  The unpredictable process of state collapse caused by quantum measurements
makes the generation of quantum randomness possible. In this paper, we explore
the quantitive connection between the randomness generation and the state
collapse and provide a randomness verification protocol under the assumptions:
(I) independence between the source and the measurement devices and (II) the
L\"{u}ders' rule for collapsing state. Without involving heavy mathematical
machinery, the amount of genereted quantum randomness can be directly estimated
with the disturbance effect originating from the state collapse. In the
protocol, we can employ general measurements that are not fully trusted.
Equipped with trusted projection measurements, we can further optimize the
randomness generation performance. Our protocol also shows a high efficiency
and yields a higher randomness generation rate than the one based on
uncertainty relation. We expect our results to provide new insights for
understanding and generating quantum randomness
