Inequalities of Holographic Entanglement of Purification from Bit Threads

TL;DR

This paper explores new inequalities and properties of holographic entanglement of purification (HEoP) using multiflow and bit thread frameworks, revealing deeper connections between quantum information and holography.

Contribution

It introduces novel inequalities for HEoP derived from multiflow configurations and relates these to properties of holographic entanglement entropy (HEE) through geometric analysis.

Findings

Derived new inequalities of HEoP under max multiflow configurations.

Established correspondence between inequalities of HEoP and HEE.

Confirmed geometric relations between HEoP inequalities and holographic entanglement entropy.

Abstract

There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology.