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Peer-reviewedCC BY 4.0Quantum

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

  • Gereon Koßmann1
  • René Schwonnek2
  1. 1Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
  2. 2Institut für Theoretische Physik, Leibniz Universität Hannover, Germany
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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.

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Cite

BibTeXRIS
BibTeX
@article{koßmann2026reliable,
  title = {{Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography}},
  author = {Gereon Koßmann and René Schwonnek},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-20-2238},
  url = {https://quantum-journal.org/papers/q-2026-10-20-2238/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography
AU  - Gereon Koßmann
AU  - René Schwonnek
PY  - 2026
DA  - 2026/10/20
JO  - Quantum
DO  - 10.22331/q-2026-10-20-2238
UR  - https://quantum-journal.org/papers/q-2026-10-20-2238/
AB  - 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.
SN  - 2521-327X
ER  -