  Nonclassical properties of correlations-- like unpredictability, no-cloning
and uncertainty-- are known to follow from two assumptions: nonlocality and
no-signaling. For two-input-two-output correlations, we derive these properties
from a single, unified assumption: namely, the excess of the communication cost
over the signaling in the correlation. This is relevant to quantum temporal
correlations, resources to simulate quantum correlations and extensions of
quantum mechanics. We generalize in the context of such correlations the
nonclassicality result for nonlocal-nonsignaling correlations (Masanes, Acin
and Gisin, 2006) and the uncertainty bound on nonlocality (Oppenheim and
Wehner, 2010), when the no-signaling condition is relaxed.
