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 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 370 |
Issue number | 1979 |
DOIs | |
Publication status | Published - 07 Nov 2012 |
Keywords
- quantum
- stochastic
- control
- input
- series product
- Trotter product formula