Toward City-Scale Quantum Timing: Wireless Synchronization via Quantum Hubs

This paper presents a novel wireless quantum synchronization framework tailored for city-scale deployment using entangled photon pairs and passive corner cube retroreflector (CCR) arrays. A centralized quantum hub, equipped with either a bulk or integrated nonlinear entangled-photon source, emits photon pairs and directs one photon toward a target device while routing its twin to a local reference unit. The target, equipped with a planar CCR array, reflects the incoming photon without active circuitry, enabling secure round-trip quantum measurements for sub-nanosecond synchronization and localization. We develop a comprehensive analytical model that captures key physical-layer phenomena, including Gaussian beam spread, spatial misalignment, atmospheric turbulence, and probabilistic photon generation. A closed-form expression is derived for the single-photon detection probability under Gamma-Gamma fading, and its distribution is used to model photon arrival events and synchronization error. Moreover, we analyze the impact of background photons, SPAD detector jitter, and quantum generation randomness on synchronization accuracy and outage probability. Simulation results confirm the accuracy of the analytical models and reveal key trade-offs among beam waist, CCR array size, and background light. The proposed architecture offers a low-power, infrastructure-free solution for secure timing in next-generation smart cities.