Abstract error groups via Jones unitary braid group representations at q = i

Abstract error groups via Jones unitary braid group representations at q = i In this paper, we classify a type of abstract groups by the central products of dihedral groups and quaternion groups. We recognize them as abstract error groups which are often not isomorphic to the Pauli groups in the literature. We show the corresponding nice error bases equivalent to the Pauli error bases modulo phase factors. The extension of these abstract groups by the symmetric group are finite images of the Jones unitary representations (or modulo a phase factor) of the braid group at q = i or r = 4. We hope this work can finally lead to new families of quantum error correction codes via the representation theory of the braid group. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Abstract error groups via Jones unitary braid group representations at q = i

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Publisher
Springer US
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-008-0092-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we classify a type of abstract groups by the central products of dihedral groups and quaternion groups. We recognize them as abstract error groups which are often not isomorphic to the Pauli groups in the literature. We show the corresponding nice error bases equivalent to the Pauli error bases modulo phase factors. The extension of these abstract groups by the symmetric group are finite images of the Jones unitary representations (or modulo a phase factor) of the braid group at q = i or r = 4. We hope this work can finally lead to new families of quantum error correction codes via the representation theory of the braid group.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 23, 2009

References

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