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

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 ρ 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 → W⁺W⁻, pp → ZZ, pp → ZW⁺, pp →$W^{+}\overline{t}$, $t\overline{t}$, and those from the Higgs boson decays H → WW^* and H → ZZ^*. Measurements are proposed for entanglement detection, exchange symmetry detection and Bell inequality violation in bipartite systems.