Optimized Quantum Parameter Estimation in Open Quantum Systems

Quantum parameter estimation has been long pursued in various physics areas, such as quantum optics, quantum information processing, gravitational wave detection, and so on. Generally, the quantum system dynamics is usually assumed to be fixed and the system is closed, the highest precision can be achieved by preparing the optimal probe state and performing the quantum measurement based on ideal basis that saturates the quantum Cramer-Rao inequality. However, how to extend this problem to a more general open quantum system is still an open question. In this paper, we apply the optimal control theory, Pontrygin optimal principle, to enhance the parameter estimation precision in open quantum systems. The control laws and the control algorithm are exactly presented. Simulation results demonstrated the efficiency of the optimal control laws.