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

Abstract : 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.
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Submitted on : Wednesday, December 21, 2011 - 6:41:24 AM
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Pierre Rouchon. Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2011, 56 (11), pp.2743 - 2747. ⟨10.1109/TAC.2011.2161792⟩. ⟨hal-00654164⟩

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