Construction and analysis of statistical correlation measures through Diophantine equations

Authors

DOI:

https://doi.org/10.31349/SuplRevMexFis.6.011307

Keywords:

Diophantine equations, Shannon entropies, higher-order correlation measures, quantum harmonic oscillators

Abstract

In this work, we explore the connection between Diophantine equations and the construction of informational measures, particularly mutual information, total correlation, and higher-order interaction information. These information measures are calculated in continuous variable quantum systems comprised of three to fifty harmonic oscillators, and their behaviour was compared among them. By analyzing the ground state of quantum harmonic oscillators, we establish a mathematical framework where Diophantine constraints emerge naturally in the computation of these quantities. There is an overall consistency in the behaviour of the introduced measures as function of the parameters of pairwise potential and the number of oscillators. Our results provide new insights into the interplay between number theory and quantum information, suggesting novel approaches to quantifying higher-order correlations in many-body quantum systems.

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Published

2025-05-21

How to Cite

1.
Salazar SJC, Laguna Galindo H, Sagar RP. Construction and analysis of statistical correlation measures through Diophantine equations. Supl. Rev. Mex. Fis. [Internet]. 2025 May 21 [cited 2025 Jul. 1];6(1):011307 1-6. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/7997

Issue

Vol. 6 No. 1 (2025): Suplemento de la Revista Mexicana de Física. Commemorating the 50th Anniversary of UAM: Applications of Information Theory in Natural Sciences

Section

13 50th Anniv. of UAM: Applications of Information Theory in Natural Sciences

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