Quantum filtering: a reference probability approach
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چکیده
These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. Next we describe the HudsonParthasarathy quantum Itô calculus and its use in the modelling of physical systems. Finally, we use a reference probability method to obtain quantum filtering equations, in the BelavkinZakai (unnormalized) form, for several system-observation models from quantum optics. The normalized (Belavkin-Kushner-Stratonovich) form is obtained through a noncommutative analogue of the Kallianpur-Striebel formula.
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تاریخ انتشار 2005