There have been some very nice discussions recently centered around the question of whether gravity and the geometry and topology of the classical world we see about us, could be phenomena which emerge in the low-energy limits of a more fundamental microscopic theory.
Among these, @Tim Van Beek's reply to the question on "How the topology of space [time] arises from more fundamental notions" contains the following description of the Reeh-Schlieder theorem:
It describes "action at a distance" in a mathematically precise way. According to the Reeh-Schlieder theorem there are correlations in the vacuum state between measurements at an arbitrary distance. The point is: The proof of the Reeh-Schlieder theorem is independent of any axiom describing causality, showing that quantum entanglement effects do not violate Einstein causality, and don't depend on the precise notion of causality. Therefore a change in spacetime topology in order to explain quantum entanglement effects won't work.
which is also preceded with an appropriate note of caution, saying that the above paragraph:
... describes an aspect of axiomatic quantum field theory which may become obsolete in the future with the development of a more complete theory.
I had a bias against AQFT as being too abstract an obtuse branch of study to be of any practical use. However, in light of the possibility (recently discussed on physics.SE) that classical geometry arises due to the entanglement between the degrees of freedom of some quantum many-body system (see Swingle's paper on Entanglement Renormalization and Holography) the content of the Rees-Schilder theorem begins to seem quite profound and far-sighted.
The question therefore is: Does the Rees-Schlieder theorem provide support for the idea of building space-time from quantum entanglement? or am I jumping the gun in presuming their is some connection between what the theorem says and the work of Vidal, Evenbly, Swingle and others on "holographic entanglement"?