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Stability of continuous-time quantum filters with measurement imperfections

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

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