Contributed Talk 3a

Abstract: Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the asymptotic limit as well as in the finite-size regime. In this work, we derive novel variational expressions for Petz-Rényi divergences instead. We also derive two critical applications of this result. First, we show how these variational expressions can be used to further improve the finite-size key rate of DI protocols, by developing a fully-Rényi entropy accumulation theorem that can utilize these expressions for key rate computations. Second, we derive a security condition for DI advantage distillation that is based on the pretty good fidelity. We implement these techniques to derive increased noise tolerances for DIQKD protocols, which surpass the previously known bounds.