Assume that we are given a big black box with two windows. Each window emits a laser beam. All our best measurement techniques show that the two beams have the same wavelength and have near-perfect mutual coherence (or as good as the self coherence of each output beam). Is it possible to tell whether the beams come from two different phase-locked lasers, or are split out of a single laser? Or perhaps a third case -- a small part of one beam is tapped off and amplified, then delivered to the other window? What experiments can distinguish between these cases?