An optical chip for self-testing quantum random number generation

We present an implementation of a semi-device-independent protocol of the generation of quantum random numbers in a fully integrated silicon chip. The system is based on a prepare-and-measure scheme, where we integrate a partially trusted source of photons and an untrusted single photon detector. The source is a silicon photomultiplier, which emits photons during the avalanche impact ionization process, while the detector is a single photon avalanche diode. The proposed protocol requires only a few and reasonable assumptions on the generated states. It is sufficient to measure the statistics of generation and detection in order to evaluate the min-entropy of the output sequence, conditioned on all possible classical side information. We demonstrate that this protocol, previously realized with a bulky laboratory setup, is totally applicable to a compact and fully integrated chip with an estimated throughput of 6 kHz of the certified quantum random bit rate.