Jonatan Bohr Brask

**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.

We propose a long-distance device-independent conference key agreement (DI-CKA) protocol. We use an efficient GHZ state distribution protocol based on entanglement swapping. We calculate a key rate of our protocol from violation of a multipartite Bell inequality and show that our protocol can distribute a secret key over longer distance than a direct transmission DI-CKA protocol. We also consider practical displacement-based measurement and show experimental feasibility of our protocol.

Measurements in quantum physics are inherently random. Moreover, it is possible to certify quantum randomness from systems that are only partially characterized by the user. Here, we propose a simple quantum random number generator (QRNG) that requires only a single photodiode and one laser. We trust only the quantum efficiency of the photodiode and the characterization of the detector, leaving the laser in control of the eavesdropper. Such a QRNG is source-device-independent and its optical setup is among the simplest setups achieving source-device independence.