# Relative entanglement entropy for widely separated regions in curved spacetime

#### Autoren: Stefan Hollands, Onirban Islam, Ko Sanders (2018)

We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions $$A$$ and $$B$$ in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in $$\mathrm{dist}(A,B)$$ at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation of our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from $$A$$ to $$B$$ if their distance is of the order of the maximum of the curvature radius and the Compton wavelength or greater.

Zeitschrift:
Journal of Mathematical Physics
Band:
59

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