A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems View Full Text


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Article Info

DATE

2017-08

AUTHORS

Igor G. Vladimirov

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. More... »

PAGES

177-192

References to SciGraph publications

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    http://scigraph.springernature.com/pub.10.1007/s11768-017-7012-2

    DOI

    http://dx.doi.org/10.1007/s11768-017-7012-2

    DIMENSIONS

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