The invention is directed to a Quantum Random Number Generator comprising an emitting device (110) triggered by a signal representing an input bit x and adapted to generate and send a physical system (130) characterized by one of two possible quantum states determined by said input bit x, a measurement device (120) adapted to detect said physical system, to identify the quantum state of said physical system through an unambiguous state discrimination measurement and to generate an output b first representing whether the quantum state has been identified or not and, if it has been identified, which quantum state among the two possible quantum states was detected by the unambiguous state discrimination measurement to a processing device (140), the processing device (140) being adapted to estimate the entropy of the output b given the probabilities p(b|x) representing the probability of observing output b for a state preparation x, and a randomness extraction device (150) adapted to extract final random bit stream given the entropy estimate provided by the processing device (140).