Experimental investigation of quantum correlations under restricted distrust in a semi-device-independent framework

Semi-device-independent (SDI) methods provide a convenient way to characterize quantum systems under additional physical assumptions, and these methods have wide applications in quantum information processing, such as quantum key distribution, quantum random number generation and quantum certification. Recently, Tavakoli proposed an SDI scheme to investigate quantum correlations based on the assumption of restricted distrust. Here, we experimentally investigate quantum correlations in an SDI framework with restricted distrust, where the preparer emits states with a bounded fidelity with respect to a set of target states and the measurer operates an uncharacterized measurement device. In our work, we experimentally realize quantum state discrimination with bounded distrust and apply it to the certification of detection efficiency. Moreover, we demonstrate the advantages of quantum systems over classical counterparts even at substantial degrees of distrust. Finally, we investigate SDI random number generation with restricted distrust and show that high rates of randomness can also be generated at experimentally realistic levels of distrust. Our work opens new avenues for SDI quantum information processing.