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The amount of intrinsic randomness that can be extracted from measurement onquantum systems depends on several factors: notably, the power given to theadversary and the level of characterization of the devices of the authorizedpartners. After presenting a systematic introduction to these notions, in thispaper we work in the class of least adversarial power, which is relevant forassessing setups operated by trusted experimentalists, and compare three levelsof characterization of the devices. Many recent studies have focused on theso-called "device-independent" level, in which a lower bound on the amount ofintrinsic randomness can be certified without any characterization. The otherextreme 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 asystematic and efficient approach to quantifying the amount of intrinsicrandomness, and show that setups involving ancillas (POVMs, pointermeasurements) may not be interesting here, insofar as one may extractrandomness from the ancilla rather than from the system under study. Finally,we study how much randomness can be obtained in presence of an intermediatelevel of characterization related to the task of "steering", in which Bob'sdevice is fully characterized while Alice's is a black box. We obtain ourresults here by adapting the NPA hierarchy of semidefinite programs to thesteering scenario.

Quantum randomness extraction for various levels of characterization of the devices