  Starting from an association scheme induced by a finite group and the
corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC),
their entangled versions, and interacting Fock spaces (IFS) using the quantum
probabilistic approach. Our constructions are based on the intersection numbers
and their duals Krien parameters of the schemes with examples focused on
regular (distance-regular and distance-transitive) graphs.
