The Theoretical Study Of Quantum Correlations In Open Systems

Fascinating conclusions can be drawn about the information processing tasks which may be accomplished in principle in closed quantum systems, which do not suffer any unwanted interactions with the outside world. However, realistic quantum systems are not closed and therefore it is fundamental importance to study the quantum correlations when the system loses its coherence due to interactions with the environment. The entanglement dynamics in open quantum systems was broadly studied in the literature but not much exists about the effect of the environment on geometric quantum discord which is a well-defined measure of quantum correlation if Schatten one-norm (trace norm, TDD) is adopted as a distance measure. In this paper, we analyze the dynamics of correlations in a two-qubit system where each qubit is subjected to a phase noisy laser modeled as a classical field. This is a commonly used model for the interaction between light and matter, and thus the dynamics of correlations for this situation (Concurrence and TDD) merits investigation.Firstly, A non-Markovian local in time master equation is obtained for a two level atom driven under a non-Markovian local phase noise, and we get the analytical expression of the reduced density matrix of single qubit, then we construct the two-qubit reduced density matrix with the knowledge of the evolution of single qubit reduced density matrix, according to a standard procedure. Next, we obtain the expressions for the correlation quantifiers of Concurrence and TDD in X states, and we commence to evaluate the correlation subsequently.Considering the two qubits initially prepared in Bell-diagonal or Werner states at the beginning, we show that there is a sudden death of Concurrence, but only instantaneous disappearance of the trace-distance discord(TDD) at some time points, in comparison to the sudden death in the same range of the parameters of interest in the non-Markovian regime. And in the Markovian regime(whether Markovian or non-Markovian depends on the selected system parameters), both Concurrence and TDD show a exponential decay, in particular, Concurrence decays faster than TDD.In the last part, we show that TDD exhibits the possibility of double sudden changes and single sudden change behavior during its evolution. And we analyze the relation between sudden change and the parameters of Bell-diagonal states, as well as their qualitative locations in terms of parameters are provided.