  The CPT invariant vacuum states of a scalar field in de Sitter space, called
$\alpha$-vacua, are not unique. We explore the $\alpha$-vacua from the quantum
information perspective by a pair of Unruh-DeWitt (UDW) detectors coupled to a
scalar field with either monopole or dipole coupling, which are in time-like
zero separation or space-like antipodal separation. The analytical form of the
reduced final state of the UDW detector is derived. We study the entanglement
harvesting and quantum discord of the reduced state, which characterize the
quantum entanglement and quantum correlation of the underlying $\alpha$-vacua,
respectively. Our results imply that the quantum entanglement gravitated by de
Sitter gravity behaves quite differently for time-like and space-like
separations. It experiences "sudden death" for the former and grows for the
latter as the measuring time or the value of $\alpha$ increases. This
demonstrates the nonlocal nature of quantum entanglement. For the quantum
discord, we find no "sudden death" behavior, and it experiences superhorizon
suppression, which explains the superhorizon decoherence in the inflationary
universe scenario. Overall, the time-like or space-like quantum entanglement
and correlation behave differently on their dependence of $\alpha$, measuring
time and spectral gaps, with details discussed in this work.
