Superoscillations underlying remote state preparation for relativistic fields

We present a physical (gedanken) implementation of a generalized remote state preparation of relativistic quantum field states for an arbitrary set of observers. The prepared states are created in regions that are outside the future light-cone of the generating region. The mechanism, which is based on utilizing the vacuum state of a relativistic quantum field as a resource, sheds light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.