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The only information available about an alleged source of entangled quantumstates 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 themeasurements that are performed. We discuss how the quality of the source canbe assessed in this black-box scenario, as compared to an ideal source thatwould produce maximally entangled states (more precisely, any state for which$S=2\sqrt{2}$). To this end, we introduce several inequivalent notions offidelity, each one related to the use one can make of the source after havingassessed it; and we derive quantitative bounds for each of them in terms of theviolation $S$. We also derive a lower bound on the entanglement of the sourceas a function of $S$ only.

Device independent state estimation based on Bell's inequalities