  How can one detect entanglement between multiple optical paths sharing a
single photon? We address this question by proposing a scalable protocol, which
only uses local measurements where single photon detection is combined with
small displacement operations. The resulting entanglement witness does not
require post-selection, nor assumptions about the photon number in each path.
Furthermore, it guarantees that entanglement lies in a subspace with at most
one photon per optical path and reveals genuinely multipartite entanglement. We
demonstrate its scalability and resistance to loss by performing various
experiments with two and three optical paths. We anticipate applications of our
results for quantum network certification.
