Quantum key distribution rates from non-symmetric conic optimization

Andrés González Lorente; Pablo V. Parellada; Miguel Castillo-Celeita; Mateus Araújo

doi:10.22331/q-2025-03-10-1657

Quantum key distribution rates from non-symmetric conic optimization

Andrés González Lorente, Pablo V. Parellada, Miguel Castillo-Celeita, and Mateus Araújo

Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain

Published:	2025-03-10, volume 9, page 1657
Editor:	Pei Zeng
Eprint:	arXiv:2407.00152v3
Doi:	https://doi.org/10.22331/q-2025-03-10-1657
Citation:	Quantum 9, 1657 (2025).

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Abstract

Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function: the (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.

Featured image: Benchmarking three techniques for computing key rates: the technique introduced here, labelled QKD cone, and the two closest competitors. Running time in seconds (logarithmic scale) as a function of the local state dimension for the mutually unbiased bases protocol.

► BibTeX data

@article{Lorente2025quantumkey,
  doi = {10.22331/q-2025-03-10-1657},
  url = {https://doi.org/10.22331/q-2025-03-10-1657},
  title = {Quantum key distribution rates from non-symmetric conic optimization},
  author = {Lorente, Andr{\'{e}}s Gonz{\'{a}}lez and Parellada, Pablo V. and Castillo-Celeita, Miguel and Ara{\'{u}}jo, Mateus},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1657},
  month = mar,
  year = {2025}
}

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Cited by

[1] Dennis I. Martínez-Moreno, Miguel Castillo-Celeita, and Diego G. Bussandri, "From top quarks to enhanced quantum key distribution: A framework for optimal predictability of quantum observables", Physical Review Applied 25 1, 014063 (2026).

[2] Lidia Ruiz and Juan Carlos Garcia-Escartin, "Routing and wavelength assignment in quantum key distribution networks: Power control heuristics for quantum–classical multiplexing", Computer Communications 256, 108572 (2026).

[3] Kerry He, James Saunderson, and Hamza Fawzi, "Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems", Mathematical Programming Computation 18 2, 481 (2026).

[4] Saida M. Alkurkushi and Malek N. Algabri, "Discord-Enhanced Quantum Key Distribution in Noisy Mixed-State Channels", (2025).

[5] Patrick Andriolo, Esteban Vasquez, Elizabeth Agudelo, Max Riegler, Matej Pivoluska, and Gláucia Murta, "Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs", Brazilian Journal of Physics 56 4, 157 (2026).

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[7] Vladyslav C. Usenko, Antonio Acín, Romain Alléaume, Ulrik L. Andersen, Eleni Diamanti, Tobias Gehring, Adnan A. E. Hajomer, Florian Kanitschar, Christoph Pacher, Stefano Pirandola, and Valerio Pruneri, "Continuous-variable quantum communication", Reviews of Modern Physics 98 1, 015003 (2026).

[8] Carlos Pascual-García, Stefan Bäuml, Mateus Araújo, Rotem Liss, and Antonio Acín, "Improved finite-size key rates for discrete-modulated continuous-variable quantum key distribution under coherent attacks", Physical Review A 111 2, 022610 (2025).

[9] Kerry He, James Saunderson, and Hamza Fawzi, "Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems", arXiv:2407.00241, (2024).

[10] Ignatius William Primaatmaja, Wen Yu Kon, and Charles Lim, "Discrete-modulated continuous-variable quantum key distribution secure against general attacks", arXiv:2409.02630, (2024).

[11] Mariana Navarro, Andrés González Lorente, Pablo V. Parellada, Carlos Pascual-García, and Mateus Araújo, "Finite-size quantum key distribution rates from Rényi entropies using conic optimization", arXiv:2511.10584, (2025).

[12] Mariana Navarro, Antonio Acín, and Carlos Pascual-García, "Effective discrete-modulated continuous variable QKD under general attacks", arXiv:2606.20346, (2026).

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