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

Department of Physics

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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.

Original language	English
Pages (from-to)	5437-5451
Number of pages	15
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	370
Issue number	1979
DOIs	https://doi.org/10.1098/rsta.2011.0525
Publication status	Published - 07 Nov 2012

Keywords

quantum
stochastic
control
input
series product
Trotter product formula

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Lie_Trotter_Rev.pdf

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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.",

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KW - control

KW - input

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KW - Trotter product formula

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

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Keywords

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