Quantum Stabilizer Codes and Classical Linear Codes

Details Quantum Stabilizer Codes and Classical Linear Codes Quantum Stabilizer Codes and Classical Linear Codes

1996-12-20

arxiv.org/abs/quant-ph/9612048v1

Physics

Quantum Physics

17 pages, ReVTeX, with two figures

Scientific paper

10.1103/PhysRevA.55.4054

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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