Experimental full calibration of quantum devices in a semi-device-independent way

Semi-device-independent (SDI) methods offer a credible way to calibrate preparation and measurement devices simultaneously in quantum information processing, using only prior knowledge such as the Hilbert space dimension. To date, the SDI method is restricted to a few state paradigms, which impedes its broader applications. Recently, Tavakoli [Phys. Rev. Lett. 125, 150503 (2020)] proposed an SDI scheme to certify t-designs with discrete and symmetric structures. In this work, we bridge the gap between discrete and continuous structures with a concept termed "covering angle," while maintaining the SDI feature. This concept enables us to evaluate a quantum device's ability to generate arbitrary quantum states in a Hilbert space via calibrating a certain t-design. This so-called full calibration method is further tailored to be tolerant of errors in realistic state production. We demonstrate this full calibration scheme for a qubit system with various t-designs and show that it renders SDI certificates for quantum key distribution, quantum random number generation, and magic state distillability.