Remote State Preparation In Noisy Conditions

The combination of modern quantum theory and information science yields a new subject of quantum information, which mainly involves quantum computation and quantum communication. As two typical protocols of quantum communication, quantum teleportation and remote state preparation, have attracted much attention in recent years. In this thesis, we mainly focus on the remote state preparation (RSP) in noisy conditions.Firstly, some basic concepts of quantum entanglement and quantum operation are introduced. Then, we review the schemes of standard teleportation and remote state preparation, including teleportation of a qubit state via EPR state, remote preparation of a qubit state via EPR state and of an entangled state via GHZ state respectively. In this thesis, we consider the remote state preparation scheme when the noise affecting the RSP channel can be expressed as the Lindblad operators. By solving the master equation in the Lindblad form, we can utilize trace distance or fidelity to describe how close the output state and the initial state are. For the case of remote preparation of a qubit with EPR state and with non-maximally entangled state as the quantum channel respectively, the trace distance is used to characterize the quality of the RSP process in various noisy conditions. Moreover, if the GHZ state is used as quantum channel for remotely preparing an entangled state and a qubit state respectively, we apply fidelity to measure how much information is transferred from the initial state to the output state. In this situation, we obtain the average fidelities in the various types of noise and discuss the influence of the various types of the noise on the remote state preparation. Our results show that the influence of the noise acting in z direction is the weakest, and the influence of the noises acting simultaneously in x, y, and z directions is the strongest.The research about the influence of the noises on the remote state preparation process may be helpful to understand and examine the practical transmission of quantum information.