General Cramér-Rao bound for parameter estimation using Gaussian multimode quantum resources

Multimode Gaussian quantum light, which includes coherent light, but also all kinds of multimode squeezed and/or multipartite quadrature entangled states, is a very general and powerful quantum resource that is now currently produced in various laboratories in the world, and is successfully used in various applications to quantum information processing. In contrast to non-classical states based on the manipulation of Fock states (such as the NOON states), such quantum light can be produced with very high values of the mean photon number N (up to 10¹⁶). It is therefore a very good candidate for quantum metrology purposes, i.e. to improve as much as possible the estimation of a parameter p that is encoded on the spatio-temporal variation of a light beam, as all the limits in parameter estimation scale with some inverse power of N.