Scalable Network of Mach-Zehnder Interferometers with a Single Entangled Resource

Abstract: Distributed quantum sensing exploits entanglement to enhance the estimation of multiple parameters across a network of spatially-separated sensors, achieving sensitivities beyond the classical limit. Potential applications cover a plethora of technologies, from precision navigation to biomedical imaging and environmental monitoring. However, practical implementations are challenged by the complex optimal distribution of entanglement throughout the sensing nodes, which affects scalability and robustness. Here we demonstrate a reconfigurable network of Mach-Zehnder interferometers entangled via a single shared squeezed-vacuum resource. We achieve joint noise suppression of $4.36 \pm 0.35$ dB below the standard quantum limit at the phase-uncertainty level of $10^{-9}$. Furthermore, after full optimization in the low-intensity regime, we demonstrate a crossover from the standard quantum limit to the Heisenberg limit. The network estimates arbitrary linear combinations of phases, saturates the quantum Cramer-Rao bound in the ideal case, remains robust under realistic photon losses, and scales favorably with the number of sensors.