Quantum randomness certification with untrusted measurements and few probe states

We present a scheme for semi-device-independent quantum randomness certification from an untrusted measurement device and a trusted source and demonstrate it experimentally. No assumptions about noise or imperfections in the measurement are required and the scheme is simple to implement with existing technology. The measurement device is probed with a few trusted states and the output entropy can be lower bounded conditioned on the observed outcome distribution. The protocol can be applied to measurements with any finite number of outcomes and in particular can be realised by homodyne measurements of the vacuum using a detector probed by coherent states, as we experimentally demonstrate by intensity modulation of a telecom-wavelength pilot laser followed by homodyne detection and discretisation by analog-to-digital conversion. We show that randomness can be certified in the presence of both Gaussian additive noise and non-Gaussian imperfections.