Russian Journal of Mathematical Physics

, Volume 21, Issue 3, pp 297–315 | Cite as

Stability of continuous-time quantum filters with measurement imperfections

  • H. Amini
  • C. Pellegrini
  • P. Rouchon


The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes and that takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems and where the measurement imperfections are modelled by a left stochastic matrix.


Mathematical Physic Markov Process Poisson Process Wiener Process Quantum Trajectory 
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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Edward L. Ginzton LaboratoryStanford UniversityStanfordUSA
  2. 2.Institut de Mathématiques, IMTUniversité de Toulouse (UMR 5219)Toulouse, Cedex 9France
  3. 3.Centre Automatique et SystèmesMines ParisTechParis cedex 06France

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