Total correlations and mutual information

Gabriel L. Moraes, R. M. Angelo, Ana C. S. Costa

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 p-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 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 argued that QMI remains a valid measure of total correlations.

M. Bönitz

Asutosh Kumar

Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information (QMI) for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems.This may, however, be no longer true for three or more party quantum systems. It is possible that three-party QMI can be negative. That QMI can assume negative value is confronting, and we give operational definition of QMI which is non-negative. We then define multiparty operational quantum discord, and give some examples. Interestingly, we observe that quantum discord increases when measurement is performed on larger number of subsystems. Consequently, the symmetric version of quantum discord, which involves measurement on all parties, reveals the maximal quantumness. This raises question on the interpretation of measured mutual information as classical correlation.

Rajiv R. P. Singh, Matthew B. Hastings, Ann B. Kallin +1 more

Farid Shähandeh

Jonas Maziero

"Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informa- tions and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong sub- additivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a mea- sure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations."