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Strong convergence of quantum random walks via semigroup decomposition

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Strong convergence of quantum random walks via semigroup decomposition. / Belton, Alexander Charles Richard; Gnacik, Michal; Lindsay, Jonathan Martin.

In: Annales Henri Poincaré, Vol. 19, No. 6, 06.2018, p. 1711-1746.

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Belton, Alexander Charles Richard ; Gnacik, Michal ; Lindsay, Jonathan Martin. / Strong convergence of quantum random walks via semigroup decomposition. In: Annales Henri Poincaré. 2018 ; Vol. 19, No. 6. pp. 1711-1746.

Bibtex

@article{74576eddacfa4ee8a1594ee4ed27b37a,
title = "Strong convergence of quantum random walks via semigroup decomposition",
abstract = "We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.",
keywords = "Quantum random walk, repeated interactions, noncommutative Markov chain, toy Fock space, quantum stochastic cocycle, series product, quantum stochastic Trotter product",
author = "Belton, {Alexander Charles Richard} and Michal Gnacik and Lindsay, {Jonathan Martin}",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-018-0676-4",
year = "2018",
month = jun
doi = "10.1007/s00023-018-0676-4",
language = "English",
volume = "19",
pages = "1711--1746",
journal = "Annales Henri Poincar{\'e}",
issn = "1424-0637",
publisher = "Birkhauser Verlag Basel",
number = "6",

}

RIS

TY - JOUR

T1 - Strong convergence of quantum random walks via semigroup decomposition

AU - Belton, Alexander Charles Richard

AU - Gnacik, Michal

AU - Lindsay, Jonathan Martin

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-018-0676-4

PY - 2018/6

Y1 - 2018/6

N2 - We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.

AB - We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.

KW - Quantum random walk

KW - repeated interactions

KW - noncommutative Markov chain

KW - toy Fock space

KW - quantum stochastic cocycle

KW - series product

KW - quantum stochastic Trotter product

U2 - 10.1007/s00023-018-0676-4

DO - 10.1007/s00023-018-0676-4

M3 - Journal article

VL - 19

SP - 1711

EP - 1746

JO - Annales Henri Poincaré

JF - Annales Henri Poincaré

SN - 1424-0637

IS - 6

ER -