  The present thesis deals with various methods of quantum error correction. It
is divided into two parts. In the first part, dynamical decoupling methods are
considered which have the task of suppressing the influence of residual
imperfections in a quantum memory. The suppression is achieved by altering the
dynamics of an imperfect quantum memory with the help of a sequence of local
unitary operations applied to the qudits. Whereas up to now the operations of
such decoupling sequences have been constructed in a deterministic fashion,
strategies are developed in this thesis which construct the operations by
random selection from a suitable set. Furthermore, it is investigated if and
how the discussed decoupling strategies can be employed to protect a quantum
computation running on the quantum memory.
  The second part of the thesis deals with quantum error-correcting codes and
protocols for quantum key distribution. The focus is on the BB84 and the
6-state protocol making use of only one-way communication during the error
correction and privacy amplification steps. It is shown that by adding
additional errors to the preliminary key (a process called noisy preprocessing)
followed by the use of a structured block code, higher secure key rates may be
obtained. For the BB84 protocol it is shown that iterating the combined
preprocessing leads to an even higher gain.
