Improved Routing of Multiparty Entanglement over Quantum Networks

TL;DR

This paper introduces two graph state-based routing protocols for sharing GHZ states in quantum networks, improving the size and efficiency of entanglement distribution by utilizing tree structures and optimized configurations.

Contribution

It proposes novel routing protocols using tree structures for sharing GHZ states, achieving larger entangled states and optimal results in grid networks.

Findings

Larger GHZ states achieved compared to previous methods

Balanced trees outperform unbalanced trees in entanglement routing

Optimal constructions for grid networks demonstrated

Abstract

Effective routing of entanglements over a quantum network is a fundamental problem in quantum communication. Due to the fragility of quantum states, it is difficult to route entanglements at long distances. Graph states can be utilized for this purpose, reducing the need for long-distance entanglement routing by leveraging local operations. In this paper, we propose two graph state-based routing protocols for sharing GHZ states, achieving larger sizes than the existing works, for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier ones. For arbitrary network topologies, we show that if such a tree is balanced, it achieves a larger size than unbalanced trees. In particular, for grid networks, we show special constructions of the above-mentioned tree that achieve optimal results. Moreover, if the user nodes among whom the entanglement is to be routed are pre-specified, we propose a strategy to accomplish the required routing.