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Scientific Reports

Geometric quantum discords of interacting qubits in thermal reservoir

Zhao Li, Xiaomin Wang, Wu Zhou, Ming‐Liang Hu

Published Jun 7, 2017• 5 citations
Publisher

Abstract

We examined decay dynamics of various geometric quantum discords (GQDs) for two interacting qubits described by the Heisenberg XY model and further coupled independently to their respective thermal reservoirs. Compared to the case of noninteracting qubits, our results showed that decay rates of the GQDs can be retarded apparently by properly choosing system parameters of the interaction term. In the long-time limit, the asymptotic values of the GQDs are enhanced evidently by tuning anisotropy of the model and strength of the transverse magnetic field. We further illuminated the relations between different GQDs on characterizing quantum correlations, and observed multiple sudden change behaviors of their dynamics.

DOI
10.1038/s41598-017-03535-w

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We examined decay dynamics of various geometric quantum discords (GQDs) for two interacting qubits described by the Heisenberg XY model and further coupled independently to their respective thermal reservoirs. Compared to the case of noninteracting qubits, our results showed that decay rates of the GQDs can be retarded apparently by properly choosing system parameters of the interaction term. In the long-time limit, the asymptotic values of the GQDs are enhanced evidently by tuning anisotropy of the model and strength of the transverse magnetic field. We further illuminated the relations between different GQDs on characterizing quantum correlations, and observed multiple sudden change behaviors of their dynamics.
Abstract Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole–dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.
We study the influences of the external magnetic field, temperature, and coupling parameter on the thermal quantum correlation in a two-qubit Heisenberg XY model, where the correlation is described in terms of two modified geometric discords and concurrence. It is shown that those three quantities behave similarly in the regions of lower temperature and weak magnetic field. However, the two geometric discords are more robust against temperature and magnetic field than the concurrence. Moreover, two geometric discords exhibit different behaviors under suitable conditions, that is, one discord increases as the magnetic field rises whereas the other discord decreases. In particular, the discord reveals the phenomenon of sudden change, while neither of other discord and concurrence displays such a phenomenon.
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.
In this work, the dynamics of quantum correlation (QC) in terms of geometric discord and its transfer coupled with dissipative reservoirs are investigated. Taken two canonical cases where the qubits of interest are initially prepared in extended Werner-like state and W-like states into account, we specifically reveal the dynamical behaviors of the geometric discord as each qubit locally interacts with its surrounding infinite degree-of-freedom reservoir. In the scenarios, the short-term and long-term dynamics of the geometric discord for the qubit- and reservoir-subsystem as well as its transfers between them are observed detailedly. It turns out that the geometric discord of qubit-subsystem decays asymptotically to zero while the counterpart of reservoir-subsystem can revive from time t = 0 to steady value, which sheds light on a transfer of the discord from the qubit-subsystem to the corresponding reservoir-subsystem.
In this paper, we study a system with two interacting qubits described by the Heisenberg model with dissipative terms, and analyze decay dynamics and the steady-state of geometric quantum discords. Our results indicate that we can ignore the interaction force in the z-direction and adjust the parameters to change the loss of quantum correlation with time when the initial state satisfies some conditions. Moreover, we show that after a long enough period of time, unlike other parameters, the energy and the intensity of the non-uniform magnetic field do not affect the steady-state.
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.