Fig. 1: Illustrative diagram and comparative advantage.

i Quantum illumination network set-up. A transmitter array sends out multiple probes {S_j} to multiple targets (or different aspects of the same target) and then stores the corresponding entangled idlers {I_j} in quantum memory marked by M. The physical parameters that need to be identified correspond to the phase {θ_j} and reflectivity {η_j} imprinted on the return state. With a single antenna to receive the returning mode R, the experimenter can conduct multi-parameter quantum estimation and hypothesis testing under the influence of background noise (marked by B). ii Discrepancy between the estimation error of QI networks and conventional QI protocols. Here, we illustrate the root-mean-square error \({\epsilon }_{\overline{\theta }}\) in estimating an average of multiple phases with reflectivity ratio η ~ 0.5, the photon numbers N_S = 0.5 and noise N_B = 32. The plot is in log scale in both x and y axis. The variable m on the x-axis represents the number of transmitters, whereas \({m}_{{{{\rm{re}}}}}\) indicates the maximum number of target’s spatial modes that can be excited. The QI network demonstrates an error scaling of \({{{\mathcal{O}}}}({m}^{-1/2})\) for \(m\le {m}_{{{{\rm{re}}}}}\), while conventional QI protocols are subject to a constant error.