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We consider the problem of certification of arbitrary ensembles of purestates and projective measurements solely from the experimental statistics inthe prepare-and-measure scenario assuming the upper bound on the dimension ofthe Hilbert space. To this aim, we propose a universal and intuitive schemebased on establishing perfect correlations between target states andsuitably-chosen projective measurements. The method works in all finitedimensions and allows for robust certification of the overlaps betweenarbitrary preparation states and between the corresponding measurementoperators. Finally, we prove that for qubits, our technique can be used torobustly self-test arbitrary configurations of pure quantum states andprojective measurements. These results pave the way towards the practicalapplication of the prepare-and-measure paradigm to certification of quantumdevices.

A universal scheme for robust self-testing in the prepare-and-measure scenario