Distributed quantum sensing with mode-entangled spin-squeezed atomic states

Quantum sensors are used for precision timekeeping, field sensing and quantum communication^1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations^4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network⁹. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes¹⁰. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.