We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement criterion as well as by the continuous-variable version of the Peres-Horodecki criterion visualized on an equivalent Poincaré sphere.

Aided by quantum sources, quantum metrology helps to enhance measurement precision. Here, we introduce a method to enhance the measurement of a rotation angle. As a proof of principle, assisted by a quantum state called the squeezed orbital-angular-position (OAP) state and balance homodyne detection, we demonstrate in experiments 3 dB-enhanced measurements of a rotation-angle beyond the shot noise limit. A precision of up to $17.7\hspace{0.17em}\text{nrad}/\sqrt{\text{Hz}}$ is obtained. Furthermore, we discuss means to further improve the measurement with a high-order precision OAP squeezed state. The method holds promise for future practical applications, such as in high-sensitive Sagnac interferometry.

We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM₀₀ and first order transverse mode TEM₁₀ as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM₁₀ mode compared with that with the TEM₀₀ mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.

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.

A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.