High-dimensional entanglement is a critical foundation for the growing demand for information capacity to implement the high-capacity quantum task. Here, we report continuous-variable high-dimensional entanglement with three degrees of freedom (frequency, polarization, and orbital angular momentum) directly generated with a single type-II optical parametric oscillator (OPO) cavity. By compensating both for dispersion in frequency modes and astigmatism in higher-order transverse modes, the OPO is capable of oscillating simultaneously and outputting thousands of entanglement pairs. The three degrees of freedom high-dimensional entanglement are verified simultaneously possessing frequency comb, spin, and orbital angular momentum entanglement via 14 pairs of Hermite–Gaussian mode correlations measurement. Then, the “space-frequency” multiplexing quantum dense coding communication is also demonstrated by using the entanglement resource. It shows the great superiority of high-dimensional entanglement in implementing the high-capacity quantum task. Apart from an increased channel capacity, it is possible to conduct deterministic high-dimensional quantum protocols, quantum imaging, and especially quantum computing.

As a highly entangled quantum network, the cluster state has the potential for greater information capacity and use in measurement-based quantum computation. Here, we report generating a continuous-variable quadripartite “square” cluster state of multiplexing orthogonal spatial modes in a single optical parametric amplifier (OPA), and further improve the quality of entanglement by optimizing the pump profile. We produce multimode entanglement of two first-order Hermite–Gauss modes within one beam in a single multimode OPA and transform it into a cluster state by phase correction. Furthermore, the pump-profile dependence of the entanglement of this state is explored. Compared with fundamental mode pumping, an enhancement of approximately 33% is achieved using the suitable pump-profile mode. Our approach is potentially scalable to multimode entanglement in the spatial domain. Such spatial cluster states may contribute to future schemes in spatial quantum information processing.