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:1004.5281 · Quantum Information and Computation

Geometric measure of quantum discord under decoherence

Xiao-Ming Lu, Zhengjun Xi, Zhe Sun, Xiaoguang Wang

Published Nov 1, 2010• 41 citations
arXivHTMLPDF

Abstract

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.

DOI
10.26421/qic10.11-12-9

Related papers

Geometric measure of quantum discord under decoherence

LuXiao-Ming, XiZhengjun, SunZhe +1 more

The dynamics of a geometric measure of the quantum discord (GMQD) under decoher-ence is investigated. We show that the GMQD of a two-qubit state can be alternativelyobtained through the singular va...

Quantum Information and Computation•Nov 1, 2010•0 citations

Pairwise correlations via quantum discord and its geometric measure in a four-qubit spin chain

Abdel‐Baset A. Mohamed

The dynamic of pairwise correlations, including quantum entanglement (QE) and discord (QD) with geometric measure of quantum discord (GMQD), are shown in the four-qubit Heisenberg XX spin chain. The results show that the effect of the entanglement degree of the initial state on the pairwise correlations is stronger for alternate qubits than it is for nearest-neighbor qubits. This parameter results in sudden death for QE, but it cannot do so for QD and GMQD. With different values for this entanglement parameter of the initial state, QD and GMQD differ and are sensitive for any change in this parameter. It is found that GMQD is more robust than both QD and QE to describe correlations with nonzero values, which offers a valuable resource for quantum computation.

Journal of the Egyptian Mathematical Society•Dec 14, 2012•14 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

Sudden decoherence transitions for quantum discord

Hyungjun Lim, Robert Joynt

We investigate the disappearance of discord in 2- and multi-qubit systems subject to decohering influences. We formulate the computation of quantum discord and quantum geometric discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits, but a similar statement for global entropic discord is more difficult to prove. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states. In agreement with previous work for 2-qubit cases (Mazzola et al 2010 Phys. Rev. Lett. 104 200401), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small.

arXiv:1309.6355•Journal of Physics A Mathematical and Theoretical•Mar 18, 2014•6 citations

Geometric measure of quantum discord for superpositions of Dicke states

Xiaolei Yin, Zhengjun Xi, Xiao-Ming Lu +2 more

The pairwise quantum correlations of symmetric multi-qubit states are studied by using the geometric measure of quantum discord (GMQD). The explicit expressions of the GMQD for the Dicke states and their superpositions are given. By comparing the GMQD with quantum discord, we conclude that they display similar behaviour. From the results, we know that most of the states we have considered exhibit pairwise quantum correlations.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 29, 2011•20 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
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.
The dynamic of pairwise correlations, including quantum entanglement (QE) and discord (QD) with geometric measure of quantum discord (GMQD), are shown in the four-qubit Heisenberg XX spin chain. The results show that the effect of the entanglement degree of the initial state on the pairwise correlations is stronger for alternate qubits than it is for nearest-neighbor qubits. This parameter results in sudden death for QE, but it cannot do so for QD and GMQD. With different values for this entanglement parameter of the initial state, QD and GMQD differ and are sensitive for any change in this parameter. It is found that GMQD is more robust than both QD and QE to describe correlations with nonzero values, which offers a valuable resource for quantum computation.
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.
We investigate the disappearance of discord in 2- and multi-qubit systems subject to decohering influences. We formulate the computation of quantum discord and quantum geometric discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits, but a similar statement for global entropic discord is more difficult to prove. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states. In agreement with previous work for 2-qubit cases (Mazzola et al 2010 Phys. Rev. Lett. 104 200401), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small.
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.