Local and scalable detection of genuine multipartite single-photon path entanglement

Patrik Caspar1, Enky Oudot2, Pavel Sekatski1, Nicolas Maring1, Anthony Martin1, Nicolas Sangouard3, Hugo Zbinden1, and Rob Thew1

1Department of Applied Physics, University of Geneva, CH-1211 Genève, Switzerland
2ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
3Institut de physique théorique, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France

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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 three 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 by the maximum 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.

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