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Entropic Uncertainty Relations for (N, M)-POVMs

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Abstract

Characterizing uncertainty relations through entropy is a hot topic in quantum information theory. In this paper, the multifarious lower entropic bounds, which can unify the existing entropic uncertainty relations, are derived, including the Tsallis entropies, the Rényi entropies, the min-entropies and the Maassen-Uffink type based on a broad family of generalized informationally complete symmetric measurements. Furthermore, some detailed examples are given and it is shown that the presented entropic uncertainty relations are more powerful and comprehensive than the existing ones.

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The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request

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Acknowledgements

This work is supported by the National Science Foundation of Sichuan Province (No. 2022NSFSC0534), the Central Guidance on Local Science and Technology Development Fund of Sichuan Province (No. 22ZYZYTS0064), the Chengdu Key Research and Development Support Program (No. 2021-YF09-0016-GX), the Key Project of Sichuan Normal University (No. XKZX-02).

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Authors and Affiliations

  1. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610066, China

    Fan Huang & Ming-Qiang Bai

  2. Research Center of Sichuan Normal University, National-Local Joint Engineering Laboratory of System Credibility Automatic Verication, Chengdu, 610066, Sichuan, China

    Fan Huang & Ming-Qiang Bai

  3. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, China

    Fan Huang & Ming-Qiang Bai

  4. School of Science, Xihua University, Chengdu, 610039, China

    Liang Tang

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  1. Fan Huang
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All of the authors contribute to this paper are important. The specific contributions are as follows. The first author played a major role in the conceptualization and writing of the article. The second and third authors worked mainly on the overall framework and language of the article

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Correspondence to Ming-Qiang Bai.

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Liang Tang and Ming-Qiang Bai are contributed equally to this work.

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Huang, F., Tang, L. & Bai, MQ. Entropic Uncertainty Relations for (N, M)-POVMs. Int J Theor Phys 62, 126 (2023). https://doi.org/10.1007/s10773-023-05372-2

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