Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

TLDR

By applying local operations to a supply of moderately impure entangled states shared through a noisy channel, the observers distill a smaller set of near‑perfect singlets that can then be used to faithfully teleport unknown quantum states across the channel. The authors derive upper and lower bounds on the distillable singlet yield D(M), proving that D(M) is positive whenever the singlet fidelity of M exceeds one‑half.

Abstract

Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.}] singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em 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 transfrom 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 ($\ket{Ψ^-}$) distillable from mixed states $M$, showing $D(M)>0$ if $\bra{Ψ^-}M\ket{Ψ^-}>\half$.