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Physica Scripta

Quantum discord for a central two-qubit system coupled to anXYspin chain with Dzyaloshinsky–Moriya interaction

Liang Qiu, An Min Wang

Published Oct 1, 2011• 11 citations
Publisher

Abstract

We investigated the quantum discord dynamics of a central two-qubit system coupled to an XY spin chain with the Dzyaloshinsky–Moriya (DM) interaction. We found that the DM interaction does not affect the behavior of the quantum phase transition induced by the external magnetic field. Moreover, the DM interaction enhances the decay of quantum discord in the weak-coupling regime, while it has no obvious effect on the quantum discord dynamics in the strong-coupling regime.

DOI
10.1088/0031-8949/84/04/045021

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We investigated the quantum discord dynamics of a central two-qubit system coupled to an XY spin chain with the Dzyaloshinsky–Moriya (DM) interaction. We found that the DM interaction does not affect the behavior of the quantum phase transition induced by the external magnetic field. Moreover, the DM interaction enhances the decay of quantum discord in the weak-coupling regime, while it has no obvious effect on the quantum discord dynamics in the strong-coupling regime.
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We numerically and analytically investigate the time evolution of quantum discord and entanglement for two-qubit initially prepared in a class of X−X-X−structure state. In the case of evolution from a pure state, quantum correlations decay to zero in a very short time at the critical point of the environment. In the case of evolution from a mixed state, It is found that quantum discord may get maximized due to the quantum critical behavior of the environment while entanglement vanishes under the same condition. Moreover, we observed sudden transition between classical and quantum decoherence when single qubit interacts with the environment. The effects of DM interaction on quantum correlations are also considered and revealed in the two cases. It can enhance the decay of quantum correlations and its effect on quantum correlations can be strengthened by anisotropy parameter.
We study the dynamics of correlations for a hybrid qubit—qutrit system in an XY spin-chain environment with Dzyaloshinsky—Moriya interaction. Our discussion involves a comparative analysis of negativity, quantum discord, and measurement-induced disturbance. It is found that the quantum discord is optimal of the three quantum correlations to detect the critical point of quantum phase transition. Only when the qubit interacts with the environment, is the phenomenon of sudden transition between the classical correlation and the quantum discord observed. Moreover, the Dzyaloshinsky—Moriya interaction enhances the decay of quantum correlations.
Quantum coherence has played a decisive role in quantum information processing. On the other hand, quantum correlation can be considered as a powerful resource for delivering quantum information. Both quantum coherence and quantum correlation may occur in an information propagating process, which challenges us to understand the relationship between coherence and correlation. This is also an important procedure for physicists to know the features of quantum resources. Any quantum system interacting with its surrounding environment will destroy the quantum coherence and fail to fulfil any task of delivering quantum information. In this sense, studying the dynamics of quantum correlation and quantum coherence is very fascinating. In this paper, we investigate the dynamics of the quantum correlation and quantum coherence for two central qubits coupled to their own spin baths modeled by the XY spin chain with Dzyaloshinsky-Moriya interaction. We employ the quantum discord to characterize the quantum correlation, and use the relative entropy to measure quantum coherence. In this way the evolution law of the quantum discord and the relative entropy of quantum coherence of two-qubit system are derived, and the evolution law depends not only on the Dzyaloshinsky-Moriya interaction, the anisotropy parameter and the total number of spin chain sites, but also on the coupling strength between the central spin and its spin chain. Our findings are as follows. Firstly, we find that near the critical point of spin chain the quantum coherence abruptly changes, which can be used to detect the existence of quantum phase transition. Secondly, at the critical point, the relative entropy of quantum coherence is the same as that of classical correlation when time tt0, and it is the same as that of quantum discord when time tt0. At time t0, the sudden transition from quantum discord to classical correlation occurs. All in all, the relative entropy of quantum coherence reflects the behaviors of classical correlation and quantum discord for times tt0 and tt0, respectively, which is caused by the change of the optimal basis for quantum discord. Thirdly, the dynamics of quantum correlation and quantum coherence keep invariant under the scaling variation of the total number of spin chain sites and the coupling strength. Moreover, we find that all the Dzyaloshinsky-Moriya interactions and the anisotropy parameters, as well as the coupling strengths will enhance the decay of quantum coherence and quantum correlation, while they have no obvious effect on the relationship between dynamics of coherence and correlation. The above discussion reveals some new features of quantum coherence and quantum correlation, which may be useful in further developing quantum information theory.
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky—Moriya interaction. In the case of a two-qubit with an initial pure state, quantum correlations decay to zero at the critical point of the environment in a very short time. In the case of a two-qubit with initial mixed state, it is found that quantum discord may get maximized due to the quantum critical behavior of the environment, while entanglement vanishes under the same condition. Besides, we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment. The effects of Dzyaloshinsky—Moriya interaction on quantum correlations are considered in the two cases. The decay of quantum correlations is always strengthened by Dzyaloshinsky—Moriya interaction.
In this paper, we address the tripartite quantum discord for the Heisenberg XY chain with the Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group (QRG) method. In thermodynamic limit, like the entanglement, the tripartite discord exhibits the quantum phase transition (QPT) between the spin-fluid and the Neel phases. The effect of the DM interaction and the anisotropy on the features of the tripartite quantum discord has been probed. It is noted that the DM interaction brings the critical point earlier and affects heavily with the size of the system. Moreover, the system requires a larger number of the iterations to achieve the QPT for the tripartite quantum discord as compared to the entanglement.
We investigate the quantum discord dynamics of a two-qubit system coupled to an XY spin-chain environment with energy current. We compared dynamical behaviors of quantum discord under different system-environment couplings, the size of the degrees of freedom of the environment, the anisotropy parameter, and the energy current. The results indicate that the energy current can strongly suppress the quantum discord in the weak-coupling region, while it has no obvious effect on the quantum discord in the strong-coupling regime.