  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.
