Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles

• URL: http://arxiv.org/abs/2209.13990v3
• Date: Tue, 18 Apr 2023 15:29:07 GMT
• Title: Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
• Authors: Rachel Ashby-Pickering, Alan J. Barr, Agnieszka Wierzchucka
• Abstract summary: The method is based on a Bloch parameterisation of the $d$-dimensional generalised Gell-Mann representation of $rho$. The Wigner $P$ and $Q$ symbols are calculated for the cases of spin-half, spin-one, and spin-3/2 systems. The methods are used to examine Monte Carlo simulations of $pp$ collisions for bipartite systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A rather general method for determining the spin density matrix of a multi-particle system from angular decay data is presented. The method is based on a Bloch parameterisation of the $d$-dimensional generalised Gell-Mann representation of $\rho$ and exploits the associated Wigner- and Weyl-transforms on the sphere. Each parameter of a (possibly multipartite) spin density matrix can be measured from a simple average over an appropriate set of experimental angular decay distributions. The general procedures for both projective and non-projective decays are described, and the Wigner $P$ and $Q$ symbols calculated for the cases of spin-half, spin-one, and spin-3/2 systems. The methods are used to examine Monte Carlo simulations of $pp$ collisions for bipartite systems: $pp\rightarrow W^+W^-$, $pp\rightarrow ZZ$, $pp\rightarrow ZW^+$, $pp\rightarrow W^+\bar{t}$, $t\bar{t}$, and those from the Higgs boson decays $H\rightarrow WW^{*}$ and $H\rightarrow ZZ^*$. Measurements are proposed for entanglement detection, exchange symmetry detection and Bell inequality violation in bipartite systems.

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