Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

Quantum trajectories represent the state of a quantum system undergoing repeated indirect measurements. A quantum trajectory is therefore a sequence of density matrices, and a natural question is to describe its asymptotic behaviour as the number of measurements goes to infinity. In generic situations, this behaviour can at best be a convergence in distribution and is therefore related to the existence of an invariant measure for the evolution. We give conditions for the existence and uniqueness of an invariant measure, and show the convergence in distribution. This is a joint work with Tristan Benoist, Martin Fraas, and Clément Pellegrini.