Perturbative approach to entanglement generation in QFT using the S matrix

Abstract

We compute the variation of the von Neumann (VN) entropy ΔS between the asymptotic in and out momenta modes of a real scalar field A, when elastically scattered against the modes of another scalar field B. This is done to see how the entanglement between the two fields’ momenta changes under the scattering procedure. The calculation is separated into two case studies, one where the fields’ asymptotic in states are separable, and another where they are arbitrarily entangled. We perform a perturbative calculation to one loop order in the separable case, and verify that ΔS changes in a non-trivial way when we vary the momentum of the incoming field modes and/or the coupling of the theory. Finally, also in the separable case, we show an explicit dependence between ΔS and the cross-section of the collision, consistent with perturbation theory.