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Quasifree Stochastic Cocycles and Quantum Random Walks

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Quasifree Stochastic Cocycles and Quantum Random Walks. / Belton, Alexander Charles Richard; Gnacik, Michal; Lindsay, Jonathan Martin; Zhong, Ping.

In: Journal of Statistical Physics, Vol. 176, No. 1, 15.07.2019, p. 1-39.

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@article{dea4b6a4e50f4674bb8799de0604a118,
title = "Quasifree Stochastic Cocycles and Quantum Random Walks",
abstract = "The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson–Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.",
keywords = "Quantum stochastic calculus, Quasifree representation, Heat bath, Repeated quantum interactions, Noncommutative Markov chain, Quantum Langevin equation",
author = "Belton, {Alexander Charles Richard} and Michal Gnacik and Lindsay, {Jonathan Martin} and Ping Zhong",
year = "2019",
month = "7",
day = "15",
doi = "10.1007/s10955-019-02273-9",
language = "English",
volume = "176",
pages = "1--39",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "1",

}

RIS

TY - JOUR

T1 - Quasifree Stochastic Cocycles and Quantum Random Walks

AU - Belton, Alexander Charles Richard

AU - Gnacik, Michal

AU - Lindsay, Jonathan Martin

AU - Zhong, Ping

PY - 2019/7/15

Y1 - 2019/7/15

N2 - The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson–Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.

AB - The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson–Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.

KW - Quantum stochastic calculus

KW - Quasifree representation

KW - Heat bath

KW - Repeated quantum interactions

KW - Noncommutative Markov chain

KW - Quantum Langevin equation

U2 - 10.1007/s10955-019-02273-9

DO - 10.1007/s10955-019-02273-9

M3 - Journal article

VL - 176

SP - 1

EP - 39

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -