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

Evans, D. Gwion; Gough, J.E.; James, Matthew


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.

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Philosophical Transactions of the Royal Society Series A
DOI: 10.1098/rsta.2011.0525


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