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

Simultaneous sudden change in the exact values of geometric quantum discord and measurement induced nonlocality

Samira Nazifkar, Hakimeh Jaghouri

Published Apr 1, 2018• 0 citations
Publisher

Abstract

Recent studies show that two completely distinct fields as quantum information and string theory realization can be related and share some of the same properties. So, the knowledge on quantum information of some special quantum systems provides new insights on the sting theory. We analytically study geometric discord and measurement induced nonlocality for a Horodeckis' 33 bound entangled state to find quantum correlation. We find that there is a simultaneous sudden change point in the geometric discord and the measurement-induced nonlocality in the region of the bound entangled states, which is considerable. Moreover, we investigate the lower bound of geometric discord and the upper bound of measurement-induced nonlocality for this system. This study leads to some new and interesting novel results as well.

DOI
10.22128/ijaa.2018.134

Related papers

Sudden change in quantum discord accompanying the transition from bound to free entanglement

Xiaokun Yan, Guo‐Hua Liu, J. Chee

We study quantum discord by using the geometric measure of quantum discord for a class of quantum states with bound entanglement. It is found that there exists a nondynamic sudden change in quantum discord accompanying transition from bound entanglement to free entanglement. The calculations presented here should be of interest to the continuing efforts to understand sudden transition of quantum correlations.

Physical Review A•Feb 26, 2013•14 citations

Relationship between average correlation and geometric measure of quantum discord for a class of two-qubit X-states

You-neng Guo, Xiaojing Ma, Hu-Ping Peng +2 more

Abstract Nonclassical correlation is widely regarded as a powerful resource offering quantum advantages in modern quantum-information processing. Various measurements of nonclassicality as well as the relations among them have recently received much attention. Motivated by works on the relations of Bell nonlocality to average correlation(one kind of nonlocal correlations) and to geometric measure of quantum discord, an interesting question arises whether one can establish directly the link of average correlation to geometric measure of quantum discord. In this paper, we address this question by concerning the link of average correlation to a fixed geometric measure of quantum discord for a specific class of two-qubit X-states. In particular, exact lower and upper bounds of average correlation versus geometric discord are derived and the respective states which have extremal bounds are also characterized. Furthermore, the their dynamical behaviors suffered from decoherence are also carefully analyzed. The results show that average correlation is closely related to geometric discord, like its relationship with Bell nonlocality.

•Apr 21, 2025•0 citations

Measurement-Induced Nonlocality

Shunlong Luo, Shuangshuang Fu

We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.

Physical Review Letters•Mar 21, 2011•356 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

Geometric measure of quantum discord under decoherence

Xiao-Ming Lu, Zhengjun Xi, Zhe Sun +1 more

The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.

arXiv:1004.5281•Quantum Information and Computation•Nov 1, 2010•41 citations

Measurement-Induced Nonlocality and Geometric Discord in the Spin-Boson Model

Guoyou Wang, Zi-Long Fan, Hao‐Sheng Zeng

Dynamics of measurement-induced-nonlocality (MIN) and geometric measure of discord (GD) in the spin-boson model is studied. Analytical results show that for two large classes of initial states, MINs are equal but GDs are different. At the end of evolution, MIN and GD initially stored in the spin system transfer completely to reservoirs. The quantum beats for MIN and GD are also found which are the results of quantum interference between two local non-Markovian dynamics via quantum correlation.

Journal of Quantum Information Science•Jan 1, 2013•0 citations
Recent studies show that two completely distinct fields as quantum information and string theory realization can be related and share some of the same properties. So, the knowledge on quantum information of some special quantum systems provides new insights on the sting theory. We analytically study geometric discord and measurement induced nonlocality for a Horodeckis' 33 bound entangled state to find quantum correlation. We find that there is a simultaneous sudden change point in the geometric discord and the measurement-induced nonlocality in the region of the bound entangled states, which is considerable. Moreover, we investigate the lower bound of geometric discord and the upper bound of measurement-induced nonlocality for this system. This study leads to some new and interesting novel results as well.
Abstract Nonclassical correlation is widely regarded as a powerful resource offering quantum advantages in modern quantum-information processing. Various measurements of nonclassicality as well as the relations among them have recently received much attention. Motivated by works on the relations of Bell nonlocality to average correlation(one kind of nonlocal correlations) and to geometric measure of quantum discord, an interesting question arises whether one can establish directly the link of average correlation to geometric measure of quantum discord. In this paper, we address this question by concerning the link of average correlation to a fixed geometric measure of quantum discord for a specific class of two-qubit X-states. In particular, exact lower and upper bounds of average correlation versus geometric discord are derived and the respective states which have extremal bounds are also characterized. Furthermore, the their dynamical behaviors suffered from decoherence are also carefully analyzed. The results show that average correlation is closely related to geometric discord, like its relationship with Bell nonlocality.
We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.
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 dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a 3×43\times43×4 matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.