Unitary error bases: Constructions, equivalence, and applications Conference Paper

abstract

• Unitary error bases are fundamental primitives in quantum computing, which are instrumental for quantum error-correcting codes and the design of teleportation and super-dense coding schemes. There are two prominent constructions of such bases: an algebraic construction using projective representations of finite groups and a combinatorial construction using Latin squares and Hadamard matrices. An open problem posed by Schlingemann and Werner relates these two constructions, and asks whether each algebraic construction is equivalent to a combinatorial construction. We answer this question by giving an explicit counterexample in dimension 165 which has been constructed with the help of a computer algebra system. Springer-Verlag Berlin Heidelberg 2003.

authors

• Klappenecker, Andreas

published proceedings

• APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES, PROCEEDINGS

author list (cited authors)

• Klappenecker, A., & Rotteler, M.

citation count

• 9

complete list of authors

• Klappenecker, A||Rotteler, M

editor list (cited editors)

• Fossorier, M., Høholdt, T., & Poli, A.

publication date

• December 2003

publisher

• Springer Nature  Publisher

published in

• Lecture Notes in Artificial Intelligence  Journal

keywords

• Hadamard Matrices
• Latin Squares
• Monomial Representations
• Quantum Codes
• Unitary Error Bases

Digital Object Identifier (DOI)

• 10.1007/3-540-44828-4_16

International Standard Book Number (ISBN) 10

• 3-540-40111-3

International Standard Book Number (ISBN) 13

• 9783540401117

start page

• 139

end page

• 149

volume

• 2643

URL

• http://dx.doi.org/10.1007/3-540-44828-4_16