Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions

D. Gwion Evans; John E. Gough; Matthew R. James

doi:10.1098/rsta.2011.0525

Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions

D. Gwion Evans
, John E. Gough^*
, Matthew R. James

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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	Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Volume	370
Issue number	1979
DOIs	https://doi.org/10.1098/rsta.2011.0525
Publication status	Published - 28 Nov 2012

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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 - Control

KW - Input

KW - Quantum

KW - Series product

KW - Stochastic

KW - Trotter product formula

UR - https://www.scopus.com/pages/publications/84868109498

U2 - 10.1098/rsta.2011.0525

DO - 10.1098/rsta.2011.0525

M3 - Article

SN - 1364-503X

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JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

JF - Philosophical transactions. Series 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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