Stability of continuous-time quantum filters with measurement imperfections

Hadis Amini (1, 2) , Clément Pellegrini (3) , Pierre Rouchon (4)

1 Swiss Finance Institute
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 CAS - Centre Automatique et Systèmes

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 sys-tem 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 in-completeness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum sys-tems and where the measurement imperfections are modeled by a left stochastic matrix.

Mots clés: measurement errors; quantum trajectories; Poisson process; Wiener process; continuous-time stochastic master equations; stability; Quantum filtering

Domaines: Automatique / Robotique; Mathématiques [math]; Physique mathématique [math-ph]

Hadis Amini, Clément Pellegrini, Pierre Rouchon. Stability of continuous-time quantum filters with measurement imperfections. Russian Journal of Mathematical Physics, 2014, 21 (3), pp.297 - 315. ⟨10.1134/S1061920814030029⟩. ⟨hal-01111672⟩