Quantum systems subject to a sequence of measurements or continuous monitoring yield a data record with probabilities governed by Born’s rule and the state of the quantum system is subject to the back action due to the measurement outcomes. The joint evolution of a classical signal record and the corresponding conditioned quantum state forms a quantum trajectory which at the same time offers a means to interpret quantum optical phenomena and to simulate the dynamics of open, dissipative quantum systems.
In this talk we will have the focus on sensors that rely on repeated or continuous monitoring of quantum meter systems over time. Here, quantum trajectory theory provides the analysis and theoretical limits of sensitivity of physical parameters or time-dependent perturbations. We offer examples of the use of quantum trajectories for optimal estimation of imposed perturbations and of the possibility to retrodict past values of a perturbation better by combining earlier and later measurement data. Both the information obtained and the back action depends on which kind of measurements are performed, and finally, we will discuss use methods to compute the Fisher information for continuous measurements, which provides deterministic results for the average performance of a given sensor.