Unbounded randomness from uncharacterized sources

Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective measurements, and its amount is bounded by the quantum system's dimension. Here, we propose a Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. Additionally, the proposed protocol doesn't require an initial seed and active basis switching, simplifying its experimental implementation and increasing the generation rates. A tight lower-bound on the quantum conditional min-entropy is derived using only the POVM structure and the experimental expectation values, taking into account the quantum side-information. For symmetric POVM on the Bloch sphere, we derive closed-form analytical bounds. Finally, we experimentally demonstrate our method with a compact and simple photonic setup that employs polarization-encoded qubits and POVM up to 6 outcomes.The laws of quantum mechanics allow for the generation of genuine random numbers, but quantum random number generation schemes need additional assumptions on the sources and detection to ensure the security and their generation is limited by the system's dimension. The authors propose and experimentally demonstrate a quantum random number generation scheme based on positive operator valued measurements, lifting the requirement of a trusted source which can arbitrarily increase the number of certified bits for any dimension.