Deriving the PEE proposal from the locking bit thread configuration

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.

Automated summary

In this study, the partial entanglement entropy is explicitly interpreted as component flow flux in a locking bit thread configuration within the holographic framework. By applying the locking theorem of bit threads, a set of uniquely determined component flow fluxes is obtained, and the PEE proposal and its generalized version in multipartite cases are successfully derived. Furthermore, a coherent explanation is presented for the coincidence between the BPE/EWCS duality and the EoP/EWCS duality, based on the perspective of bit threads.