QUASAR weekly seminar talk.

• Date: Friday, September 12, 2025
• Time: 1:00 PM ET
• Location: Virtual
• Speaker: Santiago Zamora
• Affiliation: International Institute of Physics

Abstract

Non-stabilizer states, often called “magic” states, are an essential resource for quantum computational advantage, yet their practical certification remains a significant challenge due to the intricate geometry of the stabilizer polytope. In this work, we address this by developing a semi-device-independent (SDI) framework for certifying non-stabilizerness using the prepare-and-measure (PAM) scenario. This approach requires only a minimal assumption on the system’s dimension. We introduce dimensional witnesses that distinguish quantum correlations from those achievable with only stabilizer states, and we use them to establish a strict hierarchy of correlation sets (C_(C,d) < C_(STAB,d) < C_(Q,d)). In the simplest PAM scenario (3 preparations, 2 measurements), we derive an analytical bound for stabilizer-based strategies (S_3^(STAB) = sqrt(5) + sqrt(2)) whose violation provides a robust certificate of non-stabilizerness. Furthermore, we demonstrate that the maximal quantum violation of this witness self-tests H-type non-stabilizer states, offering a novel protocol for their verification. We then extend our framework by considering Quantum Random Access Codes (QRACs), allowing us to analyze scenarios with a larger number of preparations. This approach enables a “fine-grained certification,” where the observed witness value can be used to infer a lower bound on the number of non-stabilizer states in the prepared ensemble. This research provides a systematic toolkit for verifying a key quantum resource, bridging resource theories with practical protocols under minimal trust assumptions.