Distribution of Mutual Information in Multipartite States

TL;DR

This paper explores the distribution of mutual information in multipartite quantum states, deriving new relations and bounds that deepen understanding of total correlations and their monogamy properties.

Contribution

It introduces a new expression relating mutual information in pure states to marginals and derives generalized monogamy relations for mixed states.

Findings

Derived a relation for mutual information in pure states.

Established generalized monogamy inequalities for three-partite states.

Proposed a measure for residual three-partite total correlation.

Abstract

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 informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity 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 measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.