# Quantum Itô algebra and quantum martingale

Viacheslav Belavkin; Un Cig Ji

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 47-58
- ISSN: 0137-6934

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topViacheslav 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 -

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