  We propose a novel form of classification of multipartite states, in terms of
the maximum degree of non-locality they can exhibit under any choice of local
observables. This uses the hierarchy of notions previously introduced by
Abramsky and Brandenburger: strong contextuality, logical contextuality, and
probabilistic contextuality.
  We study n-qubit pure states. We conjecture that for more than 2 parties, all
entangled states are logically contextual. We prove a number of results in
support of this conjecture: (1) We show that all permutation-symmetric states
are logically non-local. (2) We study the class of balanced states with
functional dependencies. These states are described by Boolean functions and
have a rich structure, allowing a detailed analysis, which again confirms the
conjecture in this case.
