A quantum system can never be seen as being completely isolated from its environment, thereby permanently causing disturbance to the state of the system. The resulting noise problem threatens quantum computers and their great promise, namely, to provide a computational advantage over classical computers for certain problems (see also the cross-references in the section “Cross-References”). Quantum noise is usually modeled by the notion of a quantum channel which generalizes the classical case and, in particular, includes scenarios for communication (space) and storage (time) of quantum information. For more information about quantum channels and quantum information in general, see [19]. A basic channel is the quantum mechanical analog of the classical binary symmetric channel [17]. This quantum channel is called the depolarizing channel and depends on a real parameter p 2 Œ0; 1 . Its effect is to randomly apply one of the Pauli spin matrices X , Y , and Z to the state of the system, mapping a quantum state i of one qubit to .1 p/iC p=3.XiX C Y iY C ZiZ/. It should be noted that it is always possible to map any quantum channel to a depolarizing channel by twirling operations. The basic problem of quantum error correction is to devise a mechanism that allows to recover quantum information that has been sent through a quantum channel, in particular the depolarizing channel.