Entanglement of a Relativistic Field in the Vacuum State

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We discuss gedanken
experiments for measuring local and non-local observables in QFT that

respect causality, and can by used to test the entanglement between two spatially distant regions in the vacuum. It is shown that the entanglement
decays exponentially with the distance between the regions and does not vanish, in contrast to the
case of lattice models. We discuss in this respect a possible mechanism which might
explain this persistence effect, and a connection between the Reeh-Schlieder
theorem and superoscillations.