Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal-mines-paristech.archives-ouvertes.fr/hal-00492009
Contributor : François Chaplais <>
Submitted on : Monday, June 14, 2010 - 6:18:51 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM
Long-term archiving on: : Tuesday, September 14, 2010 - 8:38:06 PM

File

StabilityQuantumFilters.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00492009, version 1

Citation

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

Share

Metrics

Record views

522

Files downloads

100