How to Correct Small Quantum Errors

The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a nonvanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T , provided the errors produced by T are small enough. This text is part of a volume entitled: “Coherent evolution in noisy environments” to be published in Lecture notes in physics, Springer Verlag, http://link.springer.de/series/lnpp/, Copyright: Springer Verlag, Berlin, Heidelberg, New York Electronic Mail: m.keyl@tu-bs.de Electronic Mail: r.werner@tu-bs.de