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Chinese Physics B

Entanglement of a two-qubit anisotropic Heisenberg XYZ chain in nonuniform magnetic fields with intrinsic decoherence

Xu Xiao-Bo, Liu Jin-Ming, Yu Peng-Fei

Published Feb 1, 2008• 16 citations
Publisher

Abstract

Taking the intrinsic decoherence effect into account, this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XYZ model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure. It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement. Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement, which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state |(0)ψ = |00〉 and | ψ′ (0)〉 = m |01〉 + n |10〉, respectively.

DOI
10.1088/1674-1056/17/2/019

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Taking the intrinsic decoherence effect into account, this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XYZ model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure. It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement. Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement, which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state |(0)ψ = |00〉 and | ψ′ (0)〉 = m |01〉 + n |10〉, respectively.
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.
Taking the intrinsic decoherence effect into account, the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymetric interaction is investigated in this paper. Concurrence, the measurement of entanglement, is calculated. Compared with the anisotropic in XY plane, the DM interaction is another kind of anisotropic antisymmetric exchange interaction. It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement. The DM interaction only acts on the time evolution of the entanglement when the initial state is |ψ(0)⟩ = cosα|01⟩ + sinα|10⟩ and weakens the degree of entanglement. The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |ψ(0)⟩ = cosα|00⟩ +sinα|11⟩. The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
Taking the intrinsic decoherence effect into account,the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski-Moriya(DM)anisotropic antisymetric interaction is investigated in this paper.Concurrence,the measurement of entanglement,is calculated.Compared with the anisotropic in XY plane,the DM interaction is another kind of anisotropic antisymmetric exchange interaction.It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement.The DM interaction only acts on the time evolution of the entanglement when the initial state is |(?)(0)=cosα|01+sinα|10 and weakens the degree of entanglement.The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |(?)(0)=cosα|00+sinα|11.The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
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.