Higher-dimensional symmetric informationally complete measurement via programmable photonic integrated optics

Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalized, non-orthogonal, and quantum measurement. In higher-dimensional systems, these measurements become both increasingly interesting and increasingly complex to implement. Here, we demonstrate an integrated quantum photonic platform, operating at high fidelities, to realize such a measurement on three-level quantum systems. We demonstrate the quality of the measurement device by verifying a genuine many-outcome quantum measurement, performing near-optimal quantum state discrimination, and beating the projective limit in quantum random number generation. Moreover, the device is programmable and can readily implement other quantum measurements at similarly high quality. Our work paves the way for the implementation of sophisticated higher-dimensional quantum measurements that go beyond the traditional orthogonal projections.