Quantum Itô algebra and quantum martingale

Viacheslav Belavkin, and Un Cig Ji. "Quantum Itô algebra and quantum martingale." Banach Center Publications 78.1 (2007): 47-58. <http://eudml.org/doc/282413>.

@article{ViacheslavBelavkin2007,
abstract = {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.},
author = {Viacheslav Belavkin, Un Cig Ji},
journal = {Banach Center Publications},
keywords = {quantum Itô algebra; Fock space; input state; output state; quantum martingale},
language = {eng},
number = {1},
pages = {47-58},
title = {Quantum Itô algebra and quantum martingale},
url = {http://eudml.org/doc/282413},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Viacheslav Belavkin
AU - Un Cig Ji
TI - Quantum Itô algebra and quantum martingale
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 47
EP - 58
AB - 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.
LA - eng
KW - quantum Itô algebra; Fock space; input state; output state; quantum martingale
UR - http://eudml.org/doc/282413
ER -