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.

Figures (3)

• Figure 1: System architecture of the proposed entanglement-based indoor quantum synchronization scheme. A central ceiling-mounted transmitter emits time-energy entangled photon pairs, directing the user photon toward a spatially selected beam corresponding to the estimated user location. The beam is aligned with a specific grid region in the room, while the reference photon is time-stamped at the transmitter. The receiver structure includes a circular aperture and SPAD array aligned to detect the photon and record its arrival time for synchronization. Local $(x', y', z')$ and global $(x, y, z)$ coordinate systems are depicted for spatial modeling.
• Figure 2: Effect of synchronization sequence duration $T_{\text{seq}}$ and grid configuration on synchronization performance. (a) Probability of synchronization failure and (b) Average synchronization error versus $T_{\text{seq}}$ under different spatial grid sizes. A failure occurs when fewer than two valid detection bits are registered within the allotted duration, making offset estimation infeasible.
• Figure 3: Average synchronization error versus photon-pair generation rate $\mu_t$ for grid size $15 \times 15$ and synchronization duration $T_{\text{seq}} = 1\,\text{ms}$.