On stability of continuous-time quantum filters

Hadis Amini (1) , Mazyar Mirrahimi (2) , Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

We prove that the fidelity between the quantum state governed by a continuous time stochastic master equation driven by a Wiener process and its associated quantum-filter state is a sub-martingale. This result is a generalization to non-pure quantum states where fidelity does not coincide in general with a simple Frobenius inner product. This result implies the stability of such filtering process but does not necessarily ensure the asymptotic convergence of such quantum-filters.

Domaines: Automatique / Robotique

Hadis Amini, Mazyar Mirrahimi, Pierre Rouchon. On stability of continuous-time quantum filters. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011, Dec 2011, Orlando, United States. pp.6242 - 6247, ⟨10.1109/CDC.2011.6160631⟩. ⟨hal-00683468⟩