Contributed Talk 3b (original 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.

Abstract: Computational entropy notions play a central role in classical cryptography, with well-developed frameworks for analyzing unpredictability, leakage resilience, and pseudo-randomness. In the quantum setting, however, computational analogues of entropy remain largely unexplored. While quantum information theory provides powerful tools based on information-theoretic entropy, these do not capture the limitations of computationally bounded quantum adversaries. In this work, we initiate the study of quantum computational entropy by defining \emph{quantum computational unpredictability entropy}, a natural generalization of classical unpredictability entropy to the quantum setting. Our definition is based on the operational meaning of quantum min-entropy, but restricts the adversary to efficient quantum guessing strategies. We prove that this entropy satisfies several important properties, including a leakage chain rule that holds even in the presence of prior quantum side-information. We also show that unpredictability entropy supports pseudo-randomness extraction against quantum adversaries with bounded computational power. Together, these results lay a foundation for developing cryptographic tools that rely on min-entropy in the quantum computational setting.