Ernest Tan

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.

Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on untrusted hardware. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite size security proofs for protocols based on the CHSH game which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on Rényi entropies, providing a simple method to obtain tighter finite-size key rates.

The postselection technique is a widely used tool to lift the security of Quantum Key Distribution (QKD) protocols against IID collective attacks to coherent attacks. While various other approaches for proving security against coherent attacks exist, they have limitations that make them less suitable for typical optical prepare-and-measure protocols. We identify and address some limitations of the postselection technique as applied to optical prepare-and-measure QKD protocols. We extend this analysis to decoy-state protocols, which are essential for long-distance QKD. Finally, we also improve the practical applicability of the postselection technique. Thus, we argue that the postselection technique, with the relevant modifications, is the only lift to coherent attacks that can be broadly applied to optical implementations of generic prepare-and-measure QKD protocols.