  The amount of intrinsic randomness that can be extracted from measurement on
quantum systems depends on several factors: notably, the power given to the
adversary and the level of characterization of the devices of the authorized
partners. After presenting a systematic introduction to these notions, in this
paper we work in the class of least adversarial power, which is relevant for
assessing setups operated by trusted experimentalists, and compare three levels
of characterization of the devices. Many recent studies have focused on the
so-called "device-independent" level, in which a lower bound on the amount of
intrinsic randomness can be certified without any characterization. The other
extreme is the case when all the devices are fully characterized: this
"tomographic" level has been known for a long time. We present for this case a
systematic and efficient approach to quantifying the amount of intrinsic
randomness, and show that setups involving ancillas (POVMs, pointer
measurements) may not be interesting here, insofar as one may extract
randomness from the ancilla rather than from the system under study. Finally,
we study how much randomness can be obtained in presence of an intermediate
level of characterization related to the task of "steering", in which Bob's
device is fully characterized while Alice's is a black box. We obtain our
results here by adapting the NPA hierarchy of semidefinite programs to the
steering scenario.
