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The fidelity between the state of a continuously observed quantum system andthe state of its associated quantum filter, is shown to be always asubmartingale. The observed system is assumed to be governed by acontinuous-time Stochastic Master Equation (SME), driven simultaneously byWiener and Poisson processes and that takes into account incompleteness anderrors in measurements. This stability result is the continuous-timecounterpart of a similar stability result already established for discrete-timequantum systems and where the measurement imperfections are modeled by a leftstochastic matrix.

Stability of continuous-time quantum filters with measurement imperfections