Nonstabilizerness is an essential resource for quantum computational advantage as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying nonstabilizer states in prepare-and-measure (PAM) scenarios, relying only on assumptions about the system's dimension. Within this framework, we introduce PAM witnesses that can distinguish stabilizer from nonstabilizer states, and we provide analytical proofs that threshold violations of these witnesses certify nonstabilizerness. 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 nonstabilizerness based on state overlaps (Gram matrices). These results offer a set of semi-device-independent tools for practically and systematically verifying nonstabilizer states using PAM inequalities.

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• Quantum computation
• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum information theory