  The notion of effectus from categorical logic is relevant in the emerging
field of categorical probability theory. In some cases, stochastic maps are
represented by maps in the Kleisli category of some probability monad. Quantum
homomorphisms from combinatorics and quantum information theory are the Kleisli
maps of certain sort of quantum monad. We show that the Kleisli category of
this quantum monad is an effectus. This gives rise to notions of quantum
probabilistic reasoning as predicates, validity, conditioning, and channels.
