  The Bell theorem expresses that quantum mechanics is not a local-realistic
theory, which is often interpreted as nonlocality of the nature. This result
has led to this belief that nonlocality and entanglement are the same
resources. However, this belief has been critically challenged in the
literature. Here, we reexamine the relation between nonlocality and
entanglement in light of the Brassard-Cleve-Tapp (BCT) model, which was
originally proposed for simulating quantum correlation of Bell's states by
using shared random variables augmented by classical communications. We derive
a new criterion for distinguishing quantum mechanics from the BCT model through
suggesting an observable event based on the perfect correlations
(anti-correlations) relation. In particular, we show that in the BCT model one
can obtain equal outputs for two opposite input settings with the nonzero
probability 0.284. Hence, in this sense we argue that the BCT model can give
rise to an unphysical result. We also show the same problem with a nonlocal
version of the BCT model.
