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In the study of quantum nonlocality, one obstacle is that the analyticalcriterion for identifying the boundaries between quantum and postquantumcorrelations has not yet been given, even in the simplest Bell scenario. Wepropose a plausible, analytical, necessary and sufficient condition ensuringthat a nonlocal quantum correlation in the simplest scenario is an extremalboundary point. Our extremality condition amounts to certifying aninformation-theoretical quantity; the probability of guessing a measurementoutcome of a distant party optimized using any quantum instrument. We show thatthis quantity can be upper and lower bounded from any correlation in adevice-independent way, and we use numerical calculations to confirm thatcoincidence of the upper and lower bounds appears to be necessary andsufficient for the extremality.

Necessary and sufficient criterion for extremal quantum correlations in the simplest Bell scenario