Laurent Bruneau

The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states, and which is called a quantum trajectory. When the system under consideration is finite dimensional, and under some natural assumption related to the non-existence of so-called dark subspaces, the state of the systems tends to become pure along the trajectory, a result which goes back to Kummerer and Maassen ('2006). This purification result is then a key step to the asymptotic analysis of the quantum trajectory (invariant measure, law of large numbers, etc.). In this talk I will present some results concerning purification and invariant measures for the quantum trajectory associated to the (infinite dimensional) one atom maser model.
This talk is based on a joint work with T. Benoist and C. Pellegrini