Characterization of multipartite entanglement for one photon shared among four optical modes

Access to genuine multipartite entanglement of quantum states enables advances in quantum information science and also contributes to the understanding of strongly correlated quantum systems. We report the detection and characterization of heralded entanglement in a multipartite quantum state composed of four spatially distinct optical modes that share one photon, a so-called W state. By randomizing the relative phase between bipartite components of the W state, we observed the transitions from four- to three- to two-mode entanglement with increasing phase noise. These observations are possible for our system because our entanglement verification protocol makes use of quantum uncertainty relations to detect the entangled states that span the Hilbert space of interest