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 $D\left(M\right)$ of pure singlets $\left(|{\Psi }^{-}〉\right)$ distillable from mixed states $M$, showing $D\left(M\right)>0\mathrm{}$ if $〈{\Psi }^{-}|M|{\Psi }^{-}〉>\frac{1}{2}$.