Title :
Beyond stabilizer codes .I. Nice error bases
Author :
Klappenecker, Andreas ; Rötteler, Martin
Author_Institution :
Dept. of Comput. Sci., Texas A&M Univ., College Station, TX, USA
fDate :
8/1/2002 12:00:00 AM
Abstract :
Nice error bases have been introduced by Knill (1996) as a generalization of the Pauli basis. These bases are shown to be projective representations of finite groups. We classify all nice error bases of small degree, and all nice error bases with Abelian index groups. We show that, in general, an index group of a nice error basis is necessarily solvable.
Keywords :
error correction codes; group theory; quantum computing; Abelian index groups; Pauli basis; finite groups; nice error bases; projective representations; quantum computing; quantum error control codes; stabilizer codes; Algebra; Associate members; Computer errors; Computer science; Error correction; Error correction codes; Fault tolerance; Large-scale systems; Quantum computing; Two dimensional displays;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2002.800471
