# Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement

## TL;DR

This paper leverages graph theory to design experimental setups for creating complex high-dimensional and multi-particle entangled states, advancing quantum information science.

## Contribution

It introduces a method connecting quantum experiments with graph theory to systematically generate various entangled states, including GHZ, W, and Dicke states.

## Key findings

- Experimental setups for diverse entangled states identified
- Enhanced understanding of entanglement producibility in photonic systems
- Framework applicable to high-dimensional multipartite entanglement

## Abstract

Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here, we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.