  The strong law of large numbers asserts that experimentally obtained mean
values, in the limit of number of repetitions of the experiment going to
infinity, converges almost surely to the theoretical predictions which are
based on a priori assumed constant values for probabilities of the random
events. Hence in most theoretical calculations, we implicitly neglect
fluctuations around the mean. However in practice, we can repeat the experiment
only finitely many times, and hence fluctuations are inevitable, and may lead
to erroneous judgments. It is theoretically possible to teleport an unknown
quantum state, using entanglement, with unit fidelity. The experimentally
achieved values are however sub-unit, and often, significantly so. We show that
when the number of repetitions of the experiment is small, there is significant
probability of achieving a sub-unit experimentally achieved quantum
teleportation fidelity that uses entanglement, even classically, i.e., without
using entanglement. We further show that only when the number of repetitions of
the experiment is of the order of a few thousands, the probability of a
classical teleportation process to reach the currently achieved experimental
quantum teleportation fidelities becomes negligibly small, and hence ensure
that the experimentally obtained fidelities are due to genuine use of the
shared entanglements.
