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Finite-Key Analysis of Quantum Key Distribution with Characterized Devices Using Entropy Accumulation

Ian George, Jie Lin, Thomas van Himbeeck, Kun Fang, and Norbert Lütkenhaus

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Researchers from the University of Waterloo and ETH Zürich demonstrated that the Entropy Accumulation Theorem (EAT) enhances finite-key rates for device-dependent quantum key distribution (QKD), extending its prior success in device-independent protocols. The team developed new mathematical tools, including sufficient conditions for Markov chain validity and algorithms to construct min-tradeoff functions, enabling practical EAT application in characterized-device QKD systems. By leveraging Dupuis’ 2023 privacy amplification technique without smoothing, they optimized key rates using sandwiched Rényi entropy instead of traditional smooth min-entropy, improving efficiency in finite-size scenarios. Case studies included BB84 with qubit and parametric down-conversion sources, six-state/four-state protocols, and high-dimensional BB84 variants, proving broad applicability across QKD implementations. This work bridges theoretical advances with real-world QKD deployments, offering tighter security bounds and higher key rates for finite-resource quantum networks.

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AbstractThe Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question would be whether it also improves the rates for device-dependent QKD. In this work, we provide an affirmative answer to this question. We present new tools for applying the EAT in the device-dependent setting. We present sufficient conditions for the Markov chain conditions to hold as well as general algorithms for constructing the needed min-tradeoff function. Utilizing Dupuis' recent privacy amplification without smoothing result, we improve the key rate by optimizing the sandwiched Rényi entropy directly rather than considering the traditional smooth min-entropy. We exemplify these new tools by considering several examples including the BB84 protocol with the qubit-based version and with a realistic parametric down-conversion source, the six-state four-state protocol and a high-dimensional analog of the BB84 protocol.► BibTeX data@article{George2025finitekeyanalysisof, doi = {10.22331/q-2025-12-12-1941}, url = {https://doi.org/10.22331/q-2025-12-12-1941}, title = {Finite-{K}ey {A}nalysis of {Q}uantum {K}ey {D}istribution with {C}haracterized {D}evices {U}sing {E}ntropy {A}ccumulation}, author = {George, Ian and Lin, Jie and van Himbeeck, Thomas and Fang, Kun and L{\"{u}}tkenhaus, Norbert}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {9}, pages = {1941}, month = dec, year = {2025} }► References [1] Charles H. Bennett and Gilles Brassard. Quantum cryptography: Public key distribution and coin tossing. 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The American Mathematical Monthly, 107 (6): 556–557, 2000. https://doi.org/10.1080/00029890.2000.12005235. https://doi.org/10.1080/00029890.2000.12005235 [58] Jonathan Borwein and Adrian S. Lewis. Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer-Verlag, New York, USA, 2006. https://doi.org/10.1007/978-0-387-31256-9. https://doi.org/10.1007/978-0-387-31256-9Cited byOn Crossref's cited-by service no data on citing works was found (last attempt 2025-12-28 15:31:26). Could not fetch ADS cited-by data during last attempt 2025-12-28 15:31:27: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question would be whether it also improves the rates for device-dependent QKD. In this work, we provide an affirmative answer to this question. We present new tools for applying the EAT in the device-dependent setting. We present sufficient conditions for the Markov chain conditions to hold as well as general algorithms for constructing the needed min-tradeoff function. Utilizing Dupuis' recent privacy amplification without smoothing result, we improve the key rate by optimizing the sandwiched Rényi entropy directly rather than considering the traditional smooth min-entropy. We exemplify these new tools by considering several examples including the BB84 protocol with the qubit-based version and with a realistic parametric down-conversion source, the six-state four-state protocol and a high-dimensional analog of the BB84 protocol.► BibTeX data@article{George2025finitekeyanalysisof, doi = {10.22331/q-2025-12-12-1941}, url = {https://doi.org/10.22331/q-2025-12-12-1941}, title = {Finite-{K}ey {A}nalysis of {Q}uantum {K}ey {D}istribution with {C}haracterized {D}evices {U}sing {E}ntropy {A}ccumulation}, author = {George, Ian and Lin, Jie and van Himbeeck, Thomas and Fang, Kun and L{\"{u}}tkenhaus, Norbert}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {9}, pages = {1941}, month = dec, year = {2025} }► References [1] Charles H. Bennett and Gilles Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pages 175–179, New York, 1984. IEEE. https://doi.org/10.1016/j.tcs.2014.05.025. https://doi.org/10.1016/j.tcs.2014.05.025 [2] Artur K. Ekert. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett., 67 (6): 661, 1991. https://doi.org/10.1103/PhysRevLett.67.661. https://doi.org/10.1103/PhysRevLett.67.661 [3] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev. The security of practical quantum key distribution. Rev. Mod. Phys., 81: 1301, 2009. https://doi.org/10.1103/RevModPhys.81.1301. https://doi.org/10.1103/RevModPhys.81.1301 [4] Feihu Xu, Xiongfeng Ma, Qiang Zhang, Hoi-Kwong Lo, and Jian-Wei Pan. Secure quantum key distribution with realistic devices. Rev. Mod. Phys., 92 (2): 025002, 2020. https://doi.org/10.1103/RevModPhys.92.025002. https://doi.org/10.1103/RevModPhys.92.025002 [5] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. 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Finite-Key Analysis of Quantum Key Distribution with Characterized Devices Using Entropy Accumulation

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