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

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.

12 pages

References in corpus (1)

• Quantum Feedback Networks: Hamiltonian Formulation

Cited by in corpus (2)

• Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
• On structure-preserving transformations of the Ito generator matrix for model reduction of quantum feedback networks