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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2011

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

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Pierre Rouchon

Résumé

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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Dates et versions

hal-00654164 , version 1 (21-12-2011)

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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⟩
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