  Reconstructions of quantum theory usually implicitly assume that experimental
events are ordered within a global causal structure. The process matrix
framework accommodates quantum correlations that violate an inequality verified
by all causally ordered correlations. Using a generalized probabilistic
framework, we propose three principles constraining bipartite correlations to
the quantum bound. Our approach highlights the role of a measure of dependence
other than mutual information for an information-theoretic reconstruction of
causal structures in quantum theory.
