Probing quantum entanglement with Generalized Parton Distributions at the Electron-Ion Collider

TL;DR

The paper develops a GPD-based framework to probe quantum entanglement in exclusive $q\bar{q}$ production during DIS and UPCs, focusing on how the real and imaginary parts of GPD amplitudes generate entanglement, Bell nonlocality, and quantum-resource magic. By computing spin-density matrices for longitudinal and transverse photons within collinear factorization and using the Goloskokov-Kroll GPD model, it maps where entanglement persists and where Bell nonlocality can emerge across ($z$, $k_\perp$) space, including heavy flavors $s,c,b$. A striking prediction is the large transverse polarization of massive $q\bar{q}$ pairs in low-energy runs, reaching up to ~80% for strange and charm and ~50% for bottom, arising from interference between amplitude parts. Numerically, entanglement is robust across much of the kinematic range, while Bell nonlocality and magic show richer, more nuanced patterns; these results offer a pathway to test quantum-information concepts in collider environments at the EIC and to explore how such nonclassical features might survive through hadronization and be observed via heavy-baryon decays.

Abstract

Within the collinear factorization framework based on Generalized Parton Distributions (GPDs), we calculate the spin density matrix of exclusively produced quark and antiquark pairs $u\bar{u}$, $d\bar{d}$, $s\bar{s}$, $c\bar{c}$, $b\bar{b}$ in Deep Inelastic Scattering. The presence of both real and imaginary parts in the GPD amplitudes leads to a rich pattern of entanglement between the quark and the antiquark. We map out kinematical regions where the pairs exhibit entanglement, Bell nonlocality and non-stabilizerness (`magic'). We also predict that massive quarks and antiquarks are transversely polarized, similar to the well-known transverse hyperon polarization in unpolarized collisions. In strangeness, charm and bottom productions, the polarization can reach 50-80% in certain kinematic regions in the low-energy runs of the Electron-Ion Collider.

Figures (8)

• Figure 1: $q\bar{q}$ production in the photon-Pomeron CM frame at $\phi=0$. Left: $z>\frac{1}{2}$, Right: $z<\frac{1}{2}$.
• Figure 2: Stabilizer Rényi entropy $M_2^L$ (\ref{['longre']}) of a massive quark-antiquark pair produced by a longitudinally polarized virtual photon. $M_2^L$ is suppressed in the blue regions where the pair forms the Bell states (\ref{['bell1']}), (\ref{['bell2']}), (\ref{['bell3']}).
• Figure 3: Upper panels: Polarization of the strange (left) and antistrange (right) quarks in UPC at $W=30$ GeV, $Q=0$ GeV. Lower panels: Polarization of the charm (left) and anticharm (right) quarks in the same process. Here and in all the plots below, $k_\perp$ in the vertical axis is in units of GeV.
• Figure 4: Left hand side of (\ref{['max']}) in UPC at $W=500$ GeV, $Q=0$. Left: $u\bar{u}$ pair, Middle: $c\bar{c}$ pair, Right: $b\bar{b}$ pair. The pairs are almost maximally entangled $\Delta_2^T\approx 2$ in the red region.
• Figure 5: Left hand side (\ref{['max']}) in DIS at $Q=10$ GeV, $W=30$ GeV. Left: $u\bar{u}$ pair, Middle: $s\bar{s}$ pair, Right: $b\bar{b}$ pair. The pair is not entangled in the white region.