Appears in collection : Observability and estimation in quantum dynamics

A significant number of quantum optics experiments (without feedback) can be model by repeated (indirect) measurement of a quantum system. For these models, with N. Cuneo, V. Jaksic, Y. Pautrat and C. -A. Pillet we studied the possibility of discriminating between two distinct setups. We studied the statistical hypothesis testing for quantum repeated measurements models. In this presentation, I will present the model and illustrate it with some experiment. I will then explain the meaning of statistical hypothesis testing in terms of ability to identify, between two alternatives, the model corresponding to the data collected in a repeated measurement of a quantum system. I will finally explain how our results imply that the log likelihood ratio is an efficient witness of the true model of the experiment. My presentation will be illustrated with physically relevant models, particularly dealing with the emergence of the arrow of time.