Quantum filtering: a reference probability approach

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dc.creatorBouten, Luc
dc.creatorvan Handel, Ramon
dc.date2005-08-01
dc.date2006-01-30
dc.date.accessioned2026-07-07T06:42:18Z
dc.date.available2026-07-07T06:42:18Z
dc.descriptionThese 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 Hudson-Parthasarathy quantum Ito calculus and its use in the modelling of physical systems. Finally, we use a reference probability method to obtain quantum filtering equations, in the Belavkin-Zakai (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.
dc.description28 pages; see also math-ph/0511021 and math.OC/0601741
dc.identifierhttps://arxiv.org/abs/math-ph/0508006
dc.identifierhttp://arxiv.org/abs/math-ph/0508006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101991
dc.subjectMathematical Physics
dc.subjectOptimization and Control
dc.subjectProbability
dc.subjectQuantum Physics
dc.titleQuantum filtering: a reference probability approach
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