Remote state preparation with bipartite entangled states in noisy environments

We investigate the influence of quantum noises on the processes of remote preparation of a qubit by using an Einstein-Podolsky-Rosen (EPR) state and a bipartite partially entangled state as the quantum channel respectively. By solving the master equation in the Lindblad form, we obtain the time evolution of the quantum channels. Then we use the trace distance to describe how close the output state and the initial state are in various noisy conditions. Our results show that the influence of the noise acting on z direction is the weakest, and the influence of the noises acting simultaneously on x, y, and z directions is the strongest.