Entanglement of back-to-back gluon pair
We investigate the polarization correlation of back-to-back gluon pairs in unpolarized $pp$ collisions and compute their density matrix. For gluon pairs produced through $q\bar{q}$ annihilation, the linear polarization correlation is sizable, even reaching unity when the final-state gluons are emitted perpendicular to the beam direction in the $q\bar{q}$ rest frame. Combining with the fact that their helicity remains maximally correlated across different scattering angle, the gluon pair system thus resides in a maximally entangled Bell state in this configuration. In contrast, for the $gg\to gg$ channel, both the helicity and linear polarization correlations are considerably suppressed, producing a separable state. Nonetheless, it still retains an appreciable linear polarization correlation of about $11\%$ at central scattering in unpolarized collisions. The linearly polarization correlation of the back-to-back gluon pair can further increase when the incoming gluons are circularly polarized. Employing the anisotropy of energy correlators, we demonstrate that the linear polarization correlation of gluon pairs can be extracted from the $\cos 2ΔΦ$ modulation.