Counterexamples to the Tensorization Property of Strong Data Processing Inequalities for Quantum Divergences
Abstract
In information theory, the data processing inequality is a fundamental property that describes the loss of information through noisy channels. A more refined description is given by the strong data processing inequality (SDPI) for a fixed channel and a full-rank reference state. In classical information theory, the strong data processing inequality tensorizes for a large family of f-divergences. However, its quantum counterpart remains largely unexplored. Tensorization of SDPI has previously been shown only for some special cases, and whether it holds more generally for quantum divergences still remains open. In this work, we report two negative results: the tensorization property fails for certain quantum chi-square divergences, and it also does not hold for the quantum relative entropy.
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BibTeX
@misc{cao2026counterexamples,
title = {{Counterexamples to the Tensorization Property of Strong Data Processing Inequalities for Quantum Divergences}},
author = {Yu Cao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13204},
eprint = {2608.13204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13204},
}
RIS
TY - UNPB
TI - Counterexamples to the Tensorization Property of Strong Data Processing Inequalities for Quantum Divergences
AU - Yu Cao
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2608.13204
UR - https://arxiv.org/abs/2608.13204
AB - In information theory, the data processing inequality is a fundamental property that describes the loss of information through noisy channels. A more refined description is given by the strong data processing inequality (SDPI) for a fixed channel and a full-rank reference state. In classical information theory, the strong data processing inequality tensorizes for a large family of f-divergences. However, its quantum counterpart remains largely unexplored. Tensorization of SDPI has previously been shown only for some special cases, and whether it holds more generally for quantum divergences still remains open. In this work, we report two negative results: the tensorization property fails for certain quantum chi-square divergences, and it also does not hold for the quantum relative entropy.
ER -