Teleportation Fidelity of Binary Tree Quantum Repeater Networks

TL;DR

This paper analyzes four types of binary tree quantum repeater networks, deriving formulas for teleportation fidelity, exploring quantum advantage conditions, and identifying the most effective topology for large-scale quantum teleportation.

Contribution

It provides a novel analytical methodology for calculating pathlengths and teleportation fidelity in various binary tree networks, highlighting the directed symmetric topology as optimal.

Findings

Directed symmetric binary tree yields highest teleportation fidelity.

Quantum advantage depends on Werner state parameters.

Fidelity approaches a limit as network size grows large.

Abstract

Binary tree network, being a subclass of Cayley tree network, is a significant topological structure used for information transfer in a hierarchical sense. In this article, we consider four types of binary tree repeater networks (directed and undirected, asymmetric and symmetric) and obtain the analytical expressions of the average of the maximum teleportation fidelities for each of these binary tree networks. We contribute a methodology for the analytical calculation of pathlengths in all considered graph types. Based on these, we have used simple Werner state-based models and are able to identify the parameter ranges for which these networks can show quantum advantage. We also explore the role of maximally entangled states in the network to enhance the quantum advantage. We provide a detailed examination of the large-scale behavior of these networks, obtaining the limiting value of the average maximum teleportation fidelity as the number of nodes, $N$, approaches infinity, same as fractal tree. Our findings reveal that the directed symmetric binary tree represents the most advantageous topology for quantum teleportation within this context. From the context of quantum repeater networks, this work makes a significant advancement in the process of identifying resourceful tree networks for distributed quantum teleportation i.e. teleportation between all possible sources and targets.