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Device independent state estimation based on Bell's inequalities · Around

2009

Device independent state estimation based on Bell's inequalities

Bardyn, C. -E., Liew, T. C. H., Massar, S. et al.

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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.

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