On the Nonlocality of the Quantum Channel in the Standard Teleportation Protocol

Clifton, Rob and Pope, Damian (2001) On the Nonlocality of the Quantum Channel in the Standard Teleportation Protocol.

Abstract

By exhibiting a violation of a novel form of the Bell-CHSH inequality,
\.{Z}ukowski
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
\.{Z}ukowski'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 \emph{not} imply a violation of
\.{Z}ukowski'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.