Quantum randomness certified by the uncertainty principle

We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.