The Estimation Lie Algebra Associated with Quantum Filters

Nina Amini, John E. Gough

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We introduce the Lie algebra of super-operators associated with a quantum filter, specifically emerging from the Stratonovich calculus. In classical filtering, the analogue algebra leads to a geometric theory of nonlinear filtering which leads to well-known results by Brockett and by Mitter characterizing potential models where the curse-of-dimensionality may be avoided, and finite dimensional filters obtained. We discuss the quantum analogue to these results. In particular, we see that, in the case where all outputs are subjected to homodyne measurement, the Lie algebra of super-operators is isomorphic to a Lie algebra of system operators from which one may approach the question of the existence of finite-dimensional filters
Original languageEnglish
Article number1950004
JournalOpen Systems and Information Dynamics
Issue number2
Publication statusPublished - 15 Jul 2019


  • Lie algebras
  • Quantum trajectories
  • estimation algebras
  • homodyning
  • quantum filtering


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