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 $e^{-}{e}^{+}\to {\mu }^{-}{\mu }^{+}$ 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, $|{\text{A}}^{\alpha }⟩\otimes |{\Psi }^{\pm }{⟩}_{\text{BC}}$ and $|{\text{A}}^{\alpha }⟩\otimes |{\Phi }^{\pm }{⟩}_{\text{BC}}$, where $\{|{\Psi }^{\pm }⟩,|{\Phi }^{\pm }⟩\}$ are the Bell basis states and $|{\text{A}}^{\alpha }⟩$ 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 $\alpha$ in the evaluation of the entropy variations and the cross section encoded in the spectator particle.

arXiv comment12 pages, 10 figures

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