Quantum filtering for multiple diffusive and Poissonian measurements

Abstract

We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations of diffusive and Poissonian processes. This covers the standard cases from quantum optics, where homodyne detection may be described as a diffusive process and photon counting may be described as a Poissonian process. We obtain a necessary and sufficient condition for any pair of such measurements taken at different output channels to satisfy a commutation relationship. Then, we derive a general, multiple measurement quantum filter as an extension of a single-measurement quantum filter. As an application we explicitly obtain the quantum filter corresponding to homodyne detection and photon counting at the output ports of a beam splitter, correcting an earlier result.

19 Pages, 4 Figures

References in corpus (4)

• Photonic Boson Sampling in a Tunable Circuit
• Feedback control of quantum state reduction
• Optimal state estimation for cavity optomechanical systems
• Quantum filtering for multiple diffusive and Poissonian measurements

Cited by in corpus (4)

• A Quantum Extended Kalman Filter
• Quantum filtering for multiple diffusive and Poissonian measurements
• A Phase-space Formulation of the Belavkin-Kushner-Stratonovich Filtering Equation for Nonlinear Quantum Stochastic Systems
• Quantum filtering for a two-level atom driven by two counter-propagating photons