Entanglement and scattering in quantum electrodynamics: S-matrix information from an entangled spectator particle

Abstract

We consider a general quantum field relativistic scattering involving two half spin fermions, A and B, which are initially entangled with another fermion C that does not participate in the scattering dynamics. We construct general expressions for the reduced spin matrices for the out-state considering a general tripartite spin-entangled state. In particular we study an inelastic QED process at tree-level, namely e − e + → µ − µ + and a half spin fermion C as an spectator particle which can be entangled to the AB system in the following ways: W state, GHZ state, |A α ⊗ |Ψ ± BC and |A α ⊗ |Φ ± BC, where {|Ψ ± , |Φ ± } are the Bell basis states and |A α is a spin superposition state of system A. We calculate the von-Neumann entropy variation before and after the scattering for the particle C and show that spin measurements in C contain numerical information about the total cross section of the process. We compare the initial states W and GHZ as well as study the role played by the parameter α in the evaluation of the entropy variations and the cross section encoded in the spectator particle.

Comment on "Spin correlations in elastic $e^+ e^-$ scattering in QED"

“…Here we are interested in studying entanglement in scattering processes from QED. Recent work on this and related tests of Bell-type inequalities at colliders can be found in [19][20][21][22][23][24][25][26][27].…”