### Abstract

Based on techniques from classical information theory, which we generalise to the quantum domain, we show how to distill secret key between two parties by local operations and public communication from given states, at an asymptotically optimal rate. By implementing this protocol "coherently", we then show how it yields actually entanglement, at the same rate, proving the long-conjectured "hashing inequality": it states that from a given quantum state, once can, using one-way LOCC, distill entanglement with rate given by the coherent information.

This is joint work with Igor Devetak; it is contained in eprints quant-ph/0306078 and quant-ph/0307053.