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Quantum tomography of helicity states for general scattering processes

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arxiv 2310.10838 v2 pith:O45WXZH7 submitted 2023-10-16 hep-ph hep-thquant-ph

Quantum tomography of helicity states for general scattering processes

classification hep-ph hep-thquant-ph
keywords quantumangularcomputegeneralhelicitymatrixphysicsscattering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Quantum tomography has become an indispensable tool in order to compute the density matrix $\rho$ 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 $\rho$ 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 $\Gamma$. 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.

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Cited by 4 Pith papers

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