A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems
Igor G.VLADIMIROV
摘要：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.
机标关键词：stochastic systemsdifferential equationGaussian approximationWiener processesmaster equationquantum stateform of
论文发表日期：2017-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：16( 177-192 )
英文信息