Certifying quantum randomness with disturbance

A quantum measurement generates genuine quantum randomness if and only if it breaks coherence and disturbs the measured state (and a following incompatible measurement). Here, we establish a quantitative relation between the generated randomness and its disturbance effect and provide a source-independent randomness verification protocol. Our protocol employs a few assumptions: (I) independence between the source and the measurement devices and (II) the L"uders' rule for measurement devices. Without involving heavy mathematical machinery, the generated quantum randomness can be directly estimated with the disturbance effect. In addition to the previously mentioned basic assumptions about measurements, we can improve our estimation by integrating additional measurement information for further optimization. Our protocol shows a high efficiency and yields a higher randomness generation rate than the existing one based on the uncertainty relation [G. Vallone et al., Phys. Rev. A 90, 052327 (2014)].