Distillation of secret key and entanglement from quantum states

Igor Devetak, Andreas Winter

Published 2003-06-11Version 1

We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specialising our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one-way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so-called "hashing inequality" which says that the coherent information (i.e., the negative conditional von Neumann entropy) is an achievable EPR rate. This result is well--known to imply a whole set of distillation and capacity formulas which we briefly review.