  We derive an inequality bounding the strength of temporal correlations for a
pair of light beams prepared in a separable state and propagating through
dispersive media with opposite signs of group velocity dispersion. The
presented inequality can be violated by entangled states of light, such as
photon pairs produced in spontaneous parametric down-conversion. Because the
class of separable states covers the entire category of classical fields as a
particular case, this result provides an unambiguously quantum feature of
nonlocal dispersion cancellation that cannot be reproduced within the classical
theory of electromagnetic radiation.
