In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.
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.
This thesis is concerned with rigorous security analyses of practical Quantum Key Distribution (QKD) protocols, using a variety of modern proof techniques. The main results are as follows. First, we establish a security proof for variable-length QKD protocols against IID collective attacks, and extend this result to coherent attacks using the postselection technique. In doing so, we resolve a long-standing flaw in the application of the postselection technique to QKD, thereby placing it on a rigorous mathematical footing. Second, we develop a method to bound phase error rates in entropic uncertainty relation-based and phase error rate-based proofs, using only the observed statistics of the protocol, even when detectors are imperfect and only approximately characterized. This removes a key assumption of identical detector behaviour and enables these techniques to be applied in realistic settings. Third, we present a very general security analysis based on the marginal-constrained entropy accumulation theorem. The resulting framework can be readily adapted to practical imperfections and side channels, and is suitable for certification efforts. Finally, we show that the security of QKD protocols under realistic authentication assumptions can be reduced to the standard idealized setting, where authentication is assumed to behave honestly, with only minor protocol modifications. A distinctive feature of this thesis is its unified presentation of several major QKD security proof frameworks using consistent protocol descriptions and notation. Consequently, this thesis is intended not only as a collection of new technical results, but also as a useful reference for understanding rigorous security analysis in quantum key distribution.
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the stateof-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments spread in the literature on the subject with the goal of making this treatment largely self-contained. More precisely, we focus on a class of prepare-and-measure protocols based on the Bennett-Brassard (BB84) protocol as well as a class of entanglement-based protocols similar to the Bennett-Brassard-Mermin (BBM92) protocol. We carefully formalize the different steps in these protocols, including randomization, measurement, parameter estimation, error correction and privacy amplification, allowing us to be mathematically precise throughout the security analysis. We start from an operational definition of what it means for a quantum key distribution protocol to be secure and derive simple conditions that serve as sufficient condition for secrecy and correctness. We then derive and eventually discuss tradeoff relations between the block length of the classical computation, the noise tolerance, the secret key length and the security parameters for our protocols. Our results significantly improve upon previously reported tradeoffs.
We develop a flexible and robust framework for finite-size security proofs of quantum key distribution (QKD) protocols under coherent attacks, applicable to both fixed- and variable-length protocols. Our approach achieves high finite-size key rates across a broad class of protocols while imposing minimal requirements. In particular, it eliminates the need for restrictive conditions such as limited repetition rates or the implementation of virtual tomography procedures. To achieve this goal, we introduce new numerical techniques for the evaluation of sandwiched conditional Rényi entropies. In doing so, we also find an alternative formulation of the "QKD cone" studied in previous work. We illustrate the versatility of our framework by applying it to several practically relevant protocols, including decoy-state protocols. Furthermore, we extend the analysis to accommodate realistic device imperfections, such as independent intensity and phase imperfections. Overall, our framework provides both greater scope of applicability and better key rates than existing techniques, especially for small block sizes, hence offering a scalable path toward secure quantum communication under realistic conditions
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
In this paper, we present a flowchart-based description of the decoy-state BB84 quantum key distribution (QKD) protocol and provide a step-by-step, self-contained information-theoretic security proof for this protocol within the universal composable security framework. As a result, our proof yields a key rate consistent with previous findings. Importantly, unlike all the prior security proofs, our approach offers a fully rigorous and mathematical justification for achieving the key rate with the claimed correctness and secrecy parameters, thereby representing a significant step toward the formal certification of QKD systems.