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 Journal of Quantum Electronics

Geometric measurement of quantum correlation for a kind of X-state

Weijun Gui

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Quantum discord(QD) can be used to characterize quantum correlation of a quantum system. Based on geometric measurement of QD(GMQD),quantum correlation of the single-parameter X- state was calculated,and the results for the case were also given under three different quantum channels.For the amplitude-damping channel,by comparing concurrence and GMQD of the X-state mentioned above using graphical method,it's concluded that GMQD exhibits more robust than concurrence when the quantum system is exposed to environment.

Related papers

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

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

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

Quantum Correlations in Heisenberg XY Chain

Yinyan Zhu, Yong Zhang

Quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing D z increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.

Communications in Theoretical Physics•Apr 1, 2013•4 citations

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

Dynamics of quantum discord and geometric quantum discord in multiqubit interacting system

Xiao-Di 晓迪 Cheng 程, Ya‐Jun Zheng, Meng-Jie 梦杰 Ran 冉 +1 more

Abstract Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole–dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.

Chinese Physics B•Apr 8, 2025•0 citations
Quantum discord(QD) can be used to characterize quantum correlation of a quantum system. Based on geometric measurement of QD(GMQD),quantum correlation of the single-parameter X- state was calculated,and the results for the case were also given under three different quantum channels.For the amplitude-damping channel,by comparing concurrence and GMQD of the X-state mentioned above using graphical method,it's concluded that GMQD exhibits more robust than concurrence when the quantum system is exposed to environment.
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.
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.
Quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing D z increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.
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.
Abstract Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole–dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.