  We construct implementations of the PR-box using quantum and classical
channels as state spaces. In both cases our constructions are very similar and
they share the same idea taken from general probabilistic theories and the
square state space model. We construct all quantum qubit channels that
maximally violate a given CHSH inequality, we show that they all are
entanglement-breaking channels, that they have certain block-diagonal structure
and we present some examples of such channels.
