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Effects of anisotropy on thermal entanglement

Wang, X

Published Jan 1, 2001• 142 citations
OpenAlex

Abstract

We study the thermal entanglement in the two-qubit anisotropic XXZ model and the Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on the thermal entanglement are studied in detail for both the antiferromagnetic and ferromagnetic cases.

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Thermal entanglement of a(1/2,1) mixed-spin Heisenberg XXZ model in the presence of Dzyaloshinski-Moriya(DM) interaction and anisotropy Δ is investigated.It is shown that the thermal entanglement and the critical temperature can be efficiently controlled by adjusting the DM interaction parameter and anisotropy coefficient Δ.Thus,by changing the values of DM interaction and anisotropy coefficient Δ,we can get a more efficient control parameter to increase the entanglement and expand the steady value region to slow down the decreace of the entanglement.

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The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.

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Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.

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Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

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Physical Review A•Mar 22, 2007•261 citations
We study the thermal entanglement in the two-qubit anisotropic XXZ model and the Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on the thermal entanglement are studied in detail for both the antiferromagnetic and ferromagnetic cases.
Thermal entanglement of a(1/2,1) mixed-spin Heisenberg XXZ model in the presence of Dzyaloshinski-Moriya(DM) interaction and anisotropy Δ is investigated.It is shown that the thermal entanglement and the critical temperature can be efficiently controlled by adjusting the DM interaction parameter and anisotropy coefficient Δ.Thus,by changing the values of DM interaction and anisotropy coefficient Δ,we can get a more efficient control parameter to increase the entanglement and expand the steady value region to slow down the decreace of the entanglement.
The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.
Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.
Optimal dense coding with thermal entangled states of a two-qubit anisotropic XXZ model and a Heisenberg model with Dzyaloshinskii–Moriya (DM) interactions is studied in this paper. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on dense coding are studied in detail for both the antiferromagnetic and ferromagnetic cases. For the two models, I give the conditions that the parameters of the models have to satisfy for a valid dense coding. I also found that even though there is entanglement, it is unavailable for our optimal dense coding, which is the same as entanglement teleportation.
Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic.