Entanglement and nonlocality dynamics of a Bell state and the GHZ state in a noisy environment

We investigate the entanglement and nonlocality dynamics of a two-qubit Bell state and the three-qubit Greenberger-Home-Zeilinger (GHZ) state in a noisy environment by solving analytically a master equation in the Lindblad form. In the case of the Bell state, we obtain the analytic expressions of the concurrence and the maximal violation of the Clauser-Horne-Shimony-Holt inequality of the evolution state. In the case of the three-qubit GHZ state, we obtain the analytic formula of the genuinely multipartite concurrence of the evolution state. Usually, it is difficult to give the analytic expression of the maximum violation of the Svetlichny inequality for a general three-qubit state, but we find the analytic expression for a class of three-qubit states whose correlation matrices are of a special form. We use this result to obtain the analytic expression of the maximum violation of the Svetlichny inequality of the evolution state when parameters in the master equation meet certain conditions.