Entanglement Entropy is Elastic Cross Section

TL;DR

This paper establishes universal, dynamics-independent relations between entanglement entropy and elastic cross sections in high-energy particle scattering, revealing a novel area law for entanglement in two-body systems.

Contribution

It introduces a universal relation linking entanglement entropy to elastic cross sections, valid at all coupling orders, and proposes a new area law for two-body quantum systems.

Findings

Entanglement entropy is proportional to elastic cross section.

Relations hold independently of quantum field theory dynamics.

A new area law for entanglement entropy is proposed.

Abstract

We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the elastic cross section, which is the primary observable for high energy particle scattering, by employing a careful formulation of wave packets for the incoming particles. For 2-to-2 elastic scattering with no initial entanglement and subdividing the system along particle labels, we show that both the R\'enyi and Tsallis entropies in the final states are directly proportional to the elastic cross section in unit of the transverse size for the initial wave packets, which is then interpreted as the elastic scattering probability. The relations do not depend on the underlying dynamics of the quantum field theory and are valid to all orders in coupling strengths. Furthermore, computing quantum correlations between momentum and non-kinematic data leads to entanglement entropies expressed as various semi-inclusive elastic cross sections. Our result gives rise to a novel ``area law'' for entanglement entropy in a two-body system.