Phase error rate estimation in QKD with imperfect detectors

Devashish Tupkary; Shlok Nahar; Pulkit Sinha; Norbert Lütkenhaus

doi:10.22331/q-2025-12-11-1937

Phase error rate estimation in QKD with imperfect detectors

Devashish Tupkary¹, Shlok Nahar¹, Pulkit Sinha², and Norbert Lütkenhaus¹

¹Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
²Institute for Quantum Computing and School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

Published:	2025-12-11, volume 9, page 1937
Editor:	Máté Farkas
Eprint:	arXiv:2408.17349v4
Doi:	https://doi.org/10.22331/q-2025-12-11-1937
Citation:	Quantum 9, 1937 (2025).

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Abstract

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly characterized basis-efficiency mismatch. Our proof works by obtaining a suitable bound on the phase error rate, without requiring any new modifications to the protocol steps or hardware. It is applicable to imperfectly characterized detectors, and only requires the maximum relative difference in detection efficiencies and dark count rates of the detectors to be characterized. Moreover, our proof allows Eve to choose detector efficiencies and dark count rates in their allowed ranges in each round, thereby addressing an important problem of detector side channels. We prove security in the variable-length framework, where users are allowed to adaptively determine the length of key to be produced, and number of bits to be used for error-correction, based on observations made during the protocol. We quantitatively demonstrate the effect of basis-efficiency mismatch by applying our results to the decoy-state BB84 protocol.

► BibTeX data

@article{Tupkary2025phaseerrorrate,
  doi = {10.22331/q-2025-12-11-1937},
  url = {https://doi.org/10.22331/q-2025-12-11-1937},
  title = {Phase error rate estimation in {QKD} with imperfect detectors},
  author = {Tupkary, Devashish and Nahar, Shlok and Sinha, Pulkit and L{\"{u}}tkenhaus, Norbert},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1937},
  month = dec,
  year = {2025}
}

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