Quantum Bit Threads and the Entropohedron

TL;DR

This paper introduces new quantum bit thread prescriptions for holographic entanglement entropy, explores their behavior with entanglement islands, and defines the entropohedron as a convex polytope of entanglement measures.

Contribution

It presents multiple novel quantum bit thread formulations, analyzes their properties in complex spacetime scenarios, and introduces the entropohedron for entanglement measure visualization.

Findings

New quantum bit thread prescriptions equivalent to quantum extremal surface formula for static states.

Analysis of bit thread behavior in the presence of entanglement islands and baby universes.

Introduction of the entropohedron as a convex polytope of entanglement distribution functions.

Abstract

We derive several new quantum bit thread prescriptions for holographic entanglement entropy, equivalent for static states to the quantum extremal surface formula. Our new prescriptions come in many varieties: vector field-based or based on measures over bulk curves, dependent or independent of the bulk UV regulator, loose and strict versions of constraints, and more. We also explore how bit threads behave in the presence of entanglement islands and baby universes. Finally, our prescriptions inspire new measures of entanglement that we call entanglement distribution functions, which can be packaged into a convex polytope that we call the entropohedron.