Nicolas Brunner

**merged with** Thomas Van Himbeeck and Stefano Pironio. Correlations and Randomness Generation based on an Energy Constraint In a previous paper, we introduced a semi-device-independent scheme consisting of an untrusted source sending quantum states to an untrusted measuring device, with the sole assumption that the average energy of the states emitted by the source is bounded. Given this energy constraint, we showed that certain correlations between the source and the measuring device can only occur if the outcomes of the measurement are non-deterministic, i.e., these correlations certify the presence of randomness. In the present paper, we go further and show how to quantify the randomness as a function of the correlations and prove the soundness of a QRNG protocol exploiting this relation. For this purpose, we introduce (1) a semidefinite characterization of the set of quantum correlations, (2) an algorithm to lower-bound the Shannon entropy as a function of the correlations and (3) a proof of soundness using finite trials compatible with our energy assumption.

When separated measurements on entangled quantum systems are performed, the theory predicts correlations that cannot be explained by any classical mechanism. All optical demonstrations of such violations have involved discrete degrees of freedom and are plagued by the detection-efficiency loophole. We present a simple method for generating large violations for feasible states using both photon counting and homodyne detections. Our scheme may lead to the first violation of Bell inequalities using continuous-variable measurements and pave the way for a loophole-free Bell test.

We investigate a class of partially device-independent quantum key distribution protocols based on a prepare-and-measure setup which simplifies their implementation. The security of the protocols is based on the assumption that Alice’s prepared states have limited overlaps, but no explicit bound on the Hilbert space dimension is required. The protocols are therefore immune to attacks on Bob’s device, such as blinding attacks. The users can establish a secret key while continuously monitoring the correct functioning of their devices through observed statistics. We report a proof- of-principle demonstration, involving mostly off-the-shelf equipment, as well as a high-efficiency superconducting nanowire detector. A positive key rate is demonstrated over a 4.8km low-loss optical fiber with finite-key analysis. The prospects of implementing these protocols over longer distances is discussed.