Control-enhanced multiparameter quantum estimation

Most studies in multiparameter estimation assume the dynamics is fixed and focus on identifying the optimal probe state and the optimal measurements. In practice, however, controls are usually available to alter the dynamics, which provides another degree of freedom. In this paper we employ optimal control methods, particularly the gradient ascent pulse engineering (GRAPE), to design optimal controls for the improvement of the precision limit in multiparameter estimation. We show that the controlled schemes are not only capable to provide a higher precision limit, but also have a higher stability to the inaccuracy of the time point performing the measurements. This high time stability will benefit the practical metrology, where it is hard to perform the measurement at a very accurate time point due to the response time of the measurement apparatus.