Geometric Quantum Discord And Measurement-induced Nonlocality Of Two-qubit In Open Systems

As important quantum correlation measures,geometric quantum discord and measurement-induced nonlocality play a crucial role in many quantum information processing tasks,such as quantum teleportation,quantum logic gates,quantum dense coding,remote state control and so on.However,quantum correlations in any system are inevitably influenced by the environment,leading to the rapid decay of them.So,it is of practical significance to investigate the dynamical behavior of quantum correlations in open systems.We examined in this paper dynamics of the geometric quantum discords and measurement-induced nonlocality for two interacting qubits described by the Heisenberg XY model and further coupled independently to their respective bosonic thermal reservoirs.We explored in detail evolution of the system with different system parameters and the reservoir parameters and demonstrated how to realize a reliable control and long-time preservation of the considered geometric quantum discords and measurement-induced nonlocality.First,we explored decay dynamics for the trace distance quantum discord,Hellinger distance quantum discord,and Bures distance quantum discord when the two-qubit system is prepared in different initial states.Compared with that of the non-interacting qubit case.Our results showed that the anisotropic of the interaction and external magnetic field have small influence on quantum discord during the short-time interval of the evolution process.But the geometric quantum discords can escape the fate of asymptotically disappearance in the long-time region and reach finite stable values by introducing anisotropy to the spin interaction.These stable values are independent of the initial states of the system and are determined solely by the anisotropic parameter,the strength of the magnetic fields,and the decoherence factors of the reservoir.The increase of the reservoir temperature always has an adverse influence on the maintenance of the geometric quantum discords.Furthermore,we also observed the multiple sudden change phenomenon of the trace distance quantum discord during its evolution process.Second,we explored decay dynamics of the measurement-induced nonlocality which are defined by the trace distance,the von Neumann entropy,and the Bures distance in the two-qubit system.By comparing their behaviors with two different initial state,we showed that nonlocality can be enhanced evidently by introducing anisotropy to the spin interaction or by applying the external magnetic fields to the system.In the infinite-time limit,we also found that the stable values are independent of the initial states of the system.For the case of zero-magnetic field,the dependence of the stable values on the anisotropic parameters and the temperature of the thermal reservoir are given.Moreover,we also showed that the temperature of the thermal reservoir is not conducive to the long-time maintenance of the measurement-induced nonlocality.The anisotropy of the spin interaction can also be used to generate measurement-induced nonlocality from the initial state without measurementinduced nonlocality.