Unitary Error Bases: Constructions, Equivalence, and Applications Conference Paper uri icon

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.

author list (cited authors)

  • Klappenecker, A., & Rötteler, M.

citation count

  • 8

editor list (cited editors)

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

publication date

  • April 2003