Universality Sacrifices Reliability in Classical-Quantum Channel Coding
Abstract
Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.
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BibTeX
@misc{watanabe2026universality,
title = {{Universality Sacrifices Reliability in Classical-Quantum Channel Coding}},
author = {Kaito Watanabe and Masahito Hayashi and Takaya Matsuura and Hao-Chung Cheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01941},
eprint = {2610.01941},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01941},
}
RIS
TY - UNPB
TI - Universality Sacrifices Reliability in Classical-Quantum Channel Coding
AU - Kaito Watanabe
AU - Masahito Hayashi
AU - Takaya Matsuura
AU - Hao-Chung Cheng
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01941
UR - https://arxiv.org/abs/2610.01941
AB - Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.
ER -