Quantum tomography of helicity states for general scattering processes

TL;DR

This paper develops a theoretical framework for quantum state reconstruction of helicity states in general scattering processes, integrating quantum tomography with high-energy physics and providing explicit angular dependence formulas.

Contribution

It introduces a method to reconstruct helicity quantum states in scattering processes using tensor operator expansion and angular distribution data, bridging quantum tomography and particle physics.

Findings

Explicit formulas for angular dependence of differential cross sections.

A novel expansion of the density matrix over irreducible tensor operators.

Re-derivation of results using Weyl-Wigner-Moyal formalism with analytical Wigner symbols.

Abstract

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.