Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions

Dafydd Gwion Evans; John Edward Gough; Matthew James

doi:10.1098/rsta.2011.0525

Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions

Dafydd Gwion Evans, John Edward Gough, Matthew James

Adran Ffiseg

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

2 Dyfyniadau (Scopus)

117 Wedi eu Llwytho i Lawr (Pure)

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We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	5437-5451
Nifer y tudalennau	15
Cyfnodolyn	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Cyfrol	370
Rhif cyhoeddi	1979
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1098/rsta.2011.0525
Statws	Cyhoeddwyd - 07 Tach 2012

Mynediad at Ddogfen

10.1098/rsta.2011.0525

Lie_Trotter_Rev.pdf

http://hdl.handle.net/2160/7905

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@article{1ba331389b734bceb7e00d69dc6c444e,

title = "Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions",

abstract = "We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.",

keywords = "quantum, stochastic, control, input, series product, Trotter product formula",

author = "Evans, {Dafydd Gwion} and Gough, {John Edward} and Matthew James",

note = "Evans, D. G., Gough, J. E., James, M. R. (2012). Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions. Philosophical Transcations of the Royal Society A. 370 (no. 1979), pp. 5437-5451.",

year = "2012",

month = nov,

day = "7",

doi = "10.1098/rsta.2011.0525",

language = "English",

volume = "370",

pages = "5437--5451",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "1364-5021",

publisher = "Royal Society",

number = "1979",

}

Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions. / Evans, Dafydd Gwion ; Gough, John Edward; James, Matthew.
Yn: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Cyfrol 370, Rhif 1979, 07.11.2012, t. 5437-5451.

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

TY - JOUR

T1 - Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions

AU - Evans, Dafydd Gwion

AU - Gough, John Edward

AU - James, Matthew

N1 - Evans, D. G., Gough, J. E., James, M. R. (2012). Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions. Philosophical Transcations of the Royal Society A. 370 (no. 1979), pp. 5437-5451.

PY - 2012/11/7

Y1 - 2012/11/7

N2 - We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.

AB - We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.

KW - quantum

KW - stochastic

KW - control

KW - input

KW - series product

KW - Trotter product formula

U2 - 10.1098/rsta.2011.0525

DO - 10.1098/rsta.2011.0525

M3 - Article

C2 - 23091219

SN - 1364-5021

VL - 370

SP - 5437

EP - 5451

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1979

ER -

Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions

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