In this paper, we study a representation of the quantum Itô algebra in Fock space and then by using a noncommutative Radon-Nikodym type theorem we study the density operators of output states as quantum martingales, where the output states are absolutely continuous with respect to an input (vacuum) state. Then by applying quantum martingale representation we prove that the density operators of regular, absolutely continuous output states belong to the commutant of the ⋆-algebra parameterizing the quantum Itô algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-3,
author = {Viacheslav Belavkin and Un Cig Ji},
title = {Quantum It\^o algebra and quantum martingale},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {47-58},
zbl = {1138.81033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-3}
}
Viacheslav Belavkin; Un Cig Ji. Quantum Itô algebra and quantum martingale. Banach Center Publications, Tome 75 (2007) pp. 47-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-3/