Relations and Quantizations in the Category of Probabilistic Bundles

In this paper we generalise the classical notion of state of a probabilistic system to include a nontrivial minimal bound on the class of observables. A product is introduced and the resulting structure is shown to be a monoidal category. Probabilistic relations are defined and compositions of relations is introduced. The resulting structure is also a category, the category of probabilistic relations. Finally we embedd the category of probabilistic relations into a category of bimodules and show that in this context it is possible to quantize some aspects of the probabilistic description.