Badurek, G., Hradil, Z., Lvovsky, A., Molina-Teriza, G., Rauch, H., Rehacek, J., Vaziri, A., & Zawisky, M. (2004). 10 Maximum-Likelihood Estimation in Experimental Quantum Physics. In M. Prais & J. Rehacek (Eds.), Quantum State Estimation (pp. 373–414). Springer-Verlag. https://doi.org/10.1007/978-3-540-44481-7_10
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.