Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters

Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes

Fidelity is known to increase through any 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, fidelity is also increasing for discrete-time quantum filters attached to an arbitrary Kraus map: fidelity between the density matrix of the underlying Markov chain and the density matrix of the associated quantum filter is a sub-martingale. This result is not restricted to pure states. It also holds true for mixed states.

Domaines: Automatique / Robotique

Pierre Rouchon. Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters. IEEE Transactions on Automatic Control, 2011, 56 (11), pp.2743 - 2747. ⟨10.1109/TAC.2011.2161792⟩. ⟨hal-00654164⟩