On asymptotic stability of quantum trajectories and their Cesaro mean
Résumé
We address the question of stability of quantum trajectories, also referred as quantum filters. We determine the limit of the quantum fidelity between the true quantum trajectory and the estimated one. Under a purification assumption we show that this limit equals to one meaning that quantum filters are stable. In the general case, under an identifiability and a spectral assumption we show that the limit of the Cesaro mean of the estimated trajectory is the same as the true one.