  Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown
to be related to the Gouy phase shifts (D. Kawase et al., Phys. Rev. Lett. 101,
050501 (2008)) allowing for a non-destructive manipulation of photonic quantum
states. In this work we exploit the relation between phase space correlations
of biphotons produced by spontaneously parametric down conversion (SPDC) as
encoded in the logarithmic negativity (LN) and the Gouy phase as they are
diffracted through an asymmetrical double slit setup. Using an analytical
approach based on a double-gaussian approximation for type-I SPDC biphotons, we
show that measurements of Gouy phase differences provide information on their
phase space entanglement variation, governed by the physical parameters of the
experiment and expressed by the LN via covariance matrix elements.
