  Randomness expansion where one generates a longer sequence of random numbers
from a short one is viable in quantum mechanics but not allowed classically.
Device-independent quantum randomness expansion provides a randomness resource
of the highest security level. Here, we report the first experimental
realization of device-independent quantum randomness expansion secure against
quantum side information established through quantum probability estimation. We
generate $5.47\times10^8$ quantum-proof random bits while consuming
$4.39\times10^8$ bits of entropy, expanding our store of randomness by
$1.08\times10^8$ bits at a latency of about $13.1$ h, with a total soundness
error $4.6\times10^{-10}$. Device-independent quantum randomness expansion not
only enriches our understanding of randomness but also sets a solid base to
bring quantum-certifiable random bits into realistic applications.
