  It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound
for Bell inequality) do exist in the existing structures of both quantum and
classical theory. In particular, we design an explicit example of
measure-and-prepare nonlocal (but no-signaling) channel being the realization
of nonlocal and no-signaling Popescu-Rohrlich box within the generalized
probabilistic theory of processes. Further we present a post-selection-based
spatially non-local implementation and show it does not require truly quantum
resources, hence, improving the previously known results. Interpretation and
potential (spatially non-local) simulation of this form of process nonlocality
and the protocol is discussed.
