Document Type

Article

Publication Date

2010

Publication Title

European Journal of Combinatorics

Abstract

Mutually unbiased bases (MUBs) in complex vector spaces play several important roles in quantum information theory. At present, even the most elementary questions concerning the maximum number of such bases in a given dimension and their construction remain open. In an attempt to understand the complex case better, some authors have also considered real MUBs, mutually unbiased bases in real vector spaces. The main results of this paper establish an equivalence between sets of real mutually unbiased bases and 4-class cometric association schemes which are both Q-bipartite and Q-antipodal. We then explore the consequences of this equivalence, constructing new cometric association schemes and describing a potential method for the construction of sets of real MUBs.

Volume

31

Issue

6

First Page Number

1499

Last Page Number

1512

DOI

http://dx.doi.org/10.1016/j.ejc.2009.11.014

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