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

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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 languageEnglish
Pages (from-to)5437-5451
Number of pages15
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume370
Issue number1979
DOIs
Publication statusPublished - 07 Nov 2012

Keywords

  • quantum
  • stochastic
  • control
  • input
  • series product
  • Trotter product formula

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