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Weighted p-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

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Abstract

We study the p-Rényi 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 Rényi version of the entropy power inequality for quantum systems.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) through a grant funded by the Ministry of Science and ICT (NRF-2022M3H3A1098237 & RS-2023-00211817) and the Ministry of Education (NRF-2021R1I1A1A01042199). This work was partly supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Ministry of Science and ICT (No. 2019-0-00003), and Korea Institute of Science and Technology Information (KISTI).

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Author notes

  1. Junseo Lee, Hyeonjun Yeo, Kabgyun Jeong These authors contributed equally to this work.

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Yonsei University, Seoul, 03722, South Korea

    Junseo Lee

  2. Quantum Computing R & D, Norma Inc., Seoul, 04799, South Korea

    Junseo Lee

  3. Department of Physics and Astronomy, Seoul National University, Seoul, 08826, South Korea

    Hyeonjun Yeo

  4. Research Institute of Mathematics, Seoul National University, Seoul, 08826, South Korea

    Kabgyun Jeong

  5. School of Computational Sciences, Korea Institute for Advanced Study, Seoul, 02455, South Korea

    Kabgyun Jeong

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  1. Junseo Lee
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Contributions

K.J. conceived the idea and proved initial statements, and J.L. and H.Y. confirmed the proof. All authors wrote, reviewed, and agreed to submit the manuscript.

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Correspondence to Kabgyun Jeong.

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Lee, J., Yeo, H. & Jeong, K. Weighted p-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory. Int J Theor Phys 62, 253 (2023). https://doi.org/10.1007/s10773-023-05512-8

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