Successful realization of Bell tests has settled an 80-year-long debate, proving the existence of correlations which cannot be explained by a local realistic model. Recent experimental progress allowed to rule out any possible loopholes in these tests, and opened up the possibility of applications in cryptography envisaged more than three decades ago. A prominent example of such an application is device-independent quantum key distribution, which has recently been demonstrated. One remaining gap in all existing experiments, however, is that access to perfect randomness is assumed. To tackle this problem, the concept of randomness amplification has been introduced, allowing to generate such randomness from a weak source -- a task impossible in classical physics. In this work, we demonstrate the amplification of imperfect randomness coming from a physical source. It is achieved by building on two recent developments: The first is a theoretical protocol implementing the concept of randomness amplification within an experimentally realistic setup, which however requires a combination of the degree of Bell inequality violation (S-value) and the amount of data not attained previously. The second is experimental progress enabling the execution of a loophole-free Bell test with superconducting circuits, which offers a platform to reach the necessary combination. Our experiment marks an important step in achieving the theoretical physical limits of privacy and randomness generation.
