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The exact strong converse exponent for private communication over quantum channels
Abstract
We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.
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BibTeX
@misc{cheng2026exact,
title = {{The exact strong converse exponent for private communication over quantum channels}},
author = {Hao-Chung Cheng and Christoph Hirche and Marco Tomamichel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38144},
eprint = {2609.38144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38144},
}
RIS
TY - UNPB
TI - The exact strong converse exponent for private communication over quantum channels
AU - Hao-Chung Cheng
AU - Christoph Hirche
AU - Marco Tomamichel
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38144
UR - https://arxiv.org/abs/2609.38144
AB - We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.
ER -