Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario

Non-stabilizerness is an essential resource for quantum computational advantage, as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying non-stabilizer states in prepare-and-measure (PAM) scenarios, relying only on assumptions about the system's dimension. Within this framework, we introduce prepare-and-measure witnesses that can distinguish stabilizer from non-stabilizer states, and we provide analytical proofs that threshold violations of these witnesses certify non-stabilizerness. In the simplest setting: three preparations, two measurements, and qubit systems, surpassing a specific threshold guarantees that at least one prepared state lies outside the stabilizer polytope, while a stronger violation can certify at least two. We extend this approach by linking it to quantum random access codes, also generalizing our results to qutrit systems and introducing a necessary condition for certifying non-stabilizerness based on state overlaps (Gram matrices). These results offer a set of semi-device-independent tools for practically and systematically verifying non-stabilizer states using prepare-and-measure inequalities.