  Identifying which correlations among distant observers are possible within
our current description of Nature, based on quantum mechanics, is a fundamental
problem in Physics. Recently, information concepts have been proposed as the
key ingredient to characterize the set of quantum correlations. Novel
information principles, such as, information causality or non-trivial
communication complexity, have been introduced in this context and successfully
applied to some concrete scenarios. We show in this work a fundamental
limitation of this approach: no principle based on bipartite information
concepts is able to single out the set of quantum correlations for an arbitrary
number of parties. Our results reflect the intricate structure of quantum
correlations and imply that new and intrinsically multipartite information
concepts are needed for their full understanding.
