Reeh-Schlieder approximation for coherent states

We present an explicit, fully local Reeh-Schlieder approximation scheme for coherent states of a free scalar field. For any bounded region $\mathcal{U}$, we construct a one-parameter family of bounded operators $\hat{A}_\zeta$ localized in the causal complement of $\mathcal{U}$. The action of $\hat{A}_\zeta$ on the vacuum approximates the target coherent state in the limit $\zeta \to 0$.