Fidelity thresholds in single copy entanglement distillation

Various aspects of distillation of noisy entanglement and some associated effects in quantum error correction are considered. In particular, we prove that if only one-way classical communication (from Alice to Bob) is allowed and the shared d⊗d state is not pure then there is a threshold for optimal entanglement fraction F of the state that can be obtained in single copy distillation process. This implies that to get (probabilistically) arbitrary good conclusive teleportation via mixed state at least one classical bit of backward communication (from Bob to Alice) has to be sent. We provide several other threshold properties in this context including in particular the existence of ultimate threshold of optimal F for states of full rank. Finally the threshold results are discussed in context of probabilistic error correction.