Bit thread, entanglement distillation, and entanglement of purification

TL;DR

This paper explores the connections between bit threads, entanglement distillation, and entanglement of purification in holography, proposing a new, more physical interpretation of these concepts through a surface growth scheme.

Contribution

It introduces a novel bit thread interpretation for the one-shot entanglement distillation tensor network and generalizes the holographic entanglement of purification interpretation within a physical framework.

Findings

Bit thread interpretation for OSED tensor network.

Holographic EoP as a special case of the surface growth scheme.

A more natural and physically motivated interpretation of holographic EoP.

Abstract

We investigate the relations between bit thread, entanglement distillation and entanglement of purification in the holographic framework. Specifically, we give a bit thread interpretation for the one-shot entanglement distillation (OSED) tensor network, which can be understood as reconstructing the geometric structure of the bulk spacetime from the entanglement information of the boundary quantum system through the "surface growth scheme". Moreover, by showing that the holographic entanglement of purification (EoP) process can be regarded as a special case of our "surface growth scheme", we naturally obtain the bit thread interpretation of the holographic EoP in our framework, which turns out to be different from the existing interpretations. Since our interpretation for holographic EoP is obtained in a more general and physical framework, the advantage of our version is that it is more natural, and possibly more reasonable to reflect the real physical entanglement structures.