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

作者：Vladimirov, Igor G.^*

来源：Control Theory and Technology, 2017, 15(3): 177-192.

DOI：10.1007/s11768-017-7012-2

• Characteristic functions
• Gaussian approximations
• Innovation process
• Nondemolition measurement
• Phase space formulation
• Quantum filtering
• Quantum stochastic differential equations
• Stochastic master equations

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 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.

• 出版日期2017-8-1
• 单位The Australian National University; Australian National university