The Reeh–Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961.
can be approximated to arbitrary precision by acting on the vacuum with an operator selected from the local algebra, even for
More precisely, 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.
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, Benni Reznik showed that vacuum entanglement can be distilled into EPR pairs used in quantum information tasks.
[3] If some finite number N of space-like separated regions is chosen, the multipartite entanglement can be analyzed in the typical quantum information setting of N abstract quantum systems, each with a Hilbert space possessing a countable basis, and the corresponding structure has been called superentanglement.