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arXiv:1208.1555 · Journal of Physics A Mathematical and Theoretical

Decoherence of quantum discord in an asymmetric-anisotropy spin system

Xiang Hao, Chunlan Ma, Jinqiao Sha

Published Sep 30, 2010• 20 citations
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Abstract

The decoherence of quantum correlation is investigated in the Heisenberg spin system with the asymmetric anisotropic interactions. The quantum entanglement and discord are used to quantify the quantumness of the correlations. By the analytical and numerical methods, we find that quantum discord decays asymptotically in time under the effects of the independent local Markovian reservoirs. This is markedly different from the sudden change of the entanglement. Before the disappearance of the entanglement, the dynamic behaviour of quantum discord is very similar to that of the entanglement. It is also shown that the discord declines rapidly for the interacting spin system compared with the case of noninteracting qubits. At an arbitrary finite temperature, the nonzero thermal discord can be enhanced by the asymmetric anisotropic interactions which induce quantum fluctuations.

DOI
10.1088/1751-8113/43/42/425302

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The decoherence of quantum correlation is investigated in the Heisenberg spin system with the asymmetric anisotropic interactions. The quantum entanglement and discord are used to quantify the quantumness of the correlations. By the analytical and numerical methods, we find that quantum discord decays asymptotically in time under the effects of the independent local Markovian reservoirs. This is markedly different from the sudden change of the entanglement. Before the disappearance of the entanglement, the dynamic behaviour of quantum discord is very similar to that of the entanglement. It is also shown that the discord declines rapidly for the interacting spin system compared with the case of noninteracting qubits. At an arbitrary finite temperature, the nonzero thermal discord can be enhanced by the asymmetric anisotropic interactions which induce quantum fluctuations.
We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.
Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord (QD). Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented: there is an “entanglement intermittently sudden death” phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter Δ . Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and Δ , whereas the parameter b is independent of the steady concurrence and QD.
Dynamics of an open two-qubit system is investigated in the post-Markovian regime, where the environments have a short-term memory. Each qubit is coupled to separate environment which is held in its own temperature. The inter-qubit interaction is modeled by XY-Heisenberg model in the presence of spin-orbit interaction and inhomogeneous magnetic field. The dynamical behavior of entanglement and discord has been considered. The results show that, quantum discord is more robust than quantum entanglement, during the evolution. Also the asymmetric feature of quantum discord can be monitored by introducing the asymmetries due to inhomogeneity of magnetic field and temperature difference between the reservoirs. By employing proper parameters of the model, it is possible to maintain non-vanishing quantum correlation at high degree of temperature. The results can provide a useful recipe for studying of dynamical behavior of two-qubit systems such as trapped spin-electrons in coupled quantum dots.
The non-Markovian decoherence of quantum and classical correlations is analytically obtained when two qubits are asymmetrically subjected to the bit flip channel and phase flip channel. For one class of initial mixed states, quantum correlations quantified by quantum discord decay synchronously with classical correlations. The discovery that the decaying rates of quantum and classical correlations suddenly change at the characteristic time is physically interpreted by the distance from quantum state to the closest classical states. In a large time interval, quantum correlations are greater than classical correlations. The quantum and classical correlations can be preserved over a longer period of time via the kernel characterizing the environment memory effects.
We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii—Moriya (DM) interaction. We find that the effects of DM interaction on antiferromagnetic system is distinct from that of ferromagnetic system. The magnetic field supplemented with DM term contribute to enhance the range of quantum discord. It is revealed that the situations where quantum discord fails to indicate a sudden change of groundstate at finite temperature though indicating such a sudden change of groundstate at zero temperature. Dynamics of pairwise thermal quantum discord is considered as well. Thermal quantum discord vanishes in asymptotic limit regardless of its initial values, however, thermal entanglement suddenly disappears in finite time.
Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an intermittently sudden phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.