On stability of discrete-time quantum filters

Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes

Fidelity is known to increase through a Kraus map: the fidelity between two density matrices is less than the fidelity between their images via a Kraus map. We prove here that, in average, the square of the fidelity is also increasing for a quantum filter: the square of the fidelity between the density matrix of the underlying Markov chain and the density matrix of its associated quantum filter is a super-martingale. Thus discrete-time quantum filters are stable processes and tend to forget their initial conditions.

Domaines: Automatique / Robotique

Pierre Rouchon. On stability of discrete-time quantum filters. 2010. ⟨hal-00492009⟩