Multiplexed multipartite quantum repeater rates in the stationary regime

TL;DR

This paper analyzes the stationary rates of multipartite quantum repeaters with multiplexing, deriving a formula for network scalability and demonstrating rate saturation as the number of memories increases.

Contribution

It provides a closed-form expression for the stationary multipartite quantum repeater rate in star networks with multiplexing, advancing understanding of quantum network scalability.

Findings

Rate saturates for large number of memories

Derived a closed-form expression for stationary rate

Results applicable to quantum repeater chains between two parties

Abstract

Multipartite quantum repeaters play an important role in quantum communication networks enabling the transmission of quantum information over larger distances. To increase the rates for multipartite entanglement distribution, multiplexing of quantum memories is included. Understanding the limitations of achievable rates in the stationary regime for different network sizes is a fundamental step to comprehend scalability of quantum networks. This work investigates the behavior of the multipartite quantum repeater rate (i.e., the number of GHZ states generated per round and per memory) in the stationary regime in multipartite star graphs with a single central multipartite quantum repeater including multiplexing using Markov chains. We derive a closed-form expression for the stationary rate depending on the network size. We support our results with numerical simulations. Further, we show that the rate saturates for large number of memories. On an abstract level, the mathematical description is equivalent to quantum repeater chains between two parties. Therefore, our results also apply to those setups.