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

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 electron-proton scattering. The presence of both real and imaginary parts in the scattering 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.