Quantum Communication and Decoherence

In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It is shown that entanglement purification can be used to create ``private entanglement'', which makes it a useful tool for cryptographic protocols.Comment: 31 pages, 10 figures, LaTeX, book chapter to appear in ``Coherent Evolution in Noisy Environments'', Lecture Notes in Physics, (Springer Verlag, Berlin-Heidelberg-New York). Minor typos correcte