Quantum tomography of helicity states for general scattering processes
- URL: http://arxiv.org/abs/2310.10838v1
- Date: Mon, 16 Oct 2023 21:23:42 GMT
- Title: Quantum tomography of helicity states for general scattering processes
- Authors: Alexander Bernal
- Abstract summary: Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics.
We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
- Score: 65.268245109828
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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