Title

Abstract Error Groups Via Jones Unitary Braid Group Representations At Q = I

Keywords

Abstract error group; Extra special two-groups; Nice error base; Unitary braid representation

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. © 2009 Springer Science+Business Media, LLC.

Publication Date

2-1-2009

Publication Title

Quantum Information Processing

Volume

8

Issue

1

Number of Pages

25-36

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11128-008-0092-7

Socpus ID

59249096643 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/59249096643

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