Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
| Autor: | Ashby-Pickering, Rachel, Barr, Alan J., Wierzchucka, Agnieszka |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | JHEP 05 (2023) 020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP05(2023)020 |
| Popis: | 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. Comment: v3: removal of bias due to MC generator selections resulted in a correction to Figure 8, and removal of Figure 9, and removal of statements related to expecting to observe Bell violation in WZ systems at the LHC. Additional factors of 1/2 added to eqns 5.21 and 5.22 to describe the symmetrisation procedures |
| Databáze: | arXiv |
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