Quantum stabilizer codes and classical linear codes

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities. Using this result---which applies to degenerate as well as nondegenerate codes---previously established necessary conditions for classical linear codes can be easily translated into necessary conditions for quantum stabilizer codes. Examples of specific consequences are as follows: for a quantum channel subject to a fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H (+2 (1-2) ) ; and, for the depolarizing channel with fidelity parameter, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H ().