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⁺t, tt, and those from the Higgs boson decays H→ WW^* and H→ ZZ^*. Measurements are proposed for entanglement detection and Bell inequality violation in bipartite systems.