Witnessing single-photon entanglement with local homodyne measurements

Single-photon entangled states constitute the simplest form of entanglement, yet they provide a valuable resource in quantum information sciences. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such resource is the difficulty in measuring it. Here, we present and experimentally test the first operational witness suited for single-photon entanglement which relies only on local homodyning and does not require post-selection. Our results highlight the potential of hybrid methods, where discrete entanglement is characterized through continuous-variable measurements, in verifying the proper functioning of future quantum networks.