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Finite-Size Quantum Key Distribution Rates from Rényi Entropies Using Conic Optimization

Mariana Navarro1,2,*,‡, Andrés González Lorente3,4,†,‡, Pablo V. Parellada3,4, Carlos Pascual-García1,2, and Mateus Araújo3,4

  • *Contact author: mariana.navarro@icfo.eu
  • †Contact author: andres.gonzalez.lorente@uva.es
  • ‡These authors contributed equally to this work.
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PRX Quantum 7, 033051 – Published 10 September, 2026

DOI: https://doi.org/10.1103/bf9s-m4jb

Abstract

Finite-size general security proofs for quantum key distribution based on Rényi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has hitherto been tackled using ad hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols and demonstrate a dramatic runtime improvement over the state of the art.

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Popular Summary

Quantum key distribution promises to enable communication with security based on the laws of quantum mechanics. In order to use it, a crucial step is to bound the amount of information an eavesdropper can have about the secret key. The tightest known bounds require optimizing Rényi entropies, which is a difficult problem without mature solution techniques. We introduce a conic optimization method that is capable of solving it quickly and reliably. We illustrate its performance on two common quantum key distribution protocols: qubit BB84 and discrete-modulated continuous variable. Our method achieves comparable or improved key rates while reducing computation times by orders of magnitude compared to previous methods. This makes it easier to use the tightest possible bounds in quantum key distribution and thus makes it more practical for real quantum communication systems.

Article Text

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Outline

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PRX Quantum 7, 033051– Published 10 September, 2026
  • Received 22 December 2025
  • Accepted 24 June 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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