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

作     者：Igor G. VLADIMIROV 

作者机构：College of Engineering and Computer Science Australian National University Canberra ACT 2601 Australia 

出 版 物：《Control Theory and Technology》 (控制理论与技术（英文版）)

年 卷 期：2017年第15卷第3期

页      面：177-192页

核心收录：

学科分类：0820[工学-石油与天然气工程] 070207[理学-光学] 07[理学] 08[工学] 0802[工学-机械工程] 0825[工学-航空宇航科学与技术] 0811[工学-控制科学与工程] 0702[理学-物理学] 080201[工学-机械制造及其自动化] 

基　　金：this work was initiated while the author was with the unsw canberra  australia  where it was supported by the australian research council  and was completed at the australian national university under support of the air force office of scientific research (afosr) under agreement number fa2386-16-1-4065. a brief version of this paper was presented at the ieee 2016conference on norbert wiener in the 21st century  13-15july 2016  melbourne  australia 

主　　题：Quantum stochastic system quantum filtering equation Gaussian approximation 

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.