Entanglement Harvesting and Quantum Discord of Alpha Vacua in de Sitter Space

Abstract

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 static 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.

32 pages, 19 figures, Typos corrected, Matched with the version accepted by JHEP; v4. some typos around (2.41) are corrected to avoid confusion

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