Advantages of Global Entanglement-Distillation Policies in Quantum Repeater Chains

Quantum repeaters are essential for achieving long-distance quantum communication due to photon loss, which grows exponentially with the channel distance. Current quantum repeater generations use entanglement distillation protocols, where the decision of when to perform distillation depends on either local or global knowledge. Recent approaches for quantum repeaters, such as Mantri et al. (arXiv:2409.06152), consider using deterministic local decision policies for entanglement distillation. We ask whether global deterministic policies outperform local ones in terms of communication rate. We simulate equidistant repeater chains, assisted by two-way classical communication, and compare local and global policies for distillation decisions, spanning large distances and varying network and hardware parameters. Our findings show that global deterministic policies consistently outperform these local ones, and in some cases, determine whether secret communication is possible. For large repeater chains ($N>512$), global policies improve SKR by two orders of magnitude. These results suggest that local distillation decisions in quantum repeater chains may not be optimal, and may inform future protocol design.