  We study the consequences of 'super-quantum non-local correlations' as
represented by the PR-box model of Popescu and Rohrlich, and show PR-boxes can
enhance the capacity of noisy interference channels between two senders and two
receivers. PR-box correlations violate Bell/CHSH inequalities and are thus
stronger -- more non-local -- than quantum mechanics; yet weak enough to
respect special relativity in prohibiting faster-than-light communication.
Understanding their power will yield insight into the non-locality of quantum
mechanics. We exhibit two proof-of-concept channels: first, we show a channel
between two sender-receiver pairs where the senders are not allowed to
communicate, for which a shared super-quantum bit (a PR-box) allows perfect
communication. This feat is not achievable with the best classical (senders
share no resources) or quantum entanglement-assisted (senders share
entanglement) strategies. Second, we demonstrate a class of channels for which
a tunable parameter achieves a double separation of capacities; for some range
of \epsilon, the super-quantum assisted strategy does better than the
entanglement-assisted strategy, which in turn does better than the classical
one.
