Quantum Information at the Electron-Ion Collider

TL;DR

This work analyzes entanglement and non-stabilizerness (magic) as quantum-information observables in electron–proton scattering at the Electron–Ion Collider. By examining spin-density matrices and helicity amplitudes, it demonstrates that transverse beam polarization is essential to generate entangled and non-stabilizer final states, with maximal effects in backward elastic scattering and in deep inelastic scattering where entanglement is governed by transversity PDFs $h_{1,q}(x)$. The results connect quantum information concepts to QCD spin dynamics, offering a new probe of hadron structure at high energies and suggesting pathways for quantum tomography and extended studies at future lepton–hadron colliders. The findings position the EIC as a feasible environment to generate quantum resources in high-energy processes and point to future directions, including higher-energy colliders and novel spin-readout techniques.

Abstract

We investigate quantum-information-theoretic observables in electron-proton scattering at the Electron-Ion Collider (EIC). Our analysis focuses on entanglement and magic, two complementary indicators of non-classicality in quantum states. We show that while unpolarized and longitudinally polarized beams yield unentangled separable outcomes, transverse beam polarization enables the generation of entangled and non-stabilizer states. This result holds for both elastic and deep inelastic electron-proton scattering in QED. In the deep inelastic regime, the degree of quantum correlation is governed by the transversity parton distribution functions, providing a novel perspective on spin dynamics within QCD. These results establish the EIC as a promising environment for generating entangled and non-stabilizer states in high-energy physics, and they highlight opportunities for future lepton-hadron colliders to extend such studies into new kinematic domains.

Figures (5)

• Figure 1: Elastic $e^-p$ ($e^- q$) scattering at the EIC.
• Figure 2: The concurrence and stabilizer Rényi entropy as a function of scattering angle for elastic $ep$ scattering with 100% transversely polarized beams.
• Figure 3: Concurrence of final state $eq$ pair as a function of parton level scattering angle and the transverse polarization of the quark. The transverse polarization of the electron beam is fixed to be 70%.
• Figure 4: Center value and uncertainty of the effective transverse polarization fraction of the proton carried by initial state quarks.
• Figure 5: Concurrence of $eq$ pair from DIS process at a $\sqrt{s} =20\,\rm GeV$ EIC. The kinematic limit $Q^2=x(20~{\rm GeV})^2$ corresponds to backward scattering with $\cos\theta=-1$.