Moraes Gabriel L, Angelo Renato M, Costa Ana C S
Department of Physics, Federal University of Paraná, P.O. Box 19044, Curitiba 81531-980, PR, Brazil.
Entropy (Basel). 2024 Dec 15;26(12):1098. doi: 10.3390/e26121098.
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 aimed to discuss the challenge of defining a reliable measure of total correlations. We first outlined the essential properties that an effective correlation measure should satisfy and reviewed existing measures, including quantum mutual information, the -norm of the correlation matrix, and the recently defined quantum Pearson correlation coefficient. Additionally, we introduced new measures based on Rényi and Tsallis relative entropies, as well as the Kullback-Leibler divergence. Our analysis revealed that while quantum mutual information, the -norm, and the Pearson measure exhibit equivalence for two-qubit systems, they all suffer from an ordering problem. Despite criticisms regarding its reliability, we argued that QMI remains a valid measure of total correlations.
相关性在科学的各个领域中都起着关键作用，尤其是在量子力学中，然而其恰当的量化仍是一个有争议的话题。在这项工作中，我们旨在讨论定义一种可靠的总相关性度量所面临的挑战。我们首先概述了一种有效的相关性度量应满足的基本属性，并回顾了现有的度量，包括量子互信息、相关矩阵的 -范数以及最近定义的量子皮尔逊相关系数。此外，我们基于雷尼熵和Tsallis相对熵以及库尔贝克 - 莱布勒散度引入了新的度量。我们的分析表明，虽然量子互信息、 -范数和皮尔逊度量在双量子比特系统中表现出等价性，但它们都存在排序问题。尽管有人对其可靠性提出批评，但我们认为量子互信息仍然是总相关性的一种有效度量。
