On chip high-dimensional entangled photon sources

High-dimensional quantum entanglement is an important resource for emerging quantum technologies such as quantum communication and quantum computation. The scalability of metres-long experimental setups limits high-dimensional entanglement in bulk optics. Advancements in quantum technology hinge on reproducible, and reconfigurable quantum devices -- including photon sources, which are challenging to achieve in a scalable manner using bulk optics. Advances in nanotechnology and CMOS-compatible integration techniques have enabled the generation of entangled photons on millimeter-scale chips, significantly enhancing scalability, stability, replicability, and miniaturization for real-world quantum applications. In recent years we have seen several chip-scale demonstrations with different degrees of freedom including path, frequency-bin, time-bin, and transverse modes, on many material platforms. A complete quantum photonic integrated circuit requires the generation, manipulation, and detection of qudits, involving various active and passive quantum photonic components which further increase the degree of complexity. Here, we review and introduce the nonlinear optical processes that facilitate on-chip high-dimensional entangled photon sources and the currently used material platforms. We discuss a range of current implementations of on-chip high-dimensional entangled photon sources and demonstrated applications. We comment on the current challenges due to the limitations of individual material platforms and present future opportunities in hybrid and heterogeneous integration strategies for the next generation of integrated quantum photonic chips.