Holographic Entropy Inequalities and the Topology of Entanglement Wedge Nesting

TL;DR

This paper proves two new infinite families of holographic entropy inequalities using a graphical approach based on entanglement wedge nesting, revealing topological structures and confirming a conjecture about the holographic entropy cone.

Contribution

It introduces a novel graphical method to derive entropy inequalities and links topological tessellations with entanglement wedge nesting, advancing understanding of holographic entropy structures.

Findings

Proved two new infinite families of holographic entropy inequalities.

Established a connection between topological tessellations and entanglement wedge nesting.

Confirmed a conjecture about the structure of the holographic entropy cone.

Abstract

We prove two new infinite families of holographic entropy inequalities. A key tool is a graphical arrangement of terms of inequalities, which is based on entanglement wedge nesting (EWN). It associates the inequalities with tessellations of the torus and the projective plane, which reflect a certain topological aspect of EWN. The inequalities prove a prior conjecture about the structure of the holographic entropy cone and show an interesting interplay with differential entropy.