Star product, discrete Wigner functions, and spin-system tomograms

We develop the star-product formalism for spin states and consider different methods for constructing operator systems forming sets of dequantizers and quantizers, establishing a relation between them. We study the physical meaning of the operator symbols related to them. Quantum tomograms can also serve as operator symbols. We show that the possibility to express discrete Wigner functions in terms of measurable quantities follows because these functions can be related to quantum tomograms. We investigate the physical meaning of tomograms and spin-system tomogram symbols, which they acquire in the framework of the star-product formalism. We study the structure of the sum kernels, which can be used to express the operator symbols, calculated using different sets of dequantizers and also arising in calculating the star product of operator symbols, in terms of one another.