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Journal of Southwest University

Influence of Decoherence of Two-Qubit Ising Model on Entanglement and Fidelity

Zhenghong He

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

An investigation of the entanglement and fidelity for two-qubit Ising model in an external uniform magnetic field showed that the entanglement degree oscillated with increasing phase decoherence in the initial stage and decreased with the increase in phase decoherence thereafter,the decline of the entanglement degree being greater with greater phase decoherence.When the initial state of the system was on its eigenstate,the concurrence was zero,or it did not change with the evolution of phase decoherence.The fidelity of the system exhibied an obvious periodic change and tended to remain at a constant value with the increase in phase decoherence.The entanglement degree and fidelity of the two-qubit Ising model could be enhanced or weakened through controlling magnetic field B.

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An investigation of the entanglement and fidelity for two-qubit Ising model in an external uniform magnetic field showed that the entanglement degree oscillated with increasing phase decoherence in the initial stage and decreased with the increase in phase decoherence thereafter,the decline of the entanglement degree being greater with greater phase decoherence.When the initial state of the system was on its eigenstate,the concurrence was zero,or it did not change with the evolution of phase decoherence.The fidelity of the system exhibied an obvious periodic change and tended to remain at a constant value with the increase in phase decoherence.The entanglement degree and fidelity of the two-qubit Ising model could be enhanced or weakened through controlling magnetic field B.
Ising model is the simplest Heisenberg model,research on the entanglement of this model will promote the development of solid quantum computer.Considering the phase decoherence of system,this paper investigates the entanglement dynamics of two qubits Ising chain with the DM interaction.It is found that the effects of phase decoherence and DM interaction on entanglement are dependent on the initial state of system.For some initial states,the entanglement of system is invariable.For some others,with the increase of time,the entanglement of system oscillates and decreases.In addition,increasing the DM interaction will decrease the entanglement and the oscillation period;increasing the phase decoherence rate will also decrease the entanglement,however,the oscillation period is unchanging.
We investigate the thermal entanglement and average fidelity in the two-qubit Ising model with a uniform and nonuniform magnetic field.The concurrence of the measurement of entanglement is calculated.The behavior of concurrence is present at different forms.Contrary to the uniform magnetic fields case,the fidelity may be enhanced under a nonuniform magnetic field.And the average fidelity shows relation with the value of coupling constant J and Temperature T.We show them clearly by presenting figures.From the figures,two conclusions can be concluded.Firstly,in other same conditions,whether the magnetic field has the opposite or the same direction,the entanglement is the same.But when the magnetic field has the opposite direction,which can have a great effect on the average fidelity of the teleportation.Secondly,to enhance the entanglement and average fidelity we should choose the proper value of B and coupling constant J and decrease the temperature T.
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.
By solving the Milburn equation, we investigate the thermal entanglement properties of a two-qubit Heisenberg XY chain in the presence of intrinsic decoherence. The controls of nonuniform magnetic field, the initial state of two qubits, the relative phases and the amplitudes of the polarized qubits on thermal entanglement are studied. The results show that for a particular initial state, the thermal entanglement can be increased by the external magnetic field. The time behavior of the entanglement exhibits a strong dependence on the initial state of two qubits, and it can be manipulated by changing the relative phase and the amplitudes of the polarized qubits. It is also notable that stable entanglement, which is dependent on initial state of the qubit, occurs even in the presence of decoherence. The magnetic field may have a constructive effect on the stable entanglement for a certain initial state, and the Bell-diagonal state turns out to be a dark state of the system in the absence of the magnetic field.