A rigorous and complete security proof of decoy-state BB84 quantum key distribution

TL;DR

This paper provides a comprehensive, mathematically rigorous security proof for the decoy-state BB84 quantum key distribution protocol, establishing a solid foundation for certification and standardization of quantum communication systems.

Contribution

It develops a general, modular framework unifying key techniques in QKD security analysis, adaptable to various protocols and practical imperfections.

Findings

Unified formalism for QKD security analysis

Framework applicable to prepare-and-measure and entanglement-based protocols

Pathway for incorporating practical imperfections

Abstract

We present a rigorous and complete security proof of the decoy-state BB84 quantum key distribution (QKD) protocol. Our analysis aims to achieve a high standard of mathematical rigour and completeness, thereby providing the necessary foundation for certification and standardization efforts. Beyond establishing the security of a specific protocol, this work develops a general and modular framework that can be readily adapted to a broad class of QKD protocols, including both prepare-and-measure and entanglement-based variants. Our framework unifies all major ingredients required for the analysis of realistic QKD protocols, including the analysis of classical authentication and classical processing, source-replacement schemes, finite-size analysis, source maps, squashing maps, and decoy-state techniques. In doing so, this work consolidates a diverse range of techniques scattered across the QKD literature into a unified formalism, representing a general and rigorous treatment of QKD security. Finally, it outlines a clear path towards incorporating practical imperfections within the same framework, thereby laying the groundwork for addressing implementation security in future analysis.