  Franson's paradigm for nonlocal dispersion cancellation [J. D. Franson, Phys.
Rev. A {\bf 45,} 3126 (1992)] is studied using two kinds of jointly
Gaussian-state signal and reference beams with phase-sensitive cross
correlations. The first joint signal-reference state is nonclassical, with a
phase-sensitive cross correlation that is at the ultimate quantum-mechanical
limit. It models the outputs obtained from continuous-wave spontaneous
parametric downconversion. The second joint signal-reference state is
classical---it has a proper $P$ representation---with a phase-sensitive cross
correlation that is at the limit set by classical physics. Using these states
we show that a version of Franson's nonlocal dispersion cancellation
configuration has essentially identical quantum and classical explanations \em
except rm for the contrast obtained, which is much higher in the quantum case
than it is in the classical case. This work bears on Franson's recent paper [J.
D. Franson, arXiv:0907:5196 [quant-ph]], which asserts that there is no
classical explanation for all the features seen in quantum nonlocal dispersion
cancellation.
