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International Journal of Quantum Information

THE INFLUENCE OF DZYALOSHINSKII–MORIYA ANISOTROPIC ANTISYMMETRIC INTERACTION ON ENTANGLEMENT IN A THREE-QUBIT ISING MODEL WITH INTRINSIC DECOHERENCE

DAN GAO, Zhao Zhen-Shuang, Hong‐Fu Wang, Shou Zhang, Kyu-Hwang Yeon

Published Mar 1, 2011• 0 citations
Publisher

Abstract

We investigate the effect of the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction on entanglement in a three-qubit Ising model with intrinsic decoherence. The entanglement of the nearest and the next-nearest neighbor qubit is calculated. The results show that, taking into account the intrinsic decoherence, when the qubits are initially in the maximal entangled state, the concurrence of the system decreases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t. When the qubits are initially in the disentangled state, the destructive effect of intrinsic decoherence on entanglement can be moderated by the Dzyaloshinskii–Moriya interaction, the concurrence increases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t.

DOI
10.1142/s0219749911007629

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We investigate the effect of the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction on entanglement in a three-qubit Ising model with intrinsic decoherence. The entanglement of the nearest and the next-nearest neighbor qubit is calculated. The results show that, taking into account the intrinsic decoherence, when the qubits are initially in the maximal entangled state, the concurrence of the system decreases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t. When the qubits are initially in the disentangled state, the destructive effect of intrinsic decoherence on entanglement can be moderated by the Dzyaloshinskii–Moriya interaction, the concurrence increases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t.
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 have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubits system. We have considered the anisotropic Heisenberg (XXZ) model in the presence of Dzyaloshinskii–Moriya (DM) interaction in addition to the Ising model in a magnetic field with DM interaction. We have found that the increment of DM interaction and magnetic field can enhance and reduce the entanglement of the system. We have shown that the non-symmetric pairwise state has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise one. For the negative anisotropy, the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy, it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in detail. The most remarkable result appears at zero temperature where the three-qubits ground state entanglement of the system (in spite of two-qubits counterpart) shows the fingerprint of the quantum phase transition for a system of infinite number of qubits.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.
With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.
In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii–Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.