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. co...

An equilibrium statistical system is known to be stable if the fluctuations of global observables are normal, when their dispersions are proportional to the number of particles, or to the system volume. A general theorem is rigorously proved for the case, when an observable is a sum of linearly independent terms: The dispersion of a global observable is normal if and only if all partial dispers...