Relative entanglement entropy for widely separated regions in curved spacetime

TL;DR

This paper establishes an exponential decay bound on the relative entanglement entropy between two distant regions in a curved spacetime, linking quantum entanglement limits to geometric and physical parameters.

Contribution

It provides the first explicit upper bound on the relative entanglement entropy for a massive Dirac-Majorana field in curved spacetime, incorporating effects of spatial curvature and mass.

Findings

Entanglement entropy decays exponentially with distance.

Decay rate depends on Compton wavelength and scalar curvature.

Vacuum entanglement cannot enable classical bit teleportation over large distances in curved space.

Abstract

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 $dist (A, B)$, at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation 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 wave length or greater.