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 B

Geometric discord of tripartite quantum systems

Chunhe Xiong, Wentao 文韬 Qi 齐, Maoke Miao, Minghui 明晖 Wu 吴

Published Jun 7, 2023• 3 citations
Publisher

Abstract

We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

DOI
10.1088/1674-1056/acdc11

Related papers

Geometric measure of quantum discord for entanglement of Dirac fields in noninertial frames

Wen-Chao Qiang, Lei Zhang

We investigate the geometric measure of quantum discord of all possible bipartite divisions of a tripartite system of Dirac fields in noninertial frames. As a comparison, we calculate the geometric measure of entanglement. We discuss the properties of geometric measure of quantum discord and geometric measure of entanglement for three qubit–qubit subsystems with acceleration parameter and the parameter describing the degree of entanglement the system in detail. We have found a conservative relationship involving two of three geometric discords in some condition and another conservative relationship involving three geometric discords for initially maximally entangled states. By the way, we also report some conservative relationships of concurrence, mutual information and geometric measure of entanglement for two bipartite subsystems.

Physics Letters B•Feb 7, 2015•26 citations

Dynamics of Geometric Measure of Quantum Discord of Two Qubits in Independent Reservoirs

Longjiang Liu, Jiang Zhang, Song Cheng +1 more

We study the dynamics of geometric measure of quantum discord. The model under consideration is a physical system of two qubits coupled with two independent bosonic reservoirs described by Ohmic-like spectral densities. We aim to find how the system's geometric measure of quantum discord evolves, and whether and in what conditions it may remain constant for a time interval or be frozen forever. Our result shows that by properly choosing the system's initial states, geometric measure of quantum discord may hold a frozen phenomenon in a time interval for all the three types of reservoirs, sub-Ohmic, Ohmic, and super-Ohmic reservoirs, and it may also hold a time-invariant phenomenon for super-Ohmic reservoirs. The conditions satisfied by the coefficients of standard Bell-diagonal states, in which the frozen phenomenon in a time interval or the time-invariant phenomenon of geometric measure of quantum discord appears, are given.

Journal of the Physical Society of Japan•May 20, 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

Dynamics of tripartite geometric quantifiers of correlations in a quantum spin system

Jiang Zhou, Hong Mei Guo

We derive an exact formula of geometric measure of quantum discord (GMQD) for an arbitrary 3-qubit state. The dynamics of GMQD in a quantum spin system coupled to a thermal bath is studied by simulation and analytical approximation. It is found that tripartite quantum discord has distinct time behaviors within two different eigenspaces. Further, we extend the square norm distance to define tripartite geometric quantifiers of total and classical correlations. We obtain their explicit expressions and discuss the possibility of having a closed additive relation among various kinds of correlations during the dynamical evolution.

Physical Review A•Jun 17, 2013•13 citations

Geometric quantum discord with Bures distance

Dominique Spehner, M Orszag

We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our measure is a geometrical version of the quantum discord. As the latter it quantifies the degree of non-classicality in the system. For pure states it is identical to the geometric measure of entanglement. We show that for mixed states it coincides with the optimal success probability of an ambiguous quantum state discrimination task. Moreover, the closest zero-discord states to a state ρ are obtained in terms of the corresponding optimal measurements.

arXiv:1304.3334•New Journal of Physics•Oct 2, 2013•128 citations

Quantum discord for multiqubit systems

Bo Li, Chen-Lu Zhu, Xiao-Bin Liang +2 more

We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three qubits and five qubits is the same, as is the quantum discord of two qubits and six qubits. We discover that the quantum discord of this family of states can be classified into three categories. The level surfaces of the quantum discord in the three categories are shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord does not exist under the phase flip channel, while it can be found in the even partite systems.

arXiv:2104.11378•Physical Review A•Jul 29, 2021•29 citations
We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.
We investigate the geometric measure of quantum discord of all possible bipartite divisions of a tripartite system of Dirac fields in noninertial frames. As a comparison, we calculate the geometric measure of entanglement. We discuss the properties of geometric measure of quantum discord and geometric measure of entanglement for three qubit–qubit subsystems with acceleration parameter and the parameter describing the degree of entanglement the system in detail. We have found a conservative relationship involving two of three geometric discords in some condition and another conservative relationship involving three geometric discords for initially maximally entangled states. By the way, we also report some conservative relationships of concurrence, mutual information and geometric measure of entanglement for two bipartite subsystems.
We study the dynamics of geometric measure of quantum discord. The model under consideration is a physical system of two qubits coupled with two independent bosonic reservoirs described by Ohmic-like spectral densities. We aim to find how the system's geometric measure of quantum discord evolves, and whether and in what conditions it may remain constant for a time interval or be frozen forever. Our result shows that by properly choosing the system's initial states, geometric measure of quantum discord may hold a frozen phenomenon in a time interval for all the three types of reservoirs, sub-Ohmic, Ohmic, and super-Ohmic reservoirs, and it may also hold a time-invariant phenomenon for super-Ohmic reservoirs. The conditions satisfied by the coefficients of standard Bell-diagonal states, in which the frozen phenomenon in a time interval or the time-invariant phenomenon of geometric measure of quantum discord appears, are given.
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.
We derive an exact formula of geometric measure of quantum discord (GMQD) for an arbitrary 3-qubit state. The dynamics of GMQD in a quantum spin system coupled to a thermal bath is studied by simulation and analytical approximation. It is found that tripartite quantum discord has distinct time behaviors within two different eigenspaces. Further, we extend the square norm distance to define tripartite geometric quantifiers of total and classical correlations. We obtain their explicit expressions and discuss the possibility of having a closed additive relation among various kinds of correlations during the dynamical evolution.
We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our measure is a geometrical version of the quantum discord. As the latter it quantifies the degree of non-classicality in the system. For pure states it is identical to the geometric measure of entanglement. We show that for mixed states it coincides with the optimal success probability of an ambiguous quantum state discrimination task. Moreover, the closest zero-discord states to a state ρ are obtained in terms of the corresponding optimal measurements.
We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three qubits and five qubits is the same, as is the quantum discord of two qubits and six qubits. We discover that the quantum discord of this family of states can be classified into three categories. The level surfaces of the quantum discord in the three categories are shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord does not exist under the phase flip channel, while it can be found in the even partite systems.