The PEE aspects of entanglement islands from bit threads

TL;DR

This paper explores the partial entanglement entropy in holographic BCFT setups with entanglement islands using bit thread formulation, proposing island rules for fine-grained PEE and offering insights into black hole information.

Contribution

It introduces a bit thread description of the AdS/BCFT setup with entanglement islands and proposes island rules for fine-grained PEE, advancing understanding of entanglement structure in holography.

Findings

Bit thread description characterizes entanglement details with islands.

Distinction between fine-grained and semi-classical PEE is established.

Proposed island rules for fine-grained PEE analogous to entropy rules.

Abstract

We study the partial entanglement entropy (PEE) aspects of the holographic BCFT setup with an entanglement island, inspired by the holographic triality of the AdS/BCFT setup developed in the recent study on the black hole information problem, and the "PEE=CFF (component flow flux)" prescription, which is proposed recently to investigate the holographic PEE in the framework of bit thread formulation. Our study provides a bit thread description of the AdS/BCFT setup, which characterizes the specific entanglement details between the different parts of the system with an entanglement island, and may provide further insight into the black hole information problem. Furthermore, we show that in the context of island, one should distinguish between the fine-grained PEE and the semi-classical PEE. Interestingly, similar to the island rule of the fine-grained entropy in the semi-classical picture, we also propose the island rules of the fine-grained PEE.