.
Some properties of the quantum discord based on the geometric measure advanced by Dakic et al (2010 Phys. Rev. Lett. 105 190502 ) are discussed here by recourse to a systematic survey of the two-qubit state-space, with emphasis on Werner and MEM states. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario. Some considerations regarding the XY model are also made.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.