The holographic entropy cone from marginal independence

TL;DR

This paper demonstrates that the complex holographic entropy cone can be reconstructed from fundamental quantum entropy data, simplifying understanding of holographic entanglement and spacetime emergence.

Contribution

It introduces conjectures and proofs showing the holographic entropy cone can be derived from basic subadditivity principles and a subset of extreme rays.

Findings

Reconstruction of the holographic entropy cone from subadditivity data

Identification of a simple subset of extreme rays sufficient for reconstruction

Rigorous proof of conjectures relating graph models to holographic entanglement

Abstract

The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler "subadditivity cone", namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime.