Secure quantum-enhanced measurements on a network of sensors

Two-party secure quantum remote sensing (SQRS) protocols enable quantum-enhanced measure- ments at remote locations with guaranteed security against eavesdroppers. This idea can be scaled up to networks of nodes where one party can directly measure functions of parameters at the different nodes using entangled states. However, the security on such networks decreases exponentially with the number of nodes. Here we show how this problem can be overcome in a hybrid protocol that utilises both entangled and separable states to achieve quantum-enhanced measurement precision and security on networks of any size.