  The characterization of quantum correlations in terms of
information-theoretic resource has been a fruitful approach to understand the
power of quantum correlations as a resource. While bipartite entanglement and
Bell inequality violation in this setting have been extensively studied,
relatively little is known about their multipartite counterpart. In this paper,
we apply and adapt the recently proposed definitions of multipartite
nonlocality [Phys. Rev. A 88, 014102] to the three- and four-partite scenario
to gain new insight on the resource aspect of multipartite nonlocal quantum
correlations. Specifically, we show that reproducing certain tripartite quantum
correlations requires mixtures of classical resources --- be it the ability to
change the groupings or the time orderings of measurements. Thus, when seen
from the perspective of biseparable one-way classical signaling resources,
certain tripartite quantum correlations do not admit a definite causal order.
In the four- partite scenario, we obtain a superset description of the set of
biseparable correlations which can be produced by allowing two groups of
bipartite non-signaling resources. Quantum violation of the resulting Bell-like
inequalities are investigated. As a byproduct, we obtain some new examples of
device-independent witnesses for genuine four-partite entanglement, and also
device-independent witnesses that allows one to infer the structure of the
underlying multipartite entanglement.
