Certification of unbounded randomness with arbitrary noise

Random number generators play an essential role in cryptography and key distribution. It is thus important to verify whether the random numbers generated from these devices are genuine and unpredictable by any adversary. Recently, quantum nonlocality has been identified as a resource that can be utilised to certify randomness. Although these schemes are device-independent and thus highly secure, the observation of quantum nonlocality is extremely difficult from a practical perspective. In this work, we provide a scheme to certify unbounded randomness in a semi-device-independent way based on the maximal violation of Leggett-Garg inequalities. Interestingly, the scheme is independent of the choice of the quantum state, and consequently even classical noise like a thermal state or even microwave background radiation could be utilized to self-test quantum measurements and generate unbounded randomness making the scheme highly efficient for practical purposes.