Many-body coherence and entanglement probed by randomized correlation measurements

We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions, and identify sufficient conditions under which low-order correlators fully characterize many-body coherences, as controlled by the constituents' mutual distinguishability. Comparison of correlators of different order detects many-body entanglement.Comment: 5 pages, 2 figures + supplemental material (1 page