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.

Journal of Mathematical Physics

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