  Entanglement is a unique resource for quantum-enhanced applications. When
employed in sensing, shared entanglement between distributed quantum sensors
enables a substantial gain in the measurement sensitivity in estimating global
parameters of the quantum sensor network. Loss incurred in the distribution of
entanglement, however, quickly dissipates the measurement-sensitivity advantage
enjoyed by the entangled quantum sensors over sensors supplied with local
quantum resources. Here, we present a viable approach to overcome the
entanglement-distribution loss and show that the measurement sensitivity
enabled by entangled quantum sensors beat that afforded by the optimum local
resource. Our approach relies on noiseless linear amplifiers (NLAs) to serve as
quantum repeaters. We show that unlike the outstanding challenge of building
quantum repeaters to suppress the repeaterless bound for quantum key
distribution, NLA-based quantum repeaters for distributed quantum sensing are
realizable by available technology. As such, distributed quantum sensing would
become the first application instance that benefits from quantum repeaters.
