# Reeh–Schlieder theorem

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$\mathcal{A}(\mathcal{O})$
to the vacuum state are, therefore, not strictly localized in its region $\mathcal{O}$, but can in effect approximate any state. In a quantitative sense, the localization remains true. The long range effects of the operators of the local algebra will diminish rapidly with distance, as seen by the cluster properties of the Wightman functions. And with increasing distance, creating a unit vector localized outside requires operators of ever increasing operator norm.