Type-I spontaneous parametric down-converted biphotons can be described approximately by a double-Gaussian wavefunction in configuration space.
Using an effective propagator in the Fresnel approximation,  the time evolution and transversal spreading of the two-particle wavefunction, we find that the pair of photons develops a Gouy phase while it propagates. We show that the two-photon entanglement can be connected to the biphoton Gouy phase, as these quantities are Rayleigh-length-related.
Furthermore, we obtain the Gouy phase of the pair of photons wavepacket being focused through a thin lens, which is in reasonable agreement with the experimental data. Indicating that the Gouy phase obtained from the effective double-Gaussian biphoton wavefunction can be used as good approximation in exploring quantum correlations of
twin photons.
 Afterwards, we exploit the relation between phase-space correlations of biphotons diffracting through a double-slit as encoded in the logarithmic negativity and the Gouy phase.
We observe that measurements of Gouy phase differences provide information on the two-photons phase-space entanglement variation, governed by the
physical parameters of the experiment and expressed by the logarithmic negativity via covariance matrix elements.
Finally, we evaluate the Sorkin parameter $\kappa$ for biphotons and massive particles, which results from nonclassical path contributions of the kink type and loops to double- and triple-slit interferometry.
This simple unidimensional model for the evaluation of $\kappa$ predicts that kinked nonclassical paths may lead to $\kappa \approx 10^{-5}$ for biphotons.
We show that such a model reproduces well the Sorkin parameter for matter waves found in more involved approaches in the literature. Moreover, we establish a hierarchy of approximations based on the shape of the nonclassical paths for matter waves and
compare their size with leading relativistic corrections to the propagator.