  Understanding the relationship between entanglement and Bell nonlocality is
one of the long-lasting open problems in quantum physics which is important
both from the fundamental and application points of view. In particular, while
both entanglement and Bell nonlocality are key resources in quantum
information, the latter appears to be a stronger one because it allows for
information processing in the device-independent framework in which the players
need not trust their devices. Thus, understanding which entangled states give
rise to Bell nonlocality and thus are resourceful in this framework is an
important and interesting task. Here we establish the equivalence between
genuine entanglement and genuine nonlocal for a broad class of multipartite
(pure and mixed) states originating from the stabilizer formalism. In fact, we
demonstrate a much stronger result that any (mixed) stabilizer state defined on
a genuinely entangled subspace is multipartite fully nonlocal meaning that it
gives rise to correlations that have no contribution coming from local hidden
variable models of any type. We thus also introduce the first examples of
genuinely nonlocal subspaces in multiqubit Hilbert spaces in which every single
pure state is genuinely nonlocal.
