Deterministic generation of large-scale hyperentanglement in three degrees of freedom

Entanglement serves as a fundamental resource for quantum information protocols, and hyperentanglement has received an increasing amount of attention for its high-capacity characteristic. Increasing the scale of hyperentanglement, i.e., the number of modes in a hyperentangled system, is crucial for enhancing its capability in quantum information processing. Here, we demonstrate the generation of large-scale continuous-variable (CV) hyperentanglement in three degrees of freedom (DOFs), including azimuthal and radial indices of Laguerre-Gaussian (LG) modes and frequency. In our experiment, 216 pairs of hyperentangled modes are deterministically generated from the four-wave mixing process in an atomic vapor. In addition, we show that the entanglement between coherent LG superposition modes denoted by both azimuthal and radial quantum numbers can also be generated from this system. Such large-scale CV hyperentanglement in three DOFs presents an efficient scheme to significantly increase the information capacity of the CV system. Our results provide a new platform for studying CV quantum information and open the avenue for constructing high-capacity parallel and multiple-DOF CV quantum information protocols.