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Chinese Physics B

Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths

Shaoying Yin, Qingxin Liu, Jie Song, Xuexin Xu, Keya Zhou, Shutian Liu

Published Sep 1, 2017• 3 citations
Publisher

Abstract

We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.

DOI
10.1088/1674-1056/26/10/100501

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We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.
We investigate the dynamic behaviors of quantum discord for a central two-qubit system coupled to an XY\mathit{XY}XY-spin-chain environment. In the weak-coupling regime, we show that the quantum discord for the two central qubits can become minimized rapidly close to the critical point of a quantum phase transition. By considering the two qubits that are initially prepared in the Werner state, we study the evolution of the quantum discord and that of entanglement under the same conditions. Our results imply that entanglement can disappear completely after a finite time, while the quantum discord decreases and tends to be a stable value according to the initial-state parameter for a very-long-time interval. In this sense, the quantum discord is more robust than entanglement for the quantum system exposed to the environment. The relation between the quantum correlations and the classical correlation is also shown for two particular cases.
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.
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 (QD) of two qubits independently coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. For this model, we drive the corresponding Kraus operators, obtain the analytic results of QD and compare the dynamics of QD with the dynamics of relative entropy of entanglement nearby the critical point. It is shown that the impact of the quantum criticality environment on QD can be concentrated in a very narrow region nearby the critical point, so it supplies an efficient way to detect the critical points. In the vicinity of the critical point, the evolution of QD is shown to be more complicated than that of entanglement. Furthermore, we find that separable states can also be used to reflect the quantum criticality of the environment.
\n\nIn this study, we investigate the dynamics of classical and quantum correlations for a two-qubit system in an XY spin-chain environment. Moreover, we focus on two coupling cases. We find that the quantum discord (QD) decay rates for the two cases differ in sudden change behavior and strongly depend on environmental parameters. An interesting scaling behavior for the QD is given under the weak-coupling condition. In the strong-coupling condition, the classical correlation (CC) and the QD oscillate quickly with time, but present regular distributions under a specific time interval. Moreover, the sudden change for the QD is presented by choosing the proper initial time and time interval. Finally, we find that the decay parts of the envelopes for the CC and QD satisfy a Gauss-related feature.\n
We investigate the dynamics of quantum discord for a two-qubit system coupled to a spin chain with three-site interaction in the weak-coupling region. For the case of the initial two-qubit pure state, the decay of quantum discord can be delayed in a special interval of the three-site coupling strength. In the absence of the transverse field, with the increase of three-site interaction, quantum discord tends to be stabler. For the case of the initial mixed state, the increase of quantum discord is delayed in the special interval of three-site interaction. In addition, a sudden transition between classical and quantum decoherence is also observed, with the transition time determined by the three-site interaction and degree of anisotropy.