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

Chinese Physics Letters

Quantum Discord for a Qutrit-Qutrit System under Depolarizing and Dephasing Noise

Yang Yang, An Min Wang

Published Aug 1, 2013• 13 citations
Publisher

Abstract

The dynamics of quantum discord for a class of qutrit-qutrit states under depolarizing and dephasing noise are investigated using the geometric measure of quantum discord. We find that in the quantum discord for these states, a sudden change near the transition point exists from a bound-entangled to a free-entangled state, and that the sudden change point remains unchanged in later evolution under depolarizing noise. Moreover, the behavior of quantum discord is independent of the parameter of the given initial states in many regions.

DOI
10.1088/0256-307x/30/8/080302

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

Sudden change of quantum discord for a system of two qubits

João Paulo Gâmbaro Pinto, Göktuğ Karpat, F. F. Fanchini

It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the $\mathsf{X}$-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits.

arXiv:1309.7945•Physical Review A•Sep 30, 2013•61 citations

Invariant quantum discord in qubit–qutrit systems under local dephasing

Göktuğ Karpat, Z. Gedik

We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit–qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit–qutrit state disappears in a finite time interval, the partial coherence left in the system enables quantum discord to remain invariant throughout the time evolution.

arXiv:1208.5705•Physica Scripta•Mar 1, 2013•21 citations

One-norm geometric quantum discord under decoherence

J. D. Montealegre, F. M. de Paula, A. Saguia +1 more

Geometric quantum discord is a well-defined measure of quantum correlation if Schatten one-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the one-norm geometric quantum discord under the effect of decoherence. By starting from arbitrary Bell-diagonal mixed states under Markovian local noise, we provide the decays of the quantum correlation as a function of the decoherence parameters. In particular, we show that the one-norm geometric discord exhibits the possibility of double sudden changes and freezing behavior during its evolution. For nontrivial Bell-diagonal states under simple Markovian channels, these are new features that are in contrast with the Schatten two-norm (Hilbert-Schmidt) geometric discord. The necessary and sufficient conditions for double sudden changes as well as their exact locations in terms of decoherence probabilities are provided. Moreover, we illustrate our results by investigating decoherence in quantum spin chains in the thermodynamic limit.

arXiv:1303.5110•Physical Review A•Apr 22, 2013•130 citations

Comparison of different measures for quantum discord under non-Markovian noise

Z Y Xu, Wan Li Yang, Xianbo Xiao +1 more

Two geometric measures for quantum discord were recently proposed by Modi et al (2010 Phys. Rev. Lett. 104 080501) and Dakić et al (2010 Phys. Rev. Lett. 105 190502). We study the similarities and differences for total quantum correlations of Bell-diagonal states using these two geometry-based quantum discord and the original quantum discord. We show that, under non-Markovian dephasing channels, quantum discord and one of the geometric measures remain constant for a finite amount of time, but not the other geometric measure. However, all the three measures share a common sudden change point. Our study on critical point of sudden transition might be useful for keeping long-time total quantum correlations under decoherence.

arXiv:1010.3521•Journal of Physics A Mathematical and Theoretical•Sep 8, 2011•20 citations

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
The dynamics of quantum discord for a class of qutrit-qutrit states under depolarizing and dephasing noise are investigated using the geometric measure of quantum discord. We find that in the quantum discord for these states, a sudden change near the transition point exists from a bound-entangled to a free-entangled state, and that the sudden change point remains unchanged in later evolution under depolarizing noise. Moreover, the behavior of quantum discord is independent of the parameter of the given initial states in many regions.
It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the X\mathsf{X}X-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits.
Geometric quantum discord is a well-defined measure of quantum correlation if Schatten one-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the one-norm geometric quantum discord under the effect of decoherence. By starting from arbitrary Bell-diagonal mixed states under Markovian local noise, we provide the decays of the quantum correlation as a function of the decoherence parameters. In particular, we show that the one-norm geometric discord exhibits the possibility of double sudden changes and freezing behavior during its evolution. For nontrivial Bell-diagonal states under simple Markovian channels, these are new features that are in contrast with the Schatten two-norm (Hilbert-Schmidt) geometric discord. The necessary and sufficient conditions for double sudden changes as well as their exact locations in terms of decoherence probabilities are provided. Moreover, we illustrate our results by investigating decoherence in quantum spin chains in the thermodynamic limit.
Two geometric measures for quantum discord were recently proposed by Modi et al (2010 Phys. Rev. Lett. 104 080501) and Dakić et al (2010 Phys. Rev. Lett. 105 190502). We study the similarities and differences for total quantum correlations of Bell-diagonal states using these two geometry-based quantum discord and the original quantum discord. We show that, under non-Markovian dephasing channels, quantum discord and one of the geometric measures remain constant for a finite amount of time, but not the other geometric measure. However, all the three measures share a common sudden change point. Our study on critical point of sudden transition might be useful for keeping long-time total quantum correlations under decoherence.
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.