Maximum likelihood versus likelihoodfree quantum system identification in the atom maser
Abstract
We consider the 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. Firstly, the maximum likelihood estimator (MLE) takes into account the full measurement data and is asymptotically optimal in terms of its mean square error. Secondly, the ‘likelihoodfree’ 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. Building on previous results which showed that atom counts are poor statistics for certain values of the Rabi angle, we apply MLE to the full measurement data and estimate its Fisher information. We then select several correlation statistics such as waiting times, distribution of successive identical detections, and use them as input of the ABC algorithm. The resulting posterior distribution follows closely the data likelihood, showing that the selected statistics capture ‘most’ statistical information about the Rabi angle.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2014
 DOI:
 10.1088/17518113/47/41/415302
 arXiv:
 arXiv:1311.4091
 Bibcode:
 2014JPhA...47O5302C
 Keywords:

 Quantum Physics;
 Statistics  Methodology
 EPrint:
 25 pages, 14 figures