  By exhibiting a violation of a novel form of the Bell-CHSH inequality,
Zukowski has recently established that the quantum correlations exploited in
the standard perfect teleportation protocol cannot be recovered by any local
hidden variables model. Allowing the quantum channel state in the protocol to
be given by any density operator of two spin-1/2 particles, we show that a
violation of a generalized form of Zukowski's teleportation inequality can only
occur if the channel state, considered by itself, violates a Bell-CHSH
inequality. On the other hand, although it is sufficient for a teleportation
process to have a nonclassical fidelity-defined as a fidelity exceeding
2/3-that the channel state employed violate a Bell-CHSH inequality, we show
that such a violation does not imply a violation of Zukowski's teleportation
inequality or any of its generalizations. The implication does hold, however,
if the fidelity of the teleportation exceeds $2/3(1+1/2\sqrt{2})\approx .90$,
suggesting the existence of a regime of nonclassical values of the fidelity,
less than .90, for which the standard teleportation protocol can be modelled by
local hidden variables.
