Quantum random-number generator with non-demolition measurements: semi-device-independent implementation

We propose and analyze a novel quantum random-number generator based on a tripartite quantum system in which two subsystems act as detectors. Within a quantum non-demolition measurement scheme, one detector is used to certify the presence of genuine quantum effects in the system's evolution, while the second generates random numbers from a distribution that can be optimized to maximize their entropy. Using one two-level system and two three-level systems, we generate random numbers from a nearly uniform three-outcome distribution, yielding close-to-maximal entropy and therefore near-optimal randomness generation. A key feature of the protocol is that randomness generation and certification occur simultaneously. Moreover, certification does not rely on spacelike separation between detectors, removing a major constraint of device-independent approaches. This property enables practical implementation and facilitates the miniaturization of the device, making the protocol a promising candidate for scalable quantum technologies.