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Chinese Physics B

Quantum correlations in a two-qubit anisotropic HeisenbergXYZchain with uniform magnetic field

Lei Li, Guo-Hui Yang

Published Jul 1, 2014• 4 citations
Publisher

Abstract

Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance (MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant J z , while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.

DOI
10.1088/1674-1056/23/7/070306

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Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance (MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant J z , while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.
Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01⟩ +sin θ|10⟩ at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B , anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.
Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord (QD). Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented: there is an “entanglement intermittently sudden death” phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter Δ . Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and Δ , whereas the parameter b is independent of the steady concurrence and QD.
Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an intermittently sudden phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.
We investigate the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system with Dzyaloshinskii-Moriya (DM) interaction in the presence of both inhomogeneity of the external magnetic field b and intrinsic decoherence which has been studied. The behavior of quantum correlation and the degree of entanglement between the two subsystems is quantified by using measurement-induced disturbance (MID), negativity (N) and Quantum Discord (QD), respectively. It is shown that in the presence of an inhomogeneity external magnetic field occur the phenomena of long-lived entanglement. It is found that the initial state is the essential role in the time evolution of the entanglement.
Abstract The thermal quantum correlations in a two-qubit one-dimensional XXZ Heisenberg spin- 1 2 chain subjected to an inhomogeneous magnetic field are investigated. The concurrence, as thermal entanglement quantifier, and the discord-like quantifiers, namely the trace distance discord and local quantum uncertainty, are computed. Their dependence on the anisotropy parameter γ , uniform magnetic field B , coupling constant J and nonuniform magnetic field b are presented in detail. The mentioned quantifiers behaviors in terms of this parameters are compared and discussed. The results show that TDD is always much stronger than the concurrence and LQU, whereas the latter two show a swinging behavior depending on system parameters. Also, we have shown that the nonuniform magnetic field can reduce the effects of temperature on thermal correlations. Furthermore, the thermal correlations, for fixed values of b , can be enhanced in the antiferromagnetic system in comparison to the ferromagnetic one. In addition, the quantum correlations amounts in the ferromagnetic system are deteriorated when γ decreases, but they are improved when the system is antiferromagnetic.