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

TL;DR

This work addresses the challenge of achieving secure, sub-nanosecond timing in urban environments without relying on terrestrial infrastructure. It introduces a city-scale wireless quantum synchronization framework that uses a centralized hub to distribute entangled photon pairs to passive targets equipped with a planar CCR array, enabling two-way timing via coincidence measurements. The authors develop a comprehensive model that captures Gaussian beam propagation, spatial misalignment, Gamma-Gamma atmospheric fading, and detector jitter, deriving closed-form expressions for single-photon reception probabilities, synchronization error, and outage probability, then validate these with Monte Carlo simulations. The results reveal clear design trade-offs among beam waist, CCR array density, and background light, and demonstrate the potential for secure, low-power quantum timing across smart-city deployments, including daytime operation with robust background suppression. This framework paves the way for infrastructure-free quantum timing and positioning in urban networks, leveraging passive remote optics and centralized quantum processing to achieve scalable, high-precision synchronization.

Abstract

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 emits entangled photons, directing one toward a target device and the other toward 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.

Figures (8)

• Figure 1: Conceptual illustration of a city-scale quantum synchronization infrastructure enabled by distributed quantum hubs. These hubs wirelessly synchronize and localize mobile and static devices (e.g., vehicles, UAVs, and sensors) across smart city environments using entanglement-assisted timing protocols. The architecture supports secure, infrastructure-free geolocation and sub-nanosecond synchronization across urban areas.
• Figure 2: (a) System-level diagram of the proposed entanglement-based synchronization setup. A central quantum hub generates entangled photon pairs, directing one photon toward a passive CCR on the target and the other to a local time reference. The CCR reflects the incoming photon along the original path, allowing the hub to capture both the direct and reflected photons for coincidence-based timing analysis. (b) Geometry of the planar CCR array at the target side.
• Figure 3: Grid-based acquisition process around the initial position estimate $\mathbf{r}_{\mathrm{dev}} = (x_{\mathrm{dev}}, y_{\mathrm{dev}})$ of the CCR array center. The true target location is assumed to be at the origin $(0,0)$. The $x$--$y$ plane is divided into $N_{\mathrm{gr}} = N_{x}^{\mathrm{gr}} \times N_{y}^{\mathrm{gr}}$ cells, each centered at $\mathbf{p}(j_x, j_y) = \mathbf{r}_{\mathrm{dev}} + \mathbf{p}'(j_x, j_y)$. A Gaussian beam is sequentially directed to each cell for entangled photon probing and reflection detection.
• Figure 4: Analytical and simulation results for the distribution $\mathbb{P}(N_{\mathrm{sig}})$ under different beam waist values: (a) $w_z = 25\,\mathrm{cm}$, (b) $w_z = 50\,\mathrm{cm}$, (c) $w_z = 75\,\mathrm{cm}$, (d) $w_z = 100\,\mathrm{cm}$. Analytical model from Proposition \ref{['prop:N_sig']} is validated via Monte Carlo simulations.
• Figure 5: Outage probability and synchronization timing error versus spatial uncertainty $\sigma_p$. Analytical results closely match Monte Carlo simulations.

Theorems & Definitions (7)

• Remark 1
• Proposition 1
• Remark 2
• Proposition 2
• Remark 3
• Proposition 3
• Proposition 4