Observable bound for Gaussian illumination

We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes discrimination error between presence and absence of a low-reflectivity target using states. The are achieved with mode-by-mode measurements. In quantum regime two-mode squeezed vacuum state, our receiver outperforms other feasible receivers whereas it cannot approach Chernoff bound. corresponding be implemented heterodyne detections due additional noise. classical thermal photon number difference measurement approaches its bound regardless signal mean number, while asymptotically in limit huge idler number.