  Certified randomness guaranteed to be unpredictable by adversaries is central
to information security. The fundamental randomness inherent in quantum physics
makes certification possible from devices that are only weakly characterised,
i.e. requiring little trust in their implementation. It was recently shown that
the amount of certifiable randomness can be greatly improved using the
so-called Entropy Accumulation Theorem generalised to prepare-and-measure
settings. Furthermore, this approach allows a finite-size analysis which avoids
assuming that all rounds are independent and identically distributed. Here, we
demonstrate this improvement in semi-device-independent randomness
certification from untrusted measurements.
