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Exponential Stability of Subspaces for Quantum Stochastic Master Equations

Annales Henri Poincaré volume 18, pages 2045–2074 (2017)Cite this article

Abstract

We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant for the average evolution and that the same equivalence holds for the global asymptotic stability. Moreover, we prove that a strict linear Lyapunov function for the average evolution always exists, and latter can be used to derive sharp bounds on the Lyapunov exponents of the associated semigroup. Nonetheless, we also show that taking into account the measurements can lead to an improved bound on stability rate for the stochastic, non-averaged dynamics. We discuss explicit examples where the almost sure stability rate can be made arbitrary large while the average one stays constant.

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Author information

Authors and Affiliations

  1. CNRS, Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse UPS, 31062, Toulouse, France

    Tristan Benoist

  2. Institut de Mathématiques de Toulouse Equipe de Statistique et de Probabilité, Université Paul Sabatier, 31062, Toulouse Cedex 9, France

    Clément Pellegrini

  3. Department of Information Engineering, Universitá degli Studi di Padova, via gradenigo 6/b, 35131, Padova, Italy

    Francesco Ticozzi

  4. Department of Physics and Astronomy, Dartmouth College, 6127 Wilder, Hanover, NH, USA

    Francesco Ticozzi

Authors
  1. Tristan Benoist
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  2. Clément Pellegrini
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  3. Francesco Ticozzi
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Correspondence to Tristan Benoist.

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Communicated by Claude Alain Pillet.

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Benoist, T., Pellegrini, C. & Ticozzi, F. Exponential Stability of Subspaces for Quantum Stochastic Master Equations. Ann. Henri Poincaré 18, 2045–2074 (2017). https://doi.org/10.1007/s00023-017-0556-3

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  • DOI: https://doi.org/10.1007/s00023-017-0556-3