Teleportation Fidelity of Binary Tree Quantum Repeater Networks

Abstract: The idea of average of maximum teleportation fidelities was introduced in [1] to measure the capability of the network to act as a resource for distributed teleportation between any pair of nodes. 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. Our work investigates the role of directionality and symmetry in this measure. Like [1], here also 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 explore the role of maximally entangled states in the network to enhance the quantum advantage. We explore the large $N$ (nodes) scenario for each of these networks and find out the limiting value of the average of the maximum teleportation fidelity for each of these networks. We also include the scenarios when the Werner state parameters for each link are different and chosen from a uniform distribution. According to our analysis, the directed symmetric binary tree is the most beneficial topology in this context. Our results pave the way to identify the resourceful network in transmitting quantum information.