| 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. |
| 关键词: Quantum stochastic system, quantum filtering equation, Gaussian approximation |
| DOI： |
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| 基金项目:This paper is dedicated to Professor Ian R. Petersen on the occasion of his 60th birthday. 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 [80] of this paper was presented at the IEEE 2016 Conference on Norbert Wiener in the 21st Century, 13-15 July 2016, Melbourne, Australia. |
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| A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems |
| I. G. Vladimirov |
| (College of Engineering and Computer Science, Australian National University, Canberra, ACT 2601, Australia) |
| 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. |
| Key words: Quantum stochastic system, quantum filtering equation, Gaussian approximation |
