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 {δ} fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H(+√2δ(1-2δ)); and, for the depolarizing channel with fidelity parameter {δ}, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H({δ}).