State certification seeks to determine whether an approximate, lab-prepared quantum state is close to a target ideal state. There is particular interest in approaches to certification that require only simple, few-qubit measurements, and recent work has culminated in protocols certifying n-qubit quantum states with only single-qubit measurements (Huang, Preskill, Soleimanifar '24; Gupta, He, O'Donnell '25). Unfortunately, existing tests are inherently non-robust: they can only positively certify lab states that are vanishingly close to the ideal state as n grows, making them difficult to apply in realistic scenarios. In this talk we describe new few-qubit measurement protocols that achieve constant robustness, for example distinguishing lab states with at least 80% fidelity from those with at most 60% fidelity, independent of system size. Our protocols succeed for all but an exponentially small fraction of target states and are based on a novel uncertainty principle for conditional fidelities.

Based on the joint work arXiv:2602.11616 with Andrea Coladangelo, Jerry Li, and Ellen Wu.

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