Quantum Information Processing with Spatially Structured Light

Qudits have proven to be a powerful resource for quantum information processing, offering enhanced channel capacities, improved robustness to noise, and highly efficient implementations of quantum algorithms. The encoding of photonic qudits in transverse-spatial degrees of freedom has emerged as a versatile tool for quantum information processing, allowing access to a vast information capacity within a single photon. In this review, we examine recent advances in quantum optical circuits with spatially structured light, focusing particularly on top-down approaches that employ complex mode-mixing transformations in free-space and fibers. In this context, we highlight circuits based on platforms such as multi-plane light conversion, complex scattering media, multimode and multi-core fibers. We discuss their applications for the manipulation and measurement of multi-dimensional and multi-mode quantum states. Furthermore, we discuss how these circuits have been employed to perform multi-party operations and multi-outcome measurements, thereby opening new avenues for scalable photonic quantum information processing.