Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies

Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies in order to increase fidelities and reduce waiting times for end-to-end entanglement distribution. In this work, we introduce \textit{quasi-local} policies for multiplexed quantum repeater chains. In fully-local policies, nodes make decisions based only on knowledge of their own states. In our quasi-local policies, nodes have increased knowledge of the state of the repeater chain, but not necessarily full, global knowledge. Our policies exploit the observation that for most decisions the nodes have to make, they only need to have information about the connected region of the chain they belong to, and not the entire chain. In this way, we not only obtain improved performance over local policies, but we reduce the classical communication (CC) costs inherent to global-knowledge policies. Our policies also outperform the well-known and widely studied nested purification and doubling swapping policy in practically relevant parameter regimes. We also carefully examine the role of entanglement distillation. Via analytical and numerical results, we identify the parameter regimes in which distillation makes sense and is useful. In these regimes, we also address the question: "Should we distill before swapping, or vice versa?" Finally, to provide further practical guidance, we propose an experimental implementation of a multiplexing-based repeater chain, and experimentally demonstrate the key element, a high-dimensional biphoton frequency comb. We then evaluate the anticipated performance of our multiplexing-based policies in such a real-world network through simulation results for two concrete memory platforms, namely rare-earth ions and diamond vacancies.