Purification of noisy entanglement and faithful teleportation via noisy channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states (e.g., singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity (e.g., near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We,give upper and lower bounds on the yield D(M) of pure singlets (\Psi(-)]) distillable from mixed states M, showing D(M) > 0 if [Psi(-)\M\Psi(-)] > 1/2.