Randomness Certification and Trade-offs in the Prepare-and-Broadcast Scenario

Abstract

We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.