Optimal Estimation Strategies for Distributed Quantum Sensing with the Vacuum Beam Guide

The proposed Vacuum Beam Guide (VBG) represents a breakthrough in quantum channel technology, providing ultra-low attenuation, broad transmission linewidth, and unprecedented quantum capacities on a continental scale. Building on this framework, we explore distributed quantum sensing as a natural and powerful application of the VBG which is relevant to many fundamental physics searches and emerging technologies. Specifically, we consider a network of spatially separated quantum sensors, which could be linked through a VBG channel, and estimate the incident angle of a weak sinusoidal signal immersed in Gaussian noise. Using a Bayesian estimation approach, we determine the optimal measurement strategies under local and collective measurement models and examine whether entangling the distributed sensors provides an advantage.  We then contrast the Bayesian framework with the traditional frequentist (Fisher information) approach. Together, these results position the VBG as an enabler of distributed quantum sensing on a continental scale, offering new pathways to improved precision limits in fundamental measurements.