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

D. G. Evans, J. E. Gough, M. R. James
2012 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
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.
doi:10.1098/rsta.2011.0525 pmid:23091219 fatcat:eiguj6hv2nfkzmeihddoeit4ne