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Quantum entanglement, the non-separability of a multipartite wave function,became essential in understanding the non-locality of quantum mechanics. Inoptics, this non-locality can be demonstrated on impressively large lengthscales, as photons travel with the speed of light and interact only weakly withtheir 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 canalso be implemented in nonlinear arrays of evanescently coupled waveguideswhich allows the generation and the investigation of correlated quantum walksof such biphotons in an integrated device. Here, we analytically andexperimentally demonstrate that the biphoton degrees of freedom are entailed inan additional spatial dimension, therefore the SPDC and the subsequent quantumrandom walk in one-dimensional (1D) arrays can be simulated through classicaloptical beam propagation in a two-dimensional (2D) photonic lattice. Thereby,the output intensity images directly represent the biphoton correlations andexhibit a clear violation of a Bell-type inequality.

Biphoton generation in quadratic waveguide arrays: A classical optical simulation