A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantu

• 作 者: Igor G.VLADIMIROV
• 机 构: College of Engineering and Computer Science, Australian National University, Canberra, ACT 2601, Aus
• 出 处: 控制理论与技术（英文版）
• 发表日期: 2017年3期
• 关键词: Quantum stochastic system quantum filtering equation Gaussian approximation

This paper is conced with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements.The system-observation dynamics are goved 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.