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, thereby demonstrating new connections between quantum codes and classical codes. 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: for a quantum channel subject to a δfraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H( 2 + √ 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). 89.80.+h, 03.65.Bz Typeset using REVTEX ∗[email protected] 1