Multipartite entanglement witnesses from photodetection statistics

Remote entanglement between quantum systems such as atomic ensembles or mechanical resonators can be created by use of linear optical networks and single-photon detectors. The detection of a single Raman photon can project a bipartite system into a Bell state (the DLCZ scheme) and a multipartite system into a W state. We present a new class of entanglement witnesses tailored to these types of states which can be evaluated from photodetection statistics only without the need for full state tomography. We also investigate these witnesses' limitations to entanglement detection in the presence of initial thermal occupation, which is of particular relevance to remote, low-frequency mechanical resonators in multipartite optomechanical systems.