  The concept of entropy and the correct application of the Second Law of
thermodynamics are essential in order to understand the reason why quantum
error correction is thermodynamically possible and no violation of the Second
Law occurs during its execution. We report in this work our first steps towards
an entropic analysis extended to approximate quantum error correction (QEC).
Special emphasis is devoted to the link among quantum state discrimination
(QSD), quantum information gain, and quantum error correction in both the exact
and approximate QEC scenarios.
