  We apply the recently developed concept of the nucleon energy-energy
correlator (NEEC) for the gluon sector to investigate the long-range azimuthal
angular correlations in proton-proton collisions at the LHC. The spinning gluon
in these collisions will introduce a significant nonzero $\cos(2\phi)$
asymmetries in both Higgs Boson and top quark pair productions. The genesis of
the $\cos(2\phi)$ correlation lies in the intricate quantum entanglement. Owing
to the substantial $\cos(2\phi)$ effect, the NEEC observable in Higgs Boson and
$t{\bar t}$ production emerges as a pivotal avenue for delving into quantum
entanglement and scrutinizing the Bell inequality at high-energy colliders.
