Vestnik КRAUNC. Fiz.-Mat. Nauki. 2026. vol. 54. no. 1. P. 64 – 71. ISSN 2079-6641

MATHEMATICS
https://doi.org/10.26117/2079-6641-2026-54-1-64-71
Research Article
Full text in English
MSC 42C15

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Product Entropic Uncertainty Principle

K. M. Krishna^{\ast}

School of Mathematics and Natural Sciences, Chanakya University Global Campus, NH-648, Haraluru Village, Devanahalli Taluk, Bengaluru North District, Karnataka State, 562 110, India

Abstract. Motivated by Deutsch entropic uncertainty principle and by various product-type uncertainty relations, we develop a new uncertainty principle that provides a rigorous lower bound on the product of entropies through the use of suitable functional techniques. Our approach broadens the traditional framework of entropic uncertainty by analyzing how carefully chosen functions modify or influence entropy measures associated with quantum states or probabilistic distributions. By viewing entropy as a functional object rather than a purely numerical quantity, we derive bounds that capture deeper structural limitations on pairs of observable that can be measured simultaneously. This functional viewpoint not only generalizes and strengthens several known product-type uncertainty principles, but also clarifies the connections between information-theoretic quantities and the analytic behavior of the functions employed. Overall, the developed framework offers a versatile method for deriving new entropy-based bounds and contributes to a
more comprehensive understanding of uncertainty within mathematical physics and quantum information theory.

Key words: uncertainty principle, frame, entropy.

Received: 03.02.2026; Revised: 13.03.2026; Accepted: 15.03.2026; First online: 29.03.2026

For citation. Krishna K.M. Product entropic uncertainty principle. Vestnik KRAUNC. Fiz.-mat. nauki. 2026, 54: 1, 64-71. EDN: DOBUMM. https://doi.org/10.26117/2079-6641-2026-54-1-64-71.

Funding. The study was conducted without the support of foundations.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for the submission of the final version of the article for publication.

^{\ast}Correspondence: E-mail: kmaheshak@gmail.com

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Krishna K. M., 2026

© Institute of Cosmophysical Research and Radio Wave Propagation, 2026 (original layout, design, compilation)

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Information about the author

Krishna Mahesh – PhD (Phys. & Math.), Assistant Professor, School of Mathematics and Natural Sciences, Chanakya University Global Campus, Haraluru, India, ORCID 0000-0003-4872-8634.

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