  The generation and manipulation of hybrid entanglement of light involving
discrete- and continuous-variable states have recently appeared as essential
resources towards the realization of heterogeneous quantum networks. Here we
investigate a scheme for the remote generation of hybrid entanglement between
particle-like and wave-like optical qubits based on a non-local heralding
photon detection. We also extend this scheme with additional local or non-local
detections. An additional local heralding allows the resulting state to exhibit
a higher fidelity with the targeted entangled qubits while a two-photon
non-local heralding detection gives access to a higher dimensionality in the
discrete-variable subspace, resulting thereby in the generation of hybrid
entangled qutrits. The implementation of the presented schemes, in combination
with ongoing works on high-fidelity quantum state engineering, will provide
novel non-classical light sources for the development of optical hybrid
architectures.
