The Symmetrized Holographic Entropy Cone

TL;DR

This paper introduces a symmetrization method for the holographic entropy cone, revealing properties of its extremal structure for any number of parties and showing holographic entropies are exponentially rare among quantum entropies.

Contribution

It presents a novel symmetrization technique that simplifies the analysis of the holographic entropy cone for arbitrary parties and compares holographic and quantum entropies.

Findings

Symmetrization projects the HEC onto a lower-dimensional space.

Properties of extremal elements of the HEC are deduced for general n.

Holographic entropies are exponentially rare among quantum entropies.

Abstract

The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, to date it has only been possible to completely characterize the HEC for at most $n=5$ numbers of parties. For larger $n$, our knowledge of the HEC falls short of incomplete: almost nothing is known about its extremal elements. Here, we introduce a symmetrization procedure that projects the HEC onto a natural lower dimensional subspace. Upon symmetrization, we are able to deduce properties that its extremal structure exhibits for general $n$. Further, by applying this symmetrization to the quantum entropy cone, we are able to quantify the typicality of holographic entropies, which we find to be exponentially rare quantum entropies in the number of parties.