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arXiv:2507.03549 · npj Quantum Information

Security of quantum key distribution with source and detector imperfections through phase-error estimation

Guillermo Currás-Lorenzo, Margarida Pereira, Shlok Nahar, Devashish Tupkary

Published May 18, 2026• 3 citations
arXivHTMLPDF

Abstract

Quantum key distribution promises information-theoretic security, but practical implementations face vulnerabilities due to device imperfections. Existing security proofs typically address source and detector imperfections separately and cannot be directly combined, while the few attempts to handle both simultaneously have assumed idealized scenarios with infinitely many protocol rounds, which is insufficient to certify the security of real-world systems. Here, we close this gap by introducing a modular lifting theorem that extends any (present or future) phase-error-based security proof for active-basis-choice BB84-type protocols to incorporate detector efficiency mismatches. By applying this theorem to a state-of-the-art analysis for source imperfections, we obtain the first finite-key security proof against general coherent attacks that simultaneously addresses both source and detector imperfections.

DOI
10.1038/s41534-026-01264-5

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Quantum key distribution promises information-theoretic security, but practical implementations face vulnerabilities due to device imperfections. Existing security proofs typically address source and detector imperfections separately and cannot be directly combined, while the few attempts to handle both simultaneously have assumed idealized scenarios with infinitely many protocol rounds, which is insufficient to certify the security of real-world systems. Here, we close this gap by introducing a modular lifting theorem that extends any (present or future) phase-error-based security proof for active-basis-choice BB84-type protocols to incorporate detector efficiency mismatches. By applying this theorem to a state-of-the-art analysis for source imperfections, we obtain the first finite-key security proof against general coherent attacks that simultaneously addresses both source and detector imperfections.
Practical quantum key distribution (QKD) receivers may leak information about their measurement outcomes and settings to the channel (e.g., through detector backflashes or back-reflected Trojan-horse light) that could compromise the protocol's security. Here we present a simple finite-key security proof based on phase-error estimation for prepare-and-measure QKD in the presence of either a priori information leakage about the basis choices and/or a posteriori information leakage about the measurement outcomes. The proof requires only a bound on the distinguishability of the side-channel states. Furthermore, the analysis is modular and compatible with existing security proofs that address detector and source imperfections, making it applicable to a wide range of practical QKD implementations.
Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.
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.
Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and existing security proofs fall short of capturing the complexity of real-world systems. Here we introduce a versatile numerical finite-key security framework valid against general coherent attacks and applicable to a broad class of practical QKD setups. It accommodates most relevant imperfections at both transmitter and receiver, including non-independent-and-identically-distributed (non-IID) signals arising in high-speed QKD systems due to the limited bandwidth of optical modulators, while requiring only partial characterization of the apparatuses. We demonstrate the power of our framework by proving the security of a realistic decoy-state QKD implementation with laser sources, providing a practical route towards rigorous security certification of real-world QKD setups.
We develop a generic framework to bound the phase error rate for quantum key distribution protocols using passive detection setups with imperfections and memory effects. This framework can be used in proof techniques based on the entropic uncertainty relation or phase error correction, to prove security in the finite-size regime against coherent attacks. Our framework can incorporate on-the-fly announcements of click/no-click outcomes on Bob's side. In the case of imperfections without memory effects, it can be combined with proofs addressing source imperfections in a modular manner. We apply our framework to compute key rates for the decoy-state BB84 protocol, when the beam splitting ratio, the detection efficiency, and dark counts of the detectors are only known to be within some ranges. We also compute key rates in the presence of memory effects in the detectors. In this case, our results allow for protocols to be run at higher repetition rates, resulting in a significant improvement in the secure key generation rate.
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.