The stability of quantum markov filters

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Abstract

When are quantum filters asymptotically independent of the initial state? We show that this is the case for absolutely continuous initial states when the quantum stochastic model satisfies an observability condition. When the initial system is finite dimensional, this condition can be verified explicitly in terms of a rank condition on the coefficients of the associated quantum stochastic differential equation.

Original languageEnglish (US)
Pages (from-to)153-172
Number of pages20
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume12
Issue number1
DOIs
StatePublished - Mar 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

Keywords

  • Asymptotic stability
  • Nondemolition observations
  • Observability
  • Quantum Markov processes
  • Quantum filtering

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