Bosonic, fermionic, and anyonic symmetry in two-photon random scattering

We experimentally demonstrate the importance of two-photon symmetry for the propagation of spatial quantum correlations in a multiple-scattering disordered system. Two distinguishable entangled photons with tunable spatial exchange symmetry are sent through the scattering medium. The two photons are observed to have an ensemble-averaged tendency to cluster together (bosonic symmetry) or to avoid each other (fermionic symmetry). An intermediate degree of clustering is observed for anyonic exchange symmetry.