Bayesian parameter estimation by continuous homodyne detection

We simulate the process of continuous homodyne detection of the radiative emission from a quantum system, and we investigate how a Bayesian analysis can be employed to determine unknown parameters that govern the system evolution. Measurement back-action quenches the system dynamics at all times and we show that the ensuing transient evolution is more sensitive to system parameters than the steady state of the system. The parameter sensitivity can be quantified by the Fisher information, and we investigate numerically and analytically how the temporal noise correlations in the measurement signal contribute to the ultimate sensitivity limit of homodyne detection.