Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography

Gereon KoÃmann; RenÃ© Schwonnek

doi:10.22331/q-2026-10-20-2238

Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography

Gereon KoÃmann¹ and RenÃ© Schwonnek²

¹Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
²Institut für Theoretische Physik, Leibniz Universität Hannover, Germany

Published:	2026-10-20, volume 10, page 2238
Editor:	Máté Farkas
Eprint:	arXiv:2411.04858v4
Doi:	https://doi.org/10.22331/q-2026-10-20-2238
Citation:	Quantum 10, 2238 (2026).

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Abstract

We introduce a numerical framework for reliably estimating conditional von Neumann entropies, a central quantity in device-independent quantum cryptography and randomness generation. Our method is based on semidefinite relaxations derived from the Navascués--Pironio--Acín hierarchy and provides entropy bounds directly from observed statistics, assuming only the validity of quantum mechanics. The approach builds on a recent integral representation of entropy and substantially improves efficiency: it requires about half as many support variables as existing methods, while allowing these variables to be chosen projectively, leading to a significant reduction in runtime. These advances enable the practical certification of randomness and security even in noisy conditions, while integrating seamlessly with modern entropy accumulation theorems. Consequently, our framework becomes a versatile tool for quantum cryptographic protocols, broadening the possibilities for secure communication in untrusted environments.

► BibTeX data

@article{KoAmann2026reliableentropy,
  doi = {10.22331/q-2026-10-20-2238},
  url = {https://doi.org/10.22331/q-2026-10-20-2238},
  title = {Reliable {E}ntropy {E}stimation from {O}bserved {S}tatistics for {D}evice-{I}ndependent {Q}uantum {C}ryptography},
  author = {Ko{\~{A}}mann, Gereon and Schwonnek, Ren{\~{A}}©},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2238},
  month = oct,
  year = {2026}
}

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Cited by

[1] Gereon Koßmann and René Schwonnek, "Optimising the relative entropy under semidefinite constraints", npj Quantum Information 12 1, 23 (2026).

[2] 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).

[3] Gereon Koßmann, Mario Berta, and René Schwonnek, "Routed Bell tests with arbitrarily many local parties", arXiv:2510.08405, (2025).

[4] Corentin Lanore, Xavier Valcarce, Jean Etesse, Anthony Martin, and Jean-Daniel Bancal, "Towards Device-Independent Quantum Key Distribution with Photonic Devices", arXiv:2601.14373, (2026).

[5] Robert Okula and Piotr Mironowicz, "Device-independent Shannon entropy certification", New Journal of Physics 27 11, 114519 (2025).

[6] Andreas Bluhm, Gereon Koßmann, and René Schwonnek, "Device independent quantum key distribution with robust self-tests", arXiv:2603.28085, (2026).

[7] Lewis Wooltorton, Peter Brown, and Omar Fawzi, "Chain rules for conditional entropies in quantum cryptography: limitations and improvements", arXiv:2605.29787, (2026).

[8] Rutvij Bhavsar, Junguk Moon, and Joonwoo Bae, "Entropy Bounds via Hypothesis Testing and Its Applications to Two-Way Key Distillation in Quantum Cryptography", arXiv:2602.05870, (2026).

[9] Gereon Koßmann, René Schwonnek, Po-Chieh Liu, and Hao-Chung Cheng, "Device-independent Quantum Key Distribution in the commuting operator framework", arXiv:2607.03579, (2026).

The above citations are from SAO/NASA ADS (last updated successfully 2026-10-20 12:59:18). The list may be incomplete as not all publishers provide suitable and complete citation data.

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