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

Internet publication

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 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, 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.

Authors: Ashby-Pickering, R; Barr, AJ; Wierzchucka, A

• Publication status: Published
• Peer review status: Not peer reviewed
• Publication date: 2022-09-28
• Language: English