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arXiv · 2311.06484

Weighted $p$-R\'{e}nyi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

Junseo Lee·Hyeonjun Yeo·Kabgyun Jeong
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Abstract

We study the $p$-R\'{e}nyi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a R\'{e}nyi version of the entropy power inequality for quantum systems.

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Junseo Lee, Hyeonjun Yeo, Kabgyun Jeong. 2023-11-11. Weighted $p$-R\'{e}nyi Entropy Power Inequality: Information Theory to Quantum Shannon Theory. https://doi.org/10.1007/s10773-023-05512-8

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