Variation of entanglement entropy in scattering process

Abstract

Editor: M. CvetičIn a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states, i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.

Relativistic effect of entanglement in fermion-fermion scattering

“…From the values of A and σ |ini , we can further confirm the conclusion in Ref. [6,11] that the change in entanglement entropy of scattering particles in a weak coupling theory is proportional to cross section. Finally, the leading perturbative contribution of the change in entanglement entropy of scattering particles is…”

“…where the coefficients satisfy σ 1 ,σ 2 a σ 1 σ 2 a † σ 1 σ 2 = 1. The final state is determined by the initial state and the S matrix [6],…”

“…In this paper, using the perturbative method in Refs. [4,6], we also study the entanglement for spin degrees of freedom of particles in the fermion-fermion scattering process with a weak coupling. It is convenient to study an elastic scattering in two-particle Fock space, where incoming and outgoing particles can be regarded as asymptotically free particles.…”

Evaluation of entanglement entropy in high energy elastic scattering

“…In Ref. [1] the entanglement in momentum Hilbert space in scattering process has been studied, and the entanglement entropy of the final state of two particles has been calculated in weak coupling perturbation by applying the method developed by Ref. [2] for momentum space entanglement.…”

“…However there is a problem of divergence in the entanglement entropy, which is caused by the infinite volume of the momentum Hilbert space in Refs, [1,3]. Indeed the formula in Ref.…”