Topology-Dependent Enhancement of Entanglement Extraction in Repeater Graph States

Abstract: Quantum repeaters are essential for establishing long-distance quantum communication to overcome the exponential decay of entanglement due to photon loss. Traditional repeater architectures rely on physical quantum memory, which introduces decoherence and poses significant practical implementation challenges. The repeater graph state (RGS) architecture offers a promising memory-less alternative that is inherently resilient to photon losses. A key challenge in implementing RGS lies in the requirement for highly efficient graph state generators and complex qubit measurement. In this work, we aim to investigate the strategies for extracting the maximum number of Bell pairs from the RGS structure via its qubit connection to resolve the well-known bottleneck problem of RGS in which only a single Bell pair can be extracted from a complete bipartite graph state. From simulations, we observe that the maximum number of extracted Bell pairs depends on its connection topology, where the Bell-pair yield tends to be maximal at low to moderate edge densities. As the number of network hops increases, the RGS must be equipped with higher inner-qubit connectivity to maintain a sufficient yield of extractable Bell pairs. Thus, the expected resource requirement shifts toward the use of RGSs with higher inner-qubit connectivity.