Discrete outcome quantum sensor networks

We model a quantum sensor network using techniques from quantum state discrimination. The interaction between a qubit detector and the environment is described by a unitary operator, and we will assume that at most one detector does interact. The task is to determine which one does or if none do. This involves choosing an initial state of the detectors and a measurement. We consider global measurements in which all detectors are measured simultaneously. We find that an entangled initial state can improve the detection probability, but this advantage decreases as the number of detectors increases.