  Efficient all-photonic quantum teleportation requires fast and deterministic
sources of highly indistinguishable and entangled photons. Solid-state-based
quantum emitters--notably semiconductor quantum dots--are a promising candidate
for the role. However, despite the remarkable progress in nanofabrication,
proof-of-concept demonstrations of quantum teleportation have highlighted that
imperfections of the emitter still place a major roadblock in the way of
applications. Here, rather than focusing on source optimization strategies, we
deal with imperfections and study different teleportation protocols with the
goal of identifying the one with maximal teleportation fidelity. Using a
quantum dot with sub-par values of entanglement and photon
indistinguishability, we show that the average teleportation fidelity can be
raised from below the classical limit to 0.842(14). Our results, which are
backed by a theoretical model that quantitatively explains the experimental
findings, loosen the very stringent requirements set on the ideal
entangled-photon source and highlight that imperfect quantum dots can still
have a say in teleportation-based quantum communication architectures.
