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arXiv · 1309.0559

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

D. Gwion Evans·J. E. Gough·M. R. James
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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.

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D. Gwion Evans, J. E. Gough, M. R. James. 2013-09-03. Non-abelian Weyl Commutation Relations and the Series Product of Quantum Stochastic Evolutions. https://doi.org/10.1098/rsta.2011.0525

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