  Quantum nonlocality without entanglement (Q-NWE) encapsulates nonlocal
behavior of multipartite product states as they may entail global operation for
optimal decoding of the classical information encoded within. Here we show that
the phenomena of NWE is not specific to quantum theory only, rather a class of
generalized probabilistic theories can exhibit such behavior. In fact several
manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local
discrimination, notion of separable but locally unimplementable measurement
arise generically in operational theories other than quantum theory. We propose
a framework to compare the strength of NWE in different theories and show that
such behavior in quantum theory is limited, suggesting a specific topological
feature of quantum theory, namely, the continuity of state space structure. Our
work adds profound foundational appeal to the study of NWE phenomena along with
its information theoretic relevance.
