|
| related topics |
| {error, code, errors} |
| {let, theorem, proof} |
| {equation, function, exp} |
| {group, space, representation} |
| {states, state, optimal} |
| {time, systems, information} |
| {algorithm, log, probability} |
| {information, entropy, channel} |
|
Quantum error-correcting codes associated with graphs
D. Schlingemann, R. F. Werner
abstract: We present a construction scheme for quantum error correcting codes. The
basic ingredients are a graph and a finite abelian group, from which the code
can explicitly be obtained. We prove necessary and sufficient conditions for
the graph such that the resulting code corrects a certain number of errors.
This allows a simple verification of the 1-error correcting property of
fivefold codes in any dimension. As new examples we construct a large class of
codes saturating the singleton bound, as well as a tenfold code detecting 3
errors.
- oai_identifier:
- oai:arXiv.org:quant-ph/0012111
- categories:
- quant-ph cs.IT math-ph math.IT math.MP
- comments:
- 8 pages revtex, 5 figures
- arxiv_id:
- quant-ph/0012111
- created:
- 2000-12-20
Full article ▸
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