On Asymptotic Stability of Non-Demolition Quantum Trajectories with Measurement Imperfections

Understand

We consider the question of asymptotic stability of quantum trajectories undergoing quantum non-demolition imperfect measurement, that is to say the convergence of the estimated trajectory towards the true trajectory whose parameters and initial state are not necessarily known.

• We give conditions on the estimated initial state and regions of validity for the estimated parameters so that this convergence is ensured.
• We illustrate these results through numerical simulations on the physical example [1] and discuss the asymptotic stability for a more realistic general case where decoherence acts on the system.
• In this case, the evolution is described by new Kraus operators which do not satisfy the quantum non-demolition property.