Optimal parameter estimation of open quantum systems*

Abstract

In quantum information technologies, quantum weak measurement is beneficial for protecting coherence of systems. In order to further improve the protection effect of quantum weak measurement on coherence, we propose an optimization scheme of quantum Fisher information (QFI) protection in an open quantum system by combing no-knowledge quantum feedback control with quantum weak measurement. On the basis of solving the dynamic equations of a stochastic two-level quantum system under feedback control, we compare the effects of different feedback Hamiltonians on QFI and find that via no-knowledge quantum feedback, the observation operator σx (or σx and σz ) can protect QFI for a long time. Namely, no-knowledge quantum feedback can improve the estimation precision of feedback coefficient as well as that of detection coefficient.