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.

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

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