Renormalization and small-world model of fractal quantum repeater networks

TL;DR

This paper introduces a framework for applying quantum repeater protocols to fractal-structured quantum networks, enabling entanglement distribution and a transition to small-world properties for scalable quantum communication.

Contribution

It develops a renormalization-based approach for fractal quantum networks and demonstrates a fractal to small-world transition to enhance scalability.

Findings

Renormalization maps entanglement distribution in fractal networks.

Recursive transformations induce a fractal to small-world transition.

Scalable quantum networks can be achieved through this transition.

Abstract

Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.