Bit threads on hypergraphs

TL;DR

This paper generalizes the concept of bit threads to hypergraphs, providing a new framework for understanding entanglement entropies and their inequalities in complex quantum systems and holography.

Contribution

It introduces a novel generalization of bit threads for hypergraphs, extending the holographic entropy cone framework to more complex entanglement structures.

Findings

Defines max multiflows on hypergraphs

Analyzes properties and interpretations in holography

Connects hypergraph entropy inequalities with bit thread framework

Abstract

Recent work has characterized the various inequalities that entanglement entropies represented by min-cuts on hypergraphs will satisfy. This collection, the hypergraph entropy cone, can be seen as a generalization of the holographic entropy cone which describes the entropies given by both min-cuts on 2-graphs and those of holographic states in AdS/CFT. In this article we describe a generalization of bit threads which allows us to describe max multiflows on hypergraphs. We further comment on its properties and interpretation in holography.