Metasurface quantum graphs for generalized Hong-Ou-Mandel interference

Multiphoton interference and entanglement are fundamental to quantum information science, yet extending these effects to higher-dimensional systems remains challenging given the imperfections and complexity of scaling conventional linear-optical setups. We present a generalized Hong-Ou-Mandel effect using metasurfaces and graph theory, achieving controlled multiphoton bunching, antibunching, and entanglement across parallel Jones matrix-encoded spatial modes-all within a single-layer metasurface. A graph-theoretic dual framework is introduced that simultaneously encodes the metasurface-based multiport interferometer designs and its resulting nonclassical correlations, enabling the direct translation of linear quantum optical networks into a single-layer metasurface. We also demonstrate the ability of metasurfaces to produce multipath-entangled states and perform transformations equivalent to higher-order Hadamard interferometers. Our results underscore metasurface quantum graphs for scalable, low-decoherence quantum information infrastructure.