# A new characterization of the holographic entropy cone

## TL;DR

This paper introduces a new way to characterize the holographic entropy cone, providing evidence that the Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulas obey the same inequalities.

## Contribution

It develops a novel test based on majorization to verify inequalities, showing RT inequalities uniquely satisfy this test, thus characterizing the cone.

## Key findings

- RT inequalities pass the majorization test
- Only RT inequalities satisfy the test, not HRT
- Provides new evidence that RT and HRT cones coincide

## Abstract

Entanglement entropies computed using the holographic Ryu-Takayanagi formula are known to obey an infinite set of linear inequalities, which define the so-called RT entropy cone. The general structure of this cone, or equivalently the set of all valid inequalities, is unknown. It is also unknown whether those same inequalities are also obeyed by entropies computed using the covariant Hubeny-Rangamani-Takayanagi formula, although significant evidence has accumulated that they are. Using Markov states, we develop a test of this conjecture in a heretofore unexplored regime. The test reduces to checking that a given inequality obeys a certain majorization property, which is easy to evaluate. We find that the RT inequalities pass this test and, surprisingly, only RT inequalities do so. Our results not only provide strong new evidence that the HRT and RT cones coincide, but also offer a completely new characterization of that cone.