Quantum limits in image processing

Abstract

We determine the limit to the maximum achievable sensitivity in the estimation of a scalar parameter from the information contained in an optical image in the presence of quantum noise. This limit, based on the Cramer-Rao bound and valid for any image processing protocol, is calculated for a shot noise limited image, for a locally squeezed light, and for a single-mode squeezed light in a well-defined "noise mode". In addition, we exhibit an image processing protocol that allows us to reach the limits in the different cases.