0012111v1

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

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