We present a comparative analysis of exact and approximate quantum error
correction by means of simple unabridged analytical computations. For the sake
of clarity, using primitive quantum codes, we study the exact and approximate
error correction of the two simplest unital (Pauli errors) and nonunital
(non-Pauli errors) noise models, respectively. The similarities and differences
between the two scenarios are stressed. In addition, the performances of
quantum codes quantified by means of the entanglement fidelity for different
recovery schemes are taken into consideration in the approximate case. Finally,
the role of self-complementarity in approximate quantum error correction is
briefly addressed.Comment: 29 pages, 1 figure, improved v2; accepted for publication in Open
Systems and Information Dynamics (2014
