This is another long-awaited article which has appeared recently (a year after submission). It is published in a special issue of Physica Scripta devoted to 16th Central European Workshop on Quantum Optics held in May 2009 in Turku, Finland.
Article details: S.N. Filippov, V.I. Man'ko: Distances between quantum states in the tomographic-probability representation, Physica Scripta T140, 014043 (2010)
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. The tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.