Maximum likelihood versus likelihood-free quantum system identification in the atom maser

Understand

We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms).

• Two estimation methods are investigated and compared.
• On the one hand, the maximum likelihood estimator (MLE) takes into account the full measurement data and is asymptotically optimal in terms of its mean square error.
• On the other hand, the `likelihood-free' method of approximate Bayesian computation (ABC) produces an approximation of the posterior distribution for a given set of summary statistics, by sampling trajectories at different parameter values and comparing them with the measurement data via chosen statistics.