TITLE

Random-walk approximation to vacuum cocycles

AUTHOR(S)
Belton, Alexander C. R.
PUB. DATE
April 2010
SOURCE
Journal of the London Mathematical Society;Apr2010, Vol. 81 Issue 2, p412
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener–Itô decomposition, a Donsker-type theorem is proved, showing that these walks, after suitable scaling, converge in a strong sense to vacuum cocycles: these are vacuum-adapted processes that are Feller cocycles in the sense of Lindsay and Wills. This is employed to give a new proof of the existence of *-homomorphic quantum-stochastic dilations for completely positive contraction semigroups on von Neumann algebras and separable unital C* algebras. The analogous approximation result is also established within the standard quantum stochastic framework, using the link between the two types of adaptedness.
ACCESSION #
53297138

 

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