  We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)],
where we restricted our attention to noisy deterministic teleportation
protocols, to noisy probabilistic (conditional) protocols. Our main goal now is
to study how we can increase the fidelity of the teleported state in the
presence of noise by working with probabilistic protocols. We work with several
scenarios involving the most common types of noise in realistic implementations
of quantum communication tasks and find many cases where adding more noise to
the probabilistic protocol increases considerably the fidelity of the
teleported state, without decreasing the probability of a successful run of the
protocol. Also, there are cases where the entanglement of the channel
connecting Alice and Bob leading to the greatest fidelity is not maximal.
Moreover, there exist cases where the optimal fidelity for the probabilistic
protocols are greater than the maximal fidelity (2/3) achievable by using only
classical resources, while the optimal ones for the deterministic protocols
under the same conditions lie below this limit. This result clearly illustrates
that in some cases we can only get a truly quantum teleportation if we use
probabilistic instead of deterministic protocols.
