  Metasurfaces based on resonant nanophotonic structures have enabled novel
types of flat-optics devices often outperforming the capabilities of bulk
components, yet these advances remain largely unexplored for quantum
applications. We show that non-classical multi-photon interferences can be
achieved at the subwavelength scale in all-dielectric metasurfaces. We
simultaneously image multiple projections of quantum states with a single
metasurface, enabling a robust reconstruction of amplitude, phase, coherence,
and entanglement of multi-photon polarization-encoded states. One- and
two-photon states are reconstructed through nonlocal photon correlation
measurements with polarization-insensitive click-detectors positioned after the
metasurface, and the scalability to higher photon numbers is established
theoretically. Our work illustrates the feasibility of ultra-thin quantum
metadevices for the manipulation and measurement of multi-photon quantum states
with applications in free-space quantum imaging and communications.
