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On stability of discrete-time quantum filters

Abstract : Fidelity is known to increase through a 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, the square of the fidelity is also increasing for a quantum filter: the square of the fidelity between the density matrix of the underlying Markov chain and the density matrix of its associated quantum filter is a super-martingale. Thus discrete-time quantum filters are stable processes and tend to forget their initial conditions.
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Preprints, Working Papers, ...
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Contributor : François Chaplais Connect in order to contact the contributor
Submitted on : Monday, June 14, 2010 - 6:18:51 PM
Last modification on : Wednesday, November 17, 2021 - 12:30:58 PM
Long-term archiving on: : Tuesday, September 14, 2010 - 8:38:06 PM


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  • HAL Id : hal-00492009, version 1


Pierre Rouchon. On stability of discrete-time quantum filters. 2010. ⟨hal-00492009⟩



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