Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories

An upper bound of the relative entanglement entropy of thermal states at an inverse temperature β of linear, massive Klein-Gordon and Dirac quantum field theories across two regions, separated by a nonzero distance d in a Cauchy hypersurface of an ultrastatic spacetime has been computed. This entanglement measure is bounded by a negative constant times ln | tanh(πd/2β)| which signifies power law decay for asymptotic d where the exponent depends on β < ∞.