Center of mass tomography for reconstructing quantum states of multipartite systems

We investigate a one random variable tomography map, describing quantum state of a multipartite system. The random variable is analogous to center of mass considered in rotated and scaled reference frames in the phase space. Starting from the star product formalism, we construct the map, investigate its properties (including the symmetry properties in respect to identical particles permutations), derive the evolution equation, and consider a multimode oscillator as an example. The physical meaning of the map is analyzed in detail