Asynchronous Multi-photon Interference for Quantum Networks

Advanced quantum communication protocols require high-visibility quantum interference between photons generated at distant nodes, which places stringent demands on optical synchronization. Conventionally, synchronization of optical wave packets relies on pulsed sources and precise optical path stabilization. An alternative approach employs continuous-wave (CW) photon-pair sources, where temporal indistinguishability is enforced by post-selecting detection events within a coincidence window $\tau_w$ shorter than the photon coherence time $T_c$. Despite its conceptual simplicity, the quantitative relation between relevant time scales, achievable interference visibility, and usable multi-photon rates has remained unclear. Here, we develop in detail and experimentally validate a theoretical framework that quantitatively describes time-resolved multi-photon interference in the CW regime. We explicitly incorporate detector timing jitter, photon coherence time, and temporal post-selection. The model is verified using four-photon Hong-Ou-Mandel interference measurements. Based on this validated framework, we determine the coincidence window that maximizes usable four-photon rates for a target visibility. Finally, we compare CW and pulsed SPDC sources under equivalent indistinguishability constraints and show that CW operation can achieve comparable rates while relaxing optical synchronization requirements.