Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions
Date
2012
Authors
Evans, D. Gwion
Gough, J.E.
James, Matthew
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Publisher
Royal Society of London
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.
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Keywords
Keywords: Input; Quantum; Series product; Stochastic; Trotter product formula; Control; Quantum theory; Stochastic systems Control; Input; Quantum; Series product; Stochastic; Trotter product formula
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Source
Philosophical Transactions of the Royal Society Series A
Type
Journal article
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2037-12-31
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