TY - GEN
T1 - A phase-space formulation of the Belavkin-Kushner-Stratonovich filtering equation for nonlinear quantum stochastic systems
AU - Vladimirov, Igor G.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/18
Y1 - 2016/8/18
N2 - 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 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 also discuss a more 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.
AB - 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 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 also discuss a more 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.
UR - http://www.scopus.com/inward/record.url?scp=84987943637&partnerID=8YFLogxK
U2 - 10.1109/NORBERT.2016.7547465
DO - 10.1109/NORBERT.2016.7547465
M3 - Conference contribution
T3 - 2016 IEEE Conference on Norbert Wiener in the 21st Century, 21CW 2016
SP - 84
EP - 89
BT - 2016 IEEE Conference on Norbert Wiener in the 21st Century, 21CW 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE Conference on Norbert Wiener in the 21st Century, 21CW 2016
Y2 - 13 July 2016 through 16 July 2016
ER -