  The only information available about an alleged source of entangled quantum
states is the amount $S$ by which the Clauser-Horne-Shimony-Holt (CHSH)
inequality is violated: nothing is known about the nature of the system or the
measurements that are performed. We discuss how the quality of the source can
be assessed in this black-box scenario, as compared to an ideal source that
would produce maximally entangled states (more precisely, any state for which
$S=2\sqrt{2}$). To this end, we introduce several inequivalent notions of
fidelity, each one related to the use one can make of the source after having
assessed it; and we derive quantitative bounds for each of them in terms of the
violation $S$. We also derive a lower bound on the entanglement of the source
as a function of $S$ only.
