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Pré-Publication, Document De Travail Année : 2010

On stability of discrete-time quantum filters

Pierre Rouchon

Résumé

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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Dates et versions

hal-00492009 , version 1 (14-06-2010)

Identifiants

  • HAL Id : hal-00492009 , version 1

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