 The Reeh-Schlieder theorem (1961) is a central result in AQFT. It asserts that acting on the vacuum state \(\Omega\) with elements of the von Neumann observable algebra \(R(O)\) for open space-time region \(O\), one can approximate as closely as one likes any state in Hilbertspace \(\mathcal{H}\), in particular one that is very different from the vacuum in some space-like separated region \(O'\). The Reeh-Schlieder theorem is thus exploiting long distance correlations of the vacuum. Or one can express the result by saying that local measurements do not allow for a distinction between an N-particle state and the vacuum state. Redhead’s (1995a) take on the Reeh-Schlieder theorem is that local measurements can never decide whether one observes an N-particle state, since a projection operator \(P_{\Psi}\) which corresponds to an N-particle state \(\Psi\) can never be an element of a local algebra \(R(O)\). Clifton &amp; Halvorson (2001) discuss what this means for the issue of entanglement. Halvorson (2001) shows that an alternative “Newton-Wigner” localization scheme fails to evade the problem of localization posed by the Reeh-Schlieder theorem. 