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 language | English |
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Pages (from-to) | 5437-5451 |
Number of pages | 15 |
Journal | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences |
Volume | 370 |
Issue number | 1979 |
DOIs | |
Publication status | Published - 28 Nov 2012 |