  Quantum Bell nonlocality allows for the design of protocols that amplify the
randomness of public and arbitrarily biased Santha-Vazirani sources, a
classically impossible task. Information-theoretical security in these
protocols is certified in a device-independent manner, i.e. solely from the
observed nonlocal statistics and without any assumption about the
inner-workings of the intervening devices. On the other hand, if one is willing
to trust on a complete quantum-mechanical description of a protocol's devices,
the elementary scheme in which a qubit is alternatively measured in a pair of
mutually unbiased bases is, straightforwardly, a protocol for randomness
amplification. In this work, we study the unexplored middle ground. We prove
that full randomness amplification can be achieved without requiring
entanglement or a complete characterization of the intervening quantum states
and measurements. Based on the energy-bounded framework introduced in [Van
Himbeeck et al., Quantum 1, 33 (2017)], our prepare-and-measure protocol is
able to amplify the randomness of any public Santha-Vazirani source, requiring
the smallest number of inputs and outcomes possible and being secure against
quantum adversaries.
