|
| related topics |
| {error, code, errors} |
| {information, entropy, channel} |
| {let, theorem, proof} |
| {vol, operators, histories} |
| {group, space, representation} |
| {qubit, qubits, gate} |
| {entanglement, phys, rev} |
|
Quantum Stabilizer Codes and Classical Linear Codes
Richard Cleve
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).
- oai_identifier:
- oai:arXiv.org:quant-ph/9612048
- categories:
- quant-ph
- comments:
- 17 pages, ReVTeX, with two figures
- doi:
- 10.1103/PhysRevA.55.4054
- arxiv_id:
- quant-ph/9612048
- created:
- 1996-12-20
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