The Reeh–Schlieder theorem is a result of relativistic local quantum field theory, stating that the vacuum is a cyclic vector for the field algebra of any open set in Minkowski space. It was published by Helmut Reeh and Siegfried Schlieder (1918-2003) in 1961.
One may remark the states created by applying elements of the local algebra
to the vacuum state are, therefore, not strictly localized in its region
This theorem is also cited in connection with quantum entanglement. But it is subject to some doubt whether the Reeh–Schlieder theorem can usefully be seen as the quantum field theory analog to quantum entanglement, since the exponentially-increasing energy needed for long range actions will prohibit any macroscopic effects. However, B.Reznik showed that vacuum entanglement can be distilled into EPR pairs used in quantum information tasks.