  Acin et al. introduced a unified framework for the study of no-signalling
correlations. Such a framework is based on the notion of local quantum
measurements, but, in order to account for beyond-quantum correlations, global
pseudo-states that are not positive semidefinite are allowed. After a short
review of the formalism, we consider its use in the quantification of both
general non-local and beyond-quantum correlations. We argue that the unified
framework for correlations provides a simple approach to such a quantification,
in particular when the quantification is meant to be operational and meaningful
in a resource-theory scenario, i.e., when considering the processing of
resources by means of non-resources. We relate different notions of robustness
of correlations, both at the level of (pseudo-)states and abstract probability
distributions, with particular focus on the beyond-quantum robustness of
correlations and pseudo-states. We revisit known results and argue that, within
the unified framework, the relation between the two levels---that of operators
and that of probability distributions---is very strict. We point out how the
consideration of robustness at the two levels leads to a natural framework for
the quantification of entanglement in a device-independent way. Finally, we
show that the beyond-quantum robustness of the non-positive operators needed to
achieve beyond-quantum correlations coincides with their negativity and their
distance from the set of quantum states. As an example, we calculate the
beyond-quantum robustness for the case of a noisy Popescu-Rohrlich box.
