No off-diagonal quantum focusing for Rényi divergences
Abstract
The quantum focusing conjecture (QFC) is a mathematical expression of the idea that semiclassical gravity remains universally attractive. In its non-gravitational limit, the diagonal inequality is the quantum null energy condition (QNEC), which requires convexity of relative entropy with respect to the vacuum under null deformations. Rényi divergences generalize relative entropy, and positive results for the diagonal Rényi QNEC raise the question of whether they also satisfy the off-diagonal inequalities required by a full focusing principle. We show that classical correlations between distinct null generators obstruct this extension for any non-affine Rényi-type divergence satisfying data processing, tensor additivity, and matched classical-quantum conditioning.
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BibTeX
@misc{kibe2026offdiagonal,
title = {{No off-diagonal quantum focusing for Rényi divergences}},
author = {Tanay Kibe and Pratik Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.07799},
eprint = {2607.07799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - No off-diagonal quantum focusing for Rényi divergences
AU - Tanay Kibe
AU - Pratik Roy
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2607.07799
UR - https://arxiv.org/abs/2607.07799
AB - The quantum focusing conjecture (QFC) is a mathematical expression of the idea that semiclassical gravity remains universally attractive. In its non-gravitational limit, the diagonal inequality is the quantum null energy condition (QNEC), which requires convexity of relative entropy with respect to the vacuum under null deformations. Rényi divergences generalize relative entropy, and positive results for the diagonal Rényi QNEC raise the question of whether they also satisfy the off-diagonal inequalities required by a full focusing principle. We show that classical correlations between distinct null generators obstruct this extension for any non-affine Rényi-type divergence satisfying data processing, tensor additivity, and matched classical-quantum conditioning.
ER -