A graphical framework for proving holographic entanglement entropy inequalities in multipartite systems

TL;DR

This paper introduces a graphical geometric framework to systematically prove holographic entanglement entropy inequalities in multipartite quantum systems, enhancing visualization and verification capabilities for complex entanglement structures.

Contribution

It develops a novel graphical method and formal theorems for proving HEIs in systems with any number of subsystems, expanding analytical tools in quantum information theory.

Findings

Validated the graphical method for systems with 4 to 7 entangled regions

Provided explicit examples demonstrating the approach

Established formal theorems underpinning the method

Abstract

We present a graphical method for proving holographic entanglement entropy inequalities (HEIs) in general multipartite systems. By introducing a geometric representation of the entanglement structure, we develop a systematic approach that enables one to visualize and verify the validity of HEIs for any number of subsystems $n$. Several theorems are established to formalize this method, and explicit examples are provided for systems with $n = 4$ to $7$ entangled regions.