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Understanding the quantitative relation between entanglement and Bellnonlocality is a longstanding open problem of both fundamental and practicalinterest. Here we provide a general approach to address this issue. Startingwith an observation that entanglement measures, while defined dramaticallydifferent in mathematics, are basically the distances between the state ofinterest and its closest separable state, we relate this minimal distancebetween states with distance-based Bell nonlocality, namely, the minimaldistance between correlation of interest with respect to the set of classicalcorrelations. This establishes the quantitative relation between entanglementand Bell nonlocality, leading to the bounds for entanglement in variouscontexts. Our approach enjoys the merits of: (i) generality, it applies to anyBell's scenario without requiring the information of devices and to manyentanglement measures, (ii) faithfulness, it gives a non-trivial entanglementestimation from any nonlocal correlation.

Lower-bounding entanglement with nonlocality in a general Bell's scenario