Abstract
Quantum tomography has become an indispensable tool in order to compute the density matrix ρ of quantum systems in Physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in High-Energy Particle Physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of ρ over the irreducible tensor operators {T^L_M} and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of both the normalised differential cross section and the generalised production matrix Γ. Finally, we re-derive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain in addition simple analytical expressions for the Wigner P and Q symbols.