Information-Theoretic Tools for Analyzing Non-IID Structures in Quantum Key Distribution - Arqand, Amir (University of Waterloo, 2025)
Quantum key distribution (QKD) is the task of establishing an information-theoretically secure key between two parties (Alice and Bob) by exploiting the rules of quantum mechanics. A central goal in QKD is to provide finite-size security proofs against the most general class of attacks—namely, coherent attacks. One approach for obtaining such proofs is through the original entropy accumulation theorem (EAT) and the generalized entropy accumulation theorem (GEAT). In this thesis, we improve and extend these EAT-style techniques in several aspects. We begin by presenting techniques for applying the GEAT in the finite-size analysis of generic prepare-and-measure protocols. We then improve the statistical analysis in these EAT-style techniques, yielding a significant improvement in the key rates obtained by these methods. In addition, these improvements can be applied directly at the level of Rényi entropies if desired, yielding fully-Rényi security proofs. Beyond this, we develop an EAT-style framework that can accommodate specific forms of marginal-state constraints ``compatible'' with the source-replacement scheme. This allows us to overcome the repetition-rate restriction previously imposed on the GEAT when analyzing prepare-and-measure protocols. Furthermore, it yields ``fully adaptive'' protocols that can, in principle, update the entropy estimation procedure during the protocol itself. Finally, we investigate the effect of imperfections in QKD by deriving a number of chain rules for mutual information suited for analyzing protocols involving information leakage from imperfect devices. In particular, we derive chain rules between smooth min-entropy and smooth max-information for characterizing one-shot information leakage caused by an additional conditioning register. Furthermore, we introduce an EAT-style theorem for mutual information to simplify the evaluation of leakage measured by smooth max-information. In addition, we derive suitable chain rules to incorporate the leakage process into the GEAT framework.
Keywords: quantum key distribution; rényi entropies; entropy accumulation; information theoretic security; quantum cryptography