On-chip generation of heralded photon-number states
Beyond the use of genuine monolithic integrated optical platforms, we report here a hybrid strategy enabling on-chip generation of configurable heralded two-photon states. More specifically, we combine two different fabrication techniques, \textit{i.e.}, non-linear waveguides on lithium niobate for efficient photon-pair generation and femtosecond-laser-direct-written waveguides on glass for photon manipulation. Through real-time device manipulation capabilities, a variety of path-coded heralded two-photon states can be produced, ranging from product to entangled states. Those states are engineered with high levels of purity, assessed by fidelities of 99.5$\pm$8\% and 95.0$\pm$8\%, respectively, obtained via quantum interferometric measurements. Our strategy therefore stands as a milestone for further exploiting entanglement-based protocols, relying on engineered quantum states, and enabled by scalable and compatible photonic circuits.