A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems
Date
2017
Authors
Vladimirov, Igor
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Link
Abstract
This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel
nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum
stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and
system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization
form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior
quasi-characteristic function (QCF) of the system conditioned on the measurements. This equation is a spatial Fourier domain
representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with
the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and
outline a Gaussian approximation of the posterior quantum state.
Description
Keywords
Quantum stochastic system, quantum filtering equation, Gaussian approximation
Citation
Collections
Source
Control Theory and Technology
Type
Journal article
Book Title
Entity type
Access Statement
License Rights
Restricted until
2099-12-31