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The regularized channel Rényi divergence is continuous
Abstract
We show that the regularized channel Rényi divergence is continuous at α= 1. As consequences, we establish an exponentially strong converse for channel discrimination, a subchannel-smoothed asymptotic equipartition property, a relative entropy accumulation theorem, and a new proof of the generalized quantum Stein's lemma. Our result further shows that the regularized channel relative entropy is computable. The continuity proof relies on a variational formula that expresses the regularized channel divergence as a single-letter optimization over variables of unrestricted finite dimension. We then establish continuity using a novel spectral confinement technique.
Related
- Continuity of Regularized Channel Rényi Divergences
- Regularized barycentric Rényi divergences
- Geometric Rényi divergence and RLD Fisher information under quantum processes without definite causal order
- Monotonicity of the Rényi channel capacity under non-signaling assisted channel simulation
- Finite attainment and efficient computation of regularized quantum channel relative entropy
BibTeX
@misc{schmitt2026regularized,
title = {{The regularized channel Rényi divergence is continuous}},
author = {Lukas Schmitt and David Sutter},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29885},
eprint = {2609.29885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29885},
}
RIS
TY - UNPB
TI - The regularized channel Rényi divergence is continuous
AU - Lukas Schmitt
AU - David Sutter
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29885
UR - https://arxiv.org/abs/2609.29885
AB - We show that the regularized channel Rényi divergence is continuous at α= 1. As consequences, we establish an exponentially strong converse for channel discrimination, a subchannel-smoothed asymptotic equipartition property, a relative entropy accumulation theorem, and a new proof of the generalized quantum Stein's lemma. Our result further shows that the regularized channel relative entropy is computable. The continuity proof relies on a variational formula that expresses the regularized channel divergence as a single-letter optimization over variables of unrestricted finite dimension. We then establish continuity using a novel spectral confinement technique.
ER -