Programmable two-photon quantum interference in ${10}^3$ channels in opaque scattering media

We investigate two-photon quantum interference in an opaque scattering medium that intrinsically supports ${10}^6$ transmission channels. By adaptive spatial phase-modulation of the incident wavefronts, the photons are directed at targeted speckle spots or output channels. From ${10}^3$ experimentally available coupled channels, we select two channels and enhance their transmission, to realize the equivalent of a fully programmable $2\times 2$ beam splitter. By sending pairs of single photons from a parametric down-conversion source through the opaque scattering medium, we observe two-photon quantum interference. The programmed beam splitter need not fulfill energy conservation over the two selected output channels and hence could be non-unitary. Consequently, we have the freedom to tune the quantum interference from bunching (Hong-Ou-Mandel-like) to antibunching. Our results establish opaque scattering media as a platform for high-dimensional quantum interference that is notably relevant for boson sampling and physical-key-based authentication.