  How can a multipartite single-photon path-entangled state be certified
efficiently by means of local measurements? We address this question by
constructing an entanglement witness based on local photon detections preceded
by displacement operations to reveal genuine multipartite entanglement. Our
witness is defined as a sum of two observables that can be measured locally and
assessed with two measurement settings for any number of parties $N$. For any
bipartition, the maximum mean value of the witness observable over biseparable
states is bounded from the maximal eigenvalue of an $N\times N$ matrix, which
can be computed efficiently. We demonstrate the applicability of our scheme by
experimentally testing the witness for heralded 4- and 8-partite single-photon
path-entangled states. Our implementation shows the scalability of our witness
and opens the door for distributing photonic multipartite entanglement in
quantum networks at high rates.
