  High-dimensional entangled states of light provide novel possibilities for
quantum information, from fundamental tests of quantum mechanics to enhanced
computation and communication protocols. In this context, the frequency degree
of freedom combines the assets of robustness to propagation and easy handling
with standard telecommunication components. Here we use an integrated
semiconductor chip to engineer the wavefunction and exchange statistics of
frequency-entangled photon pairs directly at the generation stage, without
post-manipulation. Tuning the spatial properties of the pump beam allows to
generate frequency-anticorrelated, correlated and separable states, and to
control the symmetry of the spectral wavefunction to induce either bosonic or
fermionic behaviors. These results, supported by analytical and numerical
calculations, open promising perspectives for the quantum simulation of
fermionic problems with photons on an integrated platform, as well as for
communication and computation protocols exploiting antisymmetric
high-dimensional quantum states.
