No information transmission through quantum channels above capacity
Abstract
We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of Rényi information measures that lead to asymptotic continuity bounds for Rényi capacities.
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BibTeX
@misc{cheng2026information,
title = {{No information transmission through quantum channels above capacity}},
author = {Hao-Chung Cheng and Marco Tomamichel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08998},
eprint = {2609.08998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08998},
}
RIS
TY - UNPB
TI - No information transmission through quantum channels above capacity
AU - Hao-Chung Cheng
AU - Marco Tomamichel
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08998
UR - https://arxiv.org/abs/2609.08998
AB - We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of Rényi information measures that lead to asymptotic continuity bounds for Rényi capacities.
ER -