Device independent state estimation based on Bell's inequalities
Abstract
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.