Compact generation scheme of path–frequency hyperentangled photons using 2D periodical nonlinear photonic crystal

Hyperentanglement is a promising resource for achieving high capacity quantum communication. Here, we propose a compact scheme for the generation of path–frequency hyperentangled photon pairs via spontaneous parametric down-conversion (SPDC) processes, where six different paths and two different frequencies are covered. A two-dimensional periodical χ⁽²⁾ nonlinear photonic crystal (NPC) is designed to satisfy type-I quasi-phase-matching conditions in the plane perpendicular to the incident pump beam, and a perfect phase match is achieved along the pump beam’s direction to ensure high conversion efficiency, with theoretically estimated photon flux up to 2.068 × 10⁵ pairs⋅s⁻¹⋅mm⁻². We theoretically calculate the joint-spectral amplitude (JSA) of the generated photon pair and perform Schmidt decomposition on it, where the resulting entropy S of entanglement and effective Schmidt rank K reach 3.2789 and 6.4675, respectively. Our hyperentangled photon source scheme could provide new avenues for high-dimensional quantum communication and high-speed quantum information processing.