On the construction of graph models realizing given entropy vectors

TL;DR

This paper introduces an efficient algorithm for constructing holographic simple tree graph models that realize specific entropy vectors, and explores generalizations and detection of unrealizability of entropy vectors.

Contribution

It develops a new algorithm for holographic graph model construction and advances the understanding of correlation hypergraphs and entropy vector realizability.

Findings

Algorithm efficiently constructs holographic simple tree graph models.

Toolkit enhancements for correlation hypergraphs related to subsystem coarse-graining.

First steps towards generalizing the algorithm to arbitrary holographic tree models.

Abstract

We present an efficient algorithm for the construction of a holographic simple tree graph model that realizes a given entropy vector, subject to a specific ``chordality'' condition first introduced in arXiv:2412.18018. We further develop the toolkit of the correlation hypergraph, particularly in relation to coarse-graining and fine-graining of subsystems. We then use these techniques to take the first steps towards the generalization of this new algorithm to arbitrary (not necessarily simple) holographic tree graph models, and the ``detection'' of unrealizability of an entropy vector independently from the knowledge of holographic entropy inequalities.