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 $\rho$ 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: $pp\to W^{+}{W}^{-}$, $pp\to ZZ$, $pp\to Z{W}^{+}$, $pp\to W^{+}\bar{t}$, $t\bar{t}$, and those from the Higgs boson decays $H\to W{W}^{\ast }$ and $H\to Z{Z}^{\ast }$. Measurements are proposed for entanglement detection and Bell inequality violation in bipartite systems.

Comments: Corrections (factor of 2) to equations 5.21 and 5.22, and corresponding corrections to Figures 6, 7, and 8, and to Table 2. Removal of subsection 8.4