Quantum estimation of a time-dependent perturbation

Abstract

We analyze the estimation of a time-dependent perturbation acting on a continuously monitored quantum system. We describe the temporal fluctuations of the perturbation by a hidden Markov model, and we combine quantum measurement theory and classical filter theory into a time-evolving hybrid quantum and classical trajectory. The forward-backward analysis that permits smoothed estimates of classical hidden Markov models has a counterpart in the theory of retrodiction and past quantum states. As a specific example, we apply our hybrid trajectory and past-quantum-state theory to the sensing of a fluctuating magnetic field by microwave interrogation of a single quantum spin.