Preparation of entanglement states in a two-spin system by Lyapunov-based method

A stable Lyapunov-based control law is proposed for entanglement states preparation in this paper. The mathematical model of a two-spin system is constructed in interaction picture. An average value of observable operator is selected as the Lyapunov function. This paper designs the observable operator to make sure that the target state is stable in Lyapunov sense. Then the authors analyze the convergence of the control system, and demonstrate that the Bell states are asymptotically stable under the control law designed. Compared with other methods, the control method proposed in this paper has the advantages of easy design and convergence to the target states. Numerical simulation experiments for the preparation of Bell states are implemented.