Relation between quantum illumination and quantum parameter estimation

Quantum illumination leverages entangled lights to detect the presence of low-reflectivity objects within a thermal environment. In a related vein, quantum parameter estimation utilizes nonclassical probes to precisely determine unknown system parameters. Although both fields have been studied extensively, their performances have traditionally been assessed using different figures of merit: signal-to-noise ratio for QI and quantum Fisher information for parameter estimation. In this paper, we reveal the intrinsic connection between these two measures in the context of target detection, thereby providing explicit operational criteria for identifying optimal measurements. We further apply this relationship to various target detection protocols that employ exotic non-Gaussian states derived from coherent states and two-mode squeezed vacuum states.