On-chip engineering of high-dimensional path-entangled states in a quadratic coupled-waveguide system

High-dimensional quantum entangled states are a highly desired resource for their extended possibilities in quantum information processing. In this paper, we introduce on-chip engineering of a variety of path-entangled states based on the simultaneous enabling of spontaneous parametric down-conversion and efficient coupling between waveguides in a quadratic coupled-waveguide system. By varying the properties of pump beams, the phase-matching conditions, and the coupling coefficients in a three-coupled-waveguide system, it is possible to generate the deterministic and robust three-path biphoton entangled states without any postprocessing, as well as to transform the output photons among different types of path entanglement. This integrated implementation of the entanglement source will become an important building block for practical applications of on-chip quantum technologies.