  In quantum optics, measurement statistics -- for example, photocounting
statistics -- are considered nonclassical if they cannot be reproduced with
statistical mixtures of classical radiation fields. We have formulated a
necessary and sufficient condition for such nonclassicality. This condition is
given by a set of inequalities that tightly bound the convex set of
probabilities associated with classical electromagnetic radiation. Analytical
forms for full sets and subsets of these inequalities are obtained for
important cases of realistic photocounting measurements and unbalanced homodyne
detection. As an example, we consider photocounting statistics of
phase-squeezed coherent states. Contrary to a common intuition, the analysis
developed here reveals distinct nonclassical properties of these statistics
that can be experimentally corroborated with minimal resources.
