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Parameter estimation from measurements along quantum trajectories

P. Six 1 Philippe Campagne-Ibarcq 2, 3 L Bretheau 2, 3 Benjamin Huard 3 Pierre Rouchon 1, 3
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, CNRS - Centre National de la Recherche Scientifique : UMR8551
Abstract : The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the measurement outcomes. We then describe the structure of the corresponding particle quantum filters for estimating constant parameter and we prove their stability. In the continuous-time (dif-fusive) case, we propose a new formulation of these particle quantum filters. The interest of this new formulation is first to prove stability, and also to provide an efficient algorithm preserving, for any discretization step-size, positivity of the quantum states and parameter classical probabilities. This algorithm is tested on experimental data to estimate the detection efficiency for a superconducting qubit whose fluorescence field is measured using a heterodyne detector.
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P. Six, Philippe Campagne-Ibarcq, L Bretheau, Benjamin Huard, Pierre Rouchon. Parameter estimation from measurements along quantum trajectories. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. ⟨hal-01245085⟩

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