We derive an experimentally testable criterion for the teleportation of qua
ntum states of continuous variables. This criterion is especially relevant
to the recent experiment of Furusawa et al. where an input-output fidelity
of 0.58 +/- 0.02 was achieved for optical coherent stages. Our derivation d
emonstrates that fidelities greater than 1/2 could not have been achieved t
hrough the use of a classical channel alone; quantum entanglement was a cru
cial ingredient in the experiment.