Dynamic evolution of quantum entanglement with quantum Lyapunov control in a two-qubit Heisenberg XXZ model under the effect of DM and KSEA interactions

Abstract

In this paper, we investigate the dynamic evolution of quantum correlation using the quantum Lyapunov control in the two-qubit Heisenberg XXZ model under the effect of DM and KSEA interaction. When both the DM and KSEA interactions in the x-, y- and z-direction are taken into account, quantum correlations such as concurrence exhibit the sudden death and birth and lead to chaotic behavior during evolution. To solve this problem, we apply a time-varying field, not a constant field into the x- and z-direction. In other words, the quantum Lyapunov control is used at each time to determine the strength of the magnetic field in order to increase the quantum correlation. Numerical simulation result shows that the method proposed in this paper does not generate sudden death and birth of quantum correlations during evolution, and that even after a certain time if the magnetic field is removed, quantum correlations remain unchanged and to be a certain value. This result provides the possibility to use spin chains as quantum channels to perform quantum information processing.