  Harnessing high-dimensional entangled states of light presents a frontier for
advancing quantum information technologies, from fundamental tests of quantum
mechanics to enhanced computation and communication protocols. In this context,
the spatial degree of freedom stands out as particularly suited for on-chip
integration. But while traditional demonstrations produce and manipulate
path-entangled states sequentially with discrete optical elements,
continuously-coupled nonlinear waveguide systems offer a promising alternative
where photons can be generated and interfere along the entire propagation
length, unveiling novel capabilities within a reduced footprint. Here we
exploit this concept to implement a compact and reconfigurable source of
spatially entangled photon pairs based on parametric down-conversion in AlGaAs
nonlinear waveguides arrays. We use a double-pump configuration to engineer the
output quantum state and implement various types of spatial correlations,
exploiting a quantum interference effect between the biphoton state generated
in each pumped waveguide. This demonstration, at room temperature and telecom
wavelength, illustrates the potential of continuously-coupled systems as a
promising alternative to discrete multi-component quantum circuits for
leveraging the high-dimensional spatial degree of freedom of photons.
