Studying Maximal Entanglement and Bell Nonlocality at an Electron-Ion Collider

Abstract

In this paper, we propose to test quantum entanglement and Bell nonlocality at an Electron-Ion Collider (EIC). By computing the spin correlations in quark-antiquark pairs produced via photon-gluon fusion, we find that longitudinally polarized photons produce maximal entanglement at leading order, while transversely polarized photons generate significant entanglement near the threshold and in the ultra-relativistic regime. Compared to hadron colliders, the EIC provides a cleaner experimental environment for measuring entanglement through the $γ^\ast g \to q\bar{q}$ channel, offering a strong signal and a promising avenue to verify Bell nonlocality. This study extends entanglement measurements to the EIC, presenting new opportunities to explore the interplay of quantum information phenomena and hadronic physics in the EIC era.

Figures (3)

• Figure 1: Illustration of the helicity basis vectors ${\hat{\vb n}, \hat{\vb r}, \hat{\vb k}}$ and the unit vector $\hat{\vb p}$ of the photon momentum, defined in the center-of-mass frame, alongside the unit vectors $\hat{\vb l}_+$, $\hat{\vb l}_-$ of the fermionic decay products (indicating momentum directions), shown in their respective parent particle rest frames, where the spin of each particle and the decay spin density matrices are also conventionally defined. Note that $\hat{\vb l}_+$ and $\hat{\vb l}_-$ are measured in the $\{\hat{\mathbf{n}}, \hat{\mathbf{k}}, \hat{\mathbf{r}}\}$ coordinate system within their respective quark rest frames.
• Figure 2: Examples of spin configurations of the longitudinal and transverse photon channels at $\theta =\frac{\pi}{2}$ ($z = 0$) and the production threshold $\beta = 0$.
• Figure 3: Density plots of the concurrence for the transverse polarized photon contribution at EIC as functions of quark velocity $\beta$ and the scalar projection $z$ at given values of the virtuality parameter $\alpha$, where solid lines and dashed lines indicate the boundaries for entanglement ($\mathcal{C}[\rho_T]=0$) and Bell nonlocality ($\mathcal{N}[\rho_T]=0$), respectively.