Quantum relative capacity loss for online path–wavelength allocation in dynamic entanglement distribution networks

Entanglement distribution networks (EDNs) require online assignment of limited wavelength resources under probabilistic entanglement generation and dynamic service arrivals. Classical residual-capacity metrics used in wavelength assignment cannot directly represent whether a quantum service request obtains a valid end-to-end entangled pair within its holding window. This paper establishes a time-slotted network-layer abstraction that maps entanglement generation, swapping, quality filtering, and purification into an end-to-end success probability. Based on this success-event serviceability measure, we propose quantum relative capacity loss (QRCL) for online path–wavelength allocation. QRCL combines threshold-based filtering with relative serviceability-loss minimization. Simulations over multiple representative topologies show that QRCL achieves robust best or near-best request success rates while maintaining competitive fairness, delay, and millisecond-level decision time.