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

作者：Evans D Gwion; Gough John E^*; James Matthew R

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2012, 370(1979): 5437-5451.

DOI：10.1098/rsta.2011.0525

• quantum
• stochastic
• control
• input
• series product
• Trotter product formula

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.

• 出版日期2012-11-28