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A semi-device-independent framework for prepare-and-measure experiments isintroduced in which an experimenter can tune the degree of distrust in theperformance of the quantum devices. In this framework, a receiver operates anuncharacterised measurement device and a sender operates a preparation devicethat emits states with a bounded fidelity with respect to a set of targetstates. No assumption on Hilbert space dimension is required. The set ofquantum correlations is investigated and bounded from both the interior and theexterior. Furthermore, the optimal performance of quantum state discriminationwith bounded distrust is derived and applied to certification of detectionefficiency. Quantum-over-classical advantages are demonstrated and themagnitude of distrust compatible with such advantages is explored. Finally,efficient schemes for semi-device-independent random number generation aredeveloped.

Semi-device-independent framework based on restricted distrust in prepare-and-measure experiments