Deriving the PEE proposal from the Locking bit thread configuration

TL;DR

This paper interprets the partial entanglement entropy (PEE) within the holographic framework as component flow flux in a locking bit thread configuration, deriving the PEE proposal and explaining related dualities.

Contribution

It introduces a concrete locking scheme for bit threads that explicitly derives the PEE proposal and its generalizations, linking entanglement measures to bit thread configurations.

Findings

Derived the PEE proposal from locking bit thread configurations.

Provided a unified explanation for BPE/EWCS and EoP/EWCS dualities.

Clarified the conceptual connection between PEE and locking thread configurations.

Abstract

In the holographic framework, we argue that the partial entanglement entropy (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration. By applying the locking theorem of bit threads, and constructing a concrete locking scheme, we obtain a set of uniquely determined component flow fluxes from this viewpoint, and successfully derive the PEE proposal and its generalized version in the multipartite cases. Moreover, from this perspective of bit threads, we also present a coherent explanation for the coincidence between the BPE (balanced partial entanglement)/EWCS (entanglement wedge cross section) duality proposed recently and the EoP (entanglement of purification)/EWCS duality. We also discuss the issues implied by this coincident between the idea of the PEE and the picture of locking thread configuration.