  In the study of quantum nonlocality, one obstacle is that the analytical
criterion for identifying the boundaries between quantum and postquantum
correlations has not yet been given, even in the simplest Bell scenario. We
propose a plausible, analytical, necessary and sufficient condition ensuring
that a nonlocal quantum correlation in the simplest scenario is an extremal
boundary point. Our extremality condition amounts to certifying an
information-theoretical quantity; the probability of guessing a measurement
outcome of a distant party optimized using any quantum instrument. We show that
this quantity can be upper and lower bounded from any correlation in a
device-independent way, and we use numerical calculations to confirm that
coincidence of the upper and lower bounds appears to be necessary and
sufficient for the extremality.
