Path Percolation in Quantum Communication Networks

TL;DR

This paper introduces a model of path percolation in quantum communication networks, analyzing how entanglement-based links are disrupted by communication paths and exploring the network's steady states.

Contribution

It presents the concept of path percolation, analyzing its phase diagram and showing the steady state is independent of initial topology under random link addition.

Findings

Steady state is topology-independent with random link addition.

Path percolation exhibits a distinct phase transition.

Analytical and numerical analysis of the model.

Abstract

In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, communication channels can be established between them via quantum routing protocols. However, in contrast to classical communication networks, each communication event removes all participating links along the communication path, disrupting the quantum network. Here, we propose a simple model, where randomly selected pairs of nodes communicate through shortest paths. Each time such a path is used, all participating links are eliminated, leading to a correlated percolation process that we call ``path percolation.'' We study path percolation both numerically and analytically and present the phase diagram of the steady states as a function of the rate at which new links are being added to the quantum communication network. As a key result, the steady state is found to be independent from the initial network topology when new link are added randomly between disconnected components. We close by discussing extensions of path percolation and their potential applications.