  We study different techniques that allow us to gain complete knowledge about
an unknown quantum state, e.g. to perform full tomography of this state. We
focus on two apparently simple cases, full tomography of one and two qubit
systems. We analyze and compare those techniques according to two figures of
merit. Our first criterion is the minimisation of the redundancy of the data
acquired during the tomographic process. In the case of two-qubits tomography,
we also analyze this process from the point of view of factorisability, so to
say we analyze the possibility to realise the tomographic process through local
operations and classical communications between local observers. This brings us
naturally to study the possibility to factorize the (discrete) Wigner
distribution of a composite system into the product of local Wigner
distributions. The discrete Heisenberg-Weyl group is an essential ingredient of
our approach. Possible extensions of our results to higher dimensions are
discussed in the last section and in the conclusions.
