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:1602.05451 · Chinese Physics B

Geometric global quantum discord of two-qubit states

Yunlong Xiao, Tao Li, Shao-Ming Fei, Naihuan Jing, Zhi-Xi Wang, Xianqing Li-Jost

Published Mar 1, 2016• 4 citations
arXivHTMLPDF

Abstract

We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.

DOI
10.1088/1674-1056/25/3/030301

Related papers

Geometric global quantum discord

Jianwei Xu

Geometric quantum discord, proposed by Dakic et al (2010 Phys. Rev. Lett. 105 190502), is an important measure for bipartite correlations. In this paper, we generalize it to multipartite states, we call the generalized version geometric global quantum discord (GGQD). We characterize GGQD in different ways, give a lower bound for GGQD and provide some special states which allow analytical GGQD.

arXiv:1205.0330•Journal of Physics A Mathematical and Theoretical•Sep 19, 2012•12 citations

Geometric global quantum discord

Jianwei Xu

Geometric quantum discord, proposed by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502], is an important measure for bipartite correlations. In this paper, we generalize it to multipartite states, we call the generalized version geometric global quantum discord (GGQD). We characterize GGQD in different ways, and provide some special states which allow analytical GGQD.

•Aug 17, 2016•10 citations

Quantum discord for general two-qubit states: Analytical progress

Davide Girolami, Gerardo Adesso

We present a reliable algorithm to evaluate quantum discord for general two-qubit states, amending and extending an approach recently put forward for the subclass of $X$ states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of nonclassical correlations, namely, the geometric discord. We identify the extremally nonclassically correlated two-qubit states according to the (normalized) geometric discord, at a fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits.

arXiv:1103.3189•Physical Review A•May 9, 2011•317 citations

Geometric quantum discord of an arbitrary two-qudit state: Exact value and general upper bounds

Elena R. Loubenets, Louis Hanotel

The geometric quantum discord of a two-qudit state has been studied in many papers; however, its exact analytical value in the explicit form is known only for a general two-qubit state, a general qubit-qudit state, and some special families of two-qudit states. Based on the general Bloch vectors formalism [E. R. Loubenets et al., J. Phys. A: Math. Theor. 54, 195301 (2021)], we find the explicit exact analytical value of the geometric quantum discord for an arbitrary two-qudit state of any dimension via the parameters of its correlation matrix and the Bloch vectors of its reduced states. This general analytical result includes all the known exact results on the geometric quantum discord only as particular cases and proves rigorously that the lower bound on the geometric discord presented in [S. Rana et al., Phys. Rev. A 85, 024102 (2012)] constitutes its exact value for each two-qudit state. Moreover, our general result allows us to find for an arbitrary two-qudit state, pure or mixed, the upper and lower bounds on its geometric quantum discord, expressed via the Hilbert space characteristics of this state.

arXiv:2403.09342•Physical Review A•Sep 10, 2024•4 citations

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States*

Chuanmei Xie, Yimin Liu, Hang Xing +1 more

Abstract Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [ Phys. Rev. Lett. 105 (2010) 190502 ] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.

Communications in Theoretical Physics•Apr 1, 2015•1 citation

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

谢传梅, 刘益民, 邢航 +1 more

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.

理论物理通讯：英文版•Jan 1, 2015•0 citations
We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.
We present a reliable algorithm to evaluate quantum discord for general two-qubit states, amending and extending an approach recently put forward for the subclass of XXX states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of nonclassical correlations, namely, the geometric discord. We identify the extremally nonclassically correlated two-qubit states according to the (normalized) geometric discord, at a fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits.
The geometric quantum discord of a two-qudit state has been studied in many papers; however, its exact analytical value in the explicit form is known only for a general two-qubit state, a general qubit-qudit state, and some special families of two-qudit states. Based on the general Bloch vectors formalism [E. R. Loubenets et al., J. Phys. A: Math. Theor. 54, 195301 (2021)], we find the explicit exact analytical value of the geometric quantum discord for an arbitrary two-qudit state of any dimension via the parameters of its correlation matrix and the Bloch vectors of its reduced states. This general analytical result includes all the known exact results on the geometric quantum discord only as particular cases and proves rigorously that the lower bound on the geometric discord presented in [S. Rana et al., Phys. Rev. A 85, 024102 (2012)] constitutes its exact value for each two-qudit state. Moreover, our general result allows us to find for an arbitrary two-qudit state, pure or mixed, the upper and lower bounds on its geometric quantum discord, expressed via the Hilbert space characteristics of this state.
Abstract Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [ Phys. Rev. Lett. 105 (2010) 190502 ] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.
Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.