Quantum tomography of helicity states for general scattering processes

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_M^L} 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 a novel generalization of the production matrix Γ and of the normalized differential cross section of the scattering. Finally, we rederive 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.