  Realist interpretations of quantum mechanics presuppose the existence of
elements of reality that are independent of the actions used to reveal them.
Such a view is challenged by several no-go theorems that show quantum
correlations cannot be explained by non-contextual ontological models, where
physical properties are assumed to exist prior to and independently of the act
of measurement. However, all such contextuality proofs assume a traditional
notion of causal structure, where causal influence flows from past to future
according to ordinary dynamical laws. This leaves open the question of whether
the apparent contextuality of quantum mechanics is simply the signature of some
exotic causal structure, where the future might affect the past or distant
systems might get correlated due to non-local constraints. Here we show that
quantum predictions require a deeper form of contextuality: even allowing for
arbitrary causal structure, no model can explain quantum correlations from
non-contextual ontological properties of the world, be they initial states,
dynamical laws, or global constraints.
