Optimal operation ordering outside the proven parameter regime

Determine the optimal ordering of entanglement purification and swapping along a single quantum-network path when the edge fidelities or swapping-success probabilities fall outside the parameter regime for which purify-then-swap optimality has been proved.

Background

The paper compares two canonical schedules for combining Werner-state entanglement: purify-then-swap (PtS), which purifies physical edges before swapping them along a path, and swap-then-purify (StP), which first reduces routes by swapping and then purifies the resulting states. The authors explain that PtS is provably optimal along a given path under the conditions that every edge fidelity satisfies fe≥0.7f_e\ge 0.7 and every swap succeeds with probability at most $0.818$.

The cited guarantee does not cover parameter values outside that range, and the paper explicitly states that the optimal ordering remains unresolved even for a single path. This is distinct from the paper’s network-wide results, which show that no fixed canonical ordering is generally optimal once multiple routes are available.

References

Outside that range the optimal ordering is unproven even along a single path.

— One-shot Routing in Quantum Networks  (2609.29752 - Lavi et al., 24 Sep 2026) in Section 3, subsection “Scheduling” (paragraph beginning “One partial guarantee exists.”)

This observed reduction does not prove that screening preserves the optimal action outside the tested states.

— AquaMend: Minimal Re-probing and Conditional Rollback for Latent-Belief Failures in Embodied Agents  (2609.28973 - Liu et al., 24 Sep 2026) in Appendix 'Completed paired physical evaluation', paragraph 'Decision timing and coverage'