  Quantum measurements can produce randomness arising from the uncertainty
principle. When measuring a state with von Neumann measurements, the intrinsic
randomness can be quantified by the quantum coherence of the state on the
measurement basis. Unlike projection measurements, there are additional and
possibly hidden degrees of freedom in apparatus for generic measurements. We
propose an adversary scenario for general measurements with arbitrary input
states, based on which, we characterize the intrinsic randomness.
Interestingly, we discover that under certain measurements, such as the
symmetric and information-complete measurement, all states have nonzero
randomness, inspiring a new design of source-independent random number
generators without state characterization. Furthermore, our results show that
intrinsic randomness can quantify coherence under general measurements, which
generalizes the result in the standard resource theory of state coherence.
