This note formulates a deterministic recovery result for vectors x from
quadratic measurements of the form (Ax)i(Ax)j for some
left-invertible A. Recovery is exact, or stable in the noisy case, when the
couples (i,j) are chosen as edges of a well-connected graph. One possible way
of obtaining the solution is as a feasible point of a simple semidefinite
program. Furthermore, we show how the proportionality constant in the error
estimate depends on the spectral gap of a data-weighted graph Laplacian. Such
quadratic measurements have found applications in phase retrieval, angular
synchronization, and more recently interferometric waveform inversion