  In this short note we present a new approach to non-classical correlations
that is based on the compression rates for bit strings generated by Alice and
Bob. We use normalised compression distance introduced by Cilibrasi and Vitanyi
to derive information-theoretic inequalities that must be obeyed by classically
correlated bit strings and that are violated by PR-boxes. We speculate about a
violation of our inequalities by quantum mechanical correlations.
