Maximizing the divergence from a hierarchical model of quantum states

TL;DR

This paper investigates quantum correlations using divergence from hierarchical models, highlighting differences from classical cases and analyzing maximizers of mutual information in separable qubit states.

Contribution

It introduces a quantum divergence measure from hierarchical models, explores its properties, and compares quantum and classical hierarchical correlations.

Findings

Quantum states differ from probability vectors in hierarchical models.

Discontinuity and reduced uncertainty are observed in quantum divergence.

Global maximizers of mutual information are discussed for separable qubit states.

Abstract

We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.