  Quantum entanglement, the non-separability of a multipartite wave function,
became essential in understanding the non-locality of quantum mechanics. In
optics, this non-locality can be demonstrated on impressively large length
scales, as photons travel with the speed of light and interact only weakly with
their environment. With the discovery of spontaneous parametric down-conversion
(SPDC) in nonlinear crystals, an efficient source for entangled photon pairs,
so-called biphotons, became available. It has recently been shown that SPDC can
also be implemented in nonlinear arrays of evanescently coupled waveguides
which allows the generation and the investigation of correlated quantum walks
of such biphotons in an integrated device. Here, we analytically and
experimentally demonstrate that the biphoton degrees of freedom are entailed in
an additional spatial dimension, therefore the SPDC and the subsequent quantum
random walk in one-dimensional (1D) arrays can be simulated through classical
optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby,
the output intensity images directly represent the biphoton correlations and
exhibit a clear violation of a Bell-type inequality.
