Suppose we wish to recover a signal x ∈ C^n from m intensity measurements of the form |⟨x,z_i⟩|^2 , i = 1, 2, . . . , m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and uniformly from the unit sphere, with m = O(nlogn), then with high probability, the signal x can be recovered exactly (up to a global...