%0 Journal Article
%T An introduction to quantum filtering
%A Luc Bouten
%A Ramon van Handel
%A Matthew James
%J Mathematics
%D 2006
%I arXiv
%X This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum It\^o calculus and its use in the modelling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.
%U http://arxiv.org/abs/math/0601741v1