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=22). 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.
@article{arxiv.0907.2170,
title = {Device independent state estimation based on Bell's inequalities},
author = {C. -E. Bardyn and T. C. H. Liew and S. Massar and M. McKague and V. Scarani},
journal= {arXiv preprint arXiv:0907.2170},
year = {2009}
}