Multipartite entanglement detection with one random observable

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We show that repeatedly measuring a many-body state in random local bases can detect entanglement. For pure states it is also asymptotically sufficient. In particular, if a state is sufficiently entangled, measuring only one randomly chosen observable can reveal multipartite entanglement with high probability. We demonstrate this feature with multipartite GHZ states and show that probability of success increases with number of subsystems. Finally, we discuss generalization from 2-level system to arbitrary dimension. 
 
Phys. Rev. A 92, 050301(R)(2015) 
Phys. Rev. A 94, 042302 (2016)