# Bit threads and holographic entanglement of purification

## TL;DR

This paper extends the bit thread formalism to derive dual flow programs for holographic entanglement of purification, revealing new multipartite flow behaviors and inequalities that deepen understanding of holographic entanglement structures.

## Contribution

It introduces a generalized convex duality approach to holographic entanglement of purification, uncovering novel multipartite flow behaviors and boundary flux constraints.

## Key findings

- Derived dual flow programs for bipartite and multipartite cases.
- Proved several inequalities related to holographic entanglement.
- Identified distinct multipartite flow behavior reflecting true multipartite entanglement.

## Abstract

Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite case we find the flows exhibit novel behavior which allows for a constrained flux on the boundary of the homology region. We show this flux can be made distinct from bipartite terms and reflects the truly multipartite portion of the holographic entanglement of purification.