An introduction to quantum filtering

Details An introduction to quantum filtering An introduction to quantum filtering

2006-01-30

arxiv.org/abs/math/0601741v1

SIAM J. Control Optim. 46, 2199-2241, 2007

Mathematics

Optimization and Control

41 pages, 1 figure

Scientific paper

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.

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