  Shanon's fundamental coding theorems relate classical information theory to
thermodynamics. More recent theoretical work has been successful in relating
quantum information theory to thermodynamics. For example, Schumacher proved a
quantum version of Shannon's 1948 classical noiseless coding theorem. In this
note, we extend the connection between quantum information theory and
thermodynamics to include quantum error correction. There is a standard
mechanism for describing errors that may occur during the transmission,
storage, and manipulation of quantum information. One can formulate a criterion
of necessary and sufficient conditions for the errors to be detectable and
correctable. We show that this criterion has a thermodynamical interpretation.
