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Of existing entanglement witnesses that utilize only collective measurementsof a spin ensemble, not all can detect genuine multipartite entanglement (GME),and none can detect Greenberger-Horne-Zeilinger (GHZ) states beyond thetripartite case. We fill this gap by introducing an entanglement witness thatdetects GME of spin ensembles, whose total spin is half-integer, using onlycollective spin measurements. Our witness is based on a nonclassicality testintroduced by Tsirelson, and solely requires the measurement of total angularmomentum along different directions. States detected by our witness are closeto a family of GHZ-like states, which includes GHZ states of an odd number ofspin-half particles. We also study the robustness of our witness underdepolarizing noise, and derive exact noise bounds for detecting noisy GHZstates.

A Witness of GHZ Entanglement Using Only Collective Spin Measurements