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Quantum tomography has become an indispensable tool in order to compute thedensity matrix $\rho$ of quantum systems in Physics. Recently, it has furthergained importance as a basic step to test entanglement and violation of Bellinequalities in High-Energy Particle Physics. In this work, we present thetheoretical framework for reconstructing the helicity quantum initial state ofa general scattering process. In particular, we perform an expansion of $\rho$over the irreducible tensor operators $\{T^L_M\}$ and compute the correspondingcoefficients uniquely by averaging, under properly chosen Wigner D-matricesweights, the angular distribution data of the final particles. Besides, weprovide the explicit angular dependence of both the normalised differentialcross section and the generalised production matrix $\Gamma$. Finally, were-derive all our previous results from a quantum-information perspective usingthe Weyl-Wigner-Moyal formalism and we obtain in addition simple analyticalexpressions for the Wigner $P$ and $Q$ symbols.

Quantum tomography of helicity states for general scattering processes