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

Author: Pierre Rouchon, IEEE Transactions on Automatic Control, Vol 56, no 11, pp. 2743 - 2747, July 14 2011, DOI: 10.1109/TAC.2011.2161792
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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BibTeX:
@Article{,
author = {Pierre Rouchon},
title = {Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters},
journal = {IEEE Transactions on Automatic Control},
volume = {56},
number = {11},
pages = {2743 - 2747},
year = {2011},
}