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Stability of continuous-time quantum filters with measurement imperfections

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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 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.

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Author information

Authors and Affiliations

  1. Edward L. Ginzton Laboratory, Stanford University, Stanford, CA, 94305, USA

    H. Amini

  2. Institut de Mathématiques, IMT, Université de Toulouse (UMR 5219), 31062, Toulouse, Cedex 9, France

    C. Pellegrini

  3. Centre Automatique et Systèmes, Mines ParisTech, 60 Bd Saint Michel, 75272, Paris cedex 06, France

    P. Rouchon

Authors
  1. H. Amini
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  2. C. Pellegrini
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  3. P. Rouchon
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Correspondence to H. Amini.

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Amini, H., Pellegrini, C. & Rouchon, P. Stability of continuous-time quantum filters with measurement imperfections. Russ. J. Math. Phys. 21, 297–315 (2014). https://doi.org/10.1134/S1061920814030029

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  • DOI: https://doi.org/10.1134/S1061920814030029

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