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 journalArticlepeer-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 languageEnglish
    Pages (from-to)5437-5451
    Number of pages15
    JournalPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
    Volume370
    Issue number1979
    DOIs
    Publication statusPublished - 28 Nov 2012

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