Probing the onset of maximal entanglement inside the proton in diffractive DIS

TL;DR

This paper investigates the transition to maximal quantum entanglement inside the proton at high energies using diffractive deep inelastic scattering data, suggesting the proton approaches a maximally entangled state at small Bjorken x.

Contribution

It introduces a novel method to probe the onset of maximal entanglement inside the proton using existing HERA data and relates entanglement entropy to observable hadron entropy.

Findings

Data from H1 Collaboration supports the transition to maximal entanglement.

The entanglement entropy matches experimental hadron entropy data.

The study indicates the proton approaches a maximally-entangled state at small x.

Abstract

It has been proposed that at small Bjorken $x$, or equivalently at high energy, hadrons represent maximally entangled states of quarks and gluons. This conjecture is in accord with experimental data from the electron-proton collider HERA at the smallest accessible $x$. In this Letter, we propose to study the onset of the maximal entanglement inside the proton using Diffractive Deep Inelastic Scattering. It is shown that the data collected by the H1 Collaboration at HERA allows to probe the transition to the maximal entanglement regime. By relating the entanglement entropy to the entropy of final state hadrons, we find a good agreement with the H1 data using both the exact entropy formula as well as its asymptotic expansion which indicates the presence of a nearly maximally-entangled state. Finally, future opportunities at the Electron Ion Collider are discussed.