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arXiv · 1005.3119

Fidelity is a sub-martingale for discrete-time quantum filters

Pierre Rouchon
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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 any discrete-time quantum filter: fidelity between the density matrix of the underlying Markov chain and the density matrix of its 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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Pierre Rouchon. 2011-03-19. Fidelity is a sub-martingale for discrete-time quantum filters. https://doi.org/10.1109/tac.2011.2161792

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