State and Parameter Estimation for Stochastic Open Two-Level Quantum Systems

Research in the field of quantum control usually assumes complete knowledge of the state and parameters. In this paper, a driven and damped two-level quantum system under continuous observation is considered. Its time evolution is governed by an operator-valued stochastic master equation and conditioned on the recorded measurement data. The system is transformed to state space representation and its observability is proven analytically. An extended Kalman filter is employed in order to both reconstruct the density operator describing the full state of the system, and to dynamically identify key parameters. Convincing results are obtained in numerical simulations. Overall, a practical engineering approach to quantum control is presented.