Rigorous Security Proofs for Practical Quantum Key Distribution

Abstract

This thesis is concerned with the rigorous security analysis of practical Quantum Key Distribution (QKD) protocols, using a variety of modern proof techniques. Throughout, the emphasis is on mathematical rigor across a wide range of security proof frameworks.

We begin by presenting a security proof for variable-length QKD protocols against IID collective attacks, which represents the first such result for generic QKD protocols. We then show that this analysis can be lifted to hold against coherent attacks by an adversary, using the postselection technique. In doing so, we extend the application of the postselection technique to practical QKD protocols, and resolve a long-standing flaw in the method, thereby placing its application to QKD on a rigorous mathematical footing.

We next study security proofs based on entropic uncertainty relations. These proofs proceed by bounding the so-called ``phase error rate", using the observed statistics available in the actual protocol. All known methods of bounding the phase error rate require strong assumptions on hardware: namely, that all detectors have exactly equal probability of detection. This renders these security analysis inapplicable to practical QKD scenarios. We show that such phase error rates can be bounded even when detectors are imperfect and only approximately characterized. This resolves a long-standing well-known open problem of nearly two decades, and renders this proof technique applicable to realistic scenarios.

We then study security proofs using the recently obtained marginal-constrained entropy accumulation theorem, and obtain a highly rigorous and general result for the security analysis for practical QKD protocols. Most importantly, the proof is constructed in a transparent and self-contained manner, and is designed to be a key ingredient in certification efforts for QKD. Moreover, it can be easily modified to apply to other protocols of interest, and to device imperfections and side-channels.

We also revisit the assumptions on authentication traditionally made in QKD security analyses, which assume that all classical messages are delivered faithfully and on time, without any aborts. We show that these assumptions are generally unrealistic, and that adopting realistic authentication assumptions necessitates a modification of both the standard QKD security definition and the corresponding security analysis. However, under mild and easily satisfied protocol design conditions, security under realistic authentication can be reduced to the usual idealized setting. As a result, existing QKD security proofs can be lifted to the realistic authentication setting with only a minor protocol modification.

A distinctive feature of this thesis is its unified presentation of multiple major QKD security proof frameworks using consistent protocol descriptions and notation. This first-of-its-kind treatment enables direct comparison and contrast between different approaches, a perspective that is often obscured when these techniques are developed in isolation. Consequently, this work is intended not only as a collection of new technical results, but also as a pedagogical reference for understanding rigorous security analysis in quantum key distribution.