Picosecond Wireless Synchronization with Entangled Photons via Grid-Based Quantum Coverage in Indoor Optical Systems

Abstract: In this paper, we propose a novel entanglement-assisted synchronization framework for indoor optical wireless systems based on grid-based beam steering. A central transmitter equipped with a spontaneous parametric down-conversion (SPDC) source emits time-energy entangled photon pairs, directing user photons toward spatially defined grids based on estimated user positions, while retaining reference photons for timestamping. The room is partitioned into multiple beam-aligned regions, and photon reception probability is analytically modeled using local coordinate transformations and Gaussian beam optics. To address the inherent sparsity and randomness of photon detection, we develop a robust two-stage synchronization algorithm that performs sparse bit-pattern matching and timestamp averaging to estimate timing offsets. Monte Carlo simulations are then performed to evaluate the impact of synchronization duration, grid resolution, and photon-pair generation rate on synchronization accuracy. Results show that finer grid configurations and optimal photon-pair rates significantly reduce synchronization error, achieving sub-10 ps timing accuracy within 1 ms of synchronization time. The proposed approach enables scalable, high-precision quantum synchronization in wireless indoor environments, laying the groundwork for future joint quantum communication, sensing, and positioning systems.