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

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1 Author(s)
Rouchon, P. ; Centre Autom. et Syst., Mines ParisTech, Paris, France

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 11 )