PreprintarXiv licencearXiv
The marginal is pretty good
Abstract
One-shot information theory measures often require an optimization over states, but the form of these optimizers can be complicated or depend on the initial problem in nonlinear ways. In this note, we show that in many instances using the marginal instead of the optimal state is sufficiently good and only changes the result by a small factor. We prove that for the Petz--Rényi and sandwiched--Rényi divergences of order α∈(0,1), replacing the optimizing state on B by the marginal ρB results in a multiplicative overhead of at most 1/α.
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BibTeX
@misc{schmitt2026marginal,
title = {{The marginal is pretty good}},
author = {Lukas Schmitt and Gui-Long Jiang and Shi-Bing Li and Joseph M. Renes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05225},
eprint = {2609.05225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05225},
}
RIS
TY - UNPB
TI - The marginal is pretty good
AU - Lukas Schmitt
AU - Gui-Long Jiang
AU - Shi-Bing Li
AU - Joseph M. Renes
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.05225
UR - https://arxiv.org/abs/2609.05225
AB - One-shot information theory measures often require an optimization over states, but the form of these optimizers can be complicated or depend on the initial problem in nonlinear ways. In this note, we show that in many instances using the marginal instead of the optimal state is sufficiently good and only changes the result by a small factor. We prove that for the Petz--Rényi and sandwiched--Rényi divergences of order α∈(0,1), replacing the optimizing state on B by the marginal ρ_B results in a multiplicative overhead of at most 1/α.
ER -