Abstract
A quantum stochastic product is a binary operation on the space of quantum states preserving the convex structure. We describe a class of associative stochastic products, the twirled products, that have interesting connections with quantum measurement theory. Constructing such a product involves a square integrable group representation, a probability measure and a fiducial state. By extending a twirled product to the full space of trace class operators, one obtains a Banach algebra. This algebra is commutative if the underlying group is abelian. In the case of the group of translations on phase space, one gets a quantum convolution algebra, a quantum counterpart of the classical phase-space convolution algebra. The peculiar role of the fiducial state characterizing each quantum convolution product is highlighted.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)
Subject
Applied Mathematics,Geometry and Topology,Mathematical Physics
Cited by
2 articles.
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