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  • Open Access

Improved finite-size effects in quantum key distribution with applications to decoy-state protocols

Lars Kamin*, Devashish Tupkary†, and Norbert Lütkenhaus‡

  • *Contact author: lars.kamin@outlook.com
  • †Contact author: tupkary.devashish@gmail.com
  • ‡Contact author: lutkenhaus.office@uwaterloo.ca
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Phys. Rev. Research 8, 013332 – Published 27 March, 2026

DOI: https://doi.org/10.1103/48xf-my6t

Abstract

We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks and extend it to coherent attacks using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter finite-size key rates by employing refined concentration inequalities in the acceptance testing phase. Second, we improve second-order correction terms in the key rate expression, by reducing them to scale with the number of sifted rounds rather than the total number of protocol rounds. We apply these advancements to compute finite-size key rates for a qubit and decoy-state BB84 protocol, accommodating arbitrary protocol parameters. Finally, we extend our finite-size security proof to coherent attacks and variable-length protocols and present our results for the decoy-state 4-6 protocol incorporating imperfections such as unequal intensity settings.

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Outline

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Phys. Rev. Research 8, 013332– Published 27 March, 2026
  • Received 21 April 2025
  • Accepted 28 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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