Architectural Trade-Offs in Distributed Quantum Repeaters: Distillation Scheduling Under Memory Coherence Constraints

Long-distance quantum communication relies on quantum repeaters to overcome exponential photon attenuation in optical fiber links. Connecting adjacent elementary links requires entanglement swapping, while preserving end-to-end fidelity above cryptographic thresholds requires entanglement distillation. In physical hardware, however, quantum memories suffer from decoherence during the classical round-trip signaling intervals mandated by distillation protocols. This work investigates the architectural trade-off between two core operational strategies in a dual-hop quantum repeater: Strategy A (Purify-then-Swap), wherein elementary links are distilled prior to swapping, and Strategy B (Swap-then-Purify), wherein raw links are swapped immediately and distillation is executed end-to-end. We develop an analytical and numerical simulation pipeline tracking Werner state transformations under bilateral CNOT purification and non-Markovian memory dephasing. Our results reveal an exact crossover tipping point at tau_RTT / T_2 ≈ 0.018: whenever classical signaling delay exceeds 1.8% of the memory coherence time, Strategy B strictly outperforms Strategy A. Furthermore, we show that local purification becomes actively destructive beyond tau_RTT / T_2 ≈ 0.070, delivering fidelities inferior to unpurified swapping. Finally, we establish the minimum hardware boundary, showing that raw elementary links must achieve F_init >= 0.880 for single-round purification to cross the threshold for secret key distillation (F > 0.810).