Experimental self-testing of complex projective measurements via elegant Bell inequality

Self-testing is a powerful tool that allows one to verify the security of quantum systems without relying on the characterized devices. However, conventional self-testing protocols are fundamentally restricted to real-space measurements, significantly constraining their applicability. In this work, we present an innovative protocol for self-testing projective measurements in complex Hilbert space through an elegant Bell operator. Our self-testing method shows both strong noise resistance and a high extractable randomness amount. Experimentally, we realize the self-testing of the maximally entangled state with fidelity 0.9749 and a set of complex projective measurements with average fidelity 0.9635. Moreover, we get a lower bound of 0.9302 bits of extractable randomness from outputs. These advances establish a practical pathway for implementing device-independent quantum information protocols with improved feasibility and operational flexibility.