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arXiv · 2412.08000

Axiomatic approach to measures of total correlations

Gabriel L. Moraes·Renato M. Angelo·Ana C. S. Costa
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Abstract

Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of total correlations. We first outline essential properties that an effective correlation measure should satisfy and review existing measures, including quantum mutual information, the p-norm of the correlation matrix, and the recently defined quantum Pearson correlation coefficient. Additionally, we introduce new measures based on R\'enyi and Tsallis relative entropies, as well as the Kullback-Leibler divergence. Our analysis reveals that while quantum mutual information, the p-norm, and the Pearson measure exhibit equivalence for two-qubit systems, they all suffer from an ordering problem. Despite criticisms regarding its reliability, we argue that quantum mutual information remains a valid measure of total correlations.

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Gabriel L. Moraes, Renato M. Angelo, Ana C. S. Costa. 2024-12-11. Axiomatic approach to measures of total correlations. https://doi.org/10.3390/e26121098

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