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arXiv · quant-ph/9612048

Quantum Stabilizer Codes and Classical Linear Codes

Richard Cleve
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Abstract

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 delta-fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the depolarizing channel with fidelity parameter delta, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H(delta).

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Richard Cleve. 1996-12-20. Quantum Stabilizer Codes and Classical Linear Codes. https://doi.org/10.1103/physreva.55.4054

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