10 Maximum-Likelihood Estimation in Experimental Quantum Physics

Abstract

The theory of quantum state reconstruction is illustrated here on several examples taken from modern experimental praxis. Maximum-likelihood estimation is applied to experiments on physical systems of increasing complexity, starting with a simple one-dimensional problem of quantum phase estimation, continuing with the absorption and phase neutron tomographies, further discussing quantum tomography of higher-dimensional discrete quantum systems, and closing with the homodyne tomography of an infinite dimensional system - a mode of light. All these experiments nicely demonstrate the utility of present state-of-art techniques for manipulating states of a neutron and internal as well as external states of a photon.