Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
Rachel Ashby-Pickering, A. J. Barr, Agnieszka Wierzchucka
Abstract
A bstract 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 → $$ {W}^{+}\overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , $$ t\overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , 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.