On the equivalence between real mutually unbiased bases and a certain class of association schemes

Citation data:

European Journal of Combinatorics, ISSN: 0195-6698, Vol: 31, Issue: 6, Page: 1499-1512

Publication Year:
2010
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Repository URL:
https://digitalcommons.wpi.edu/mathematicalsciences-pubs/69
DOI:
10.1016/j.ejc.2009.11.014
Author(s):
LeCompte, Nicholas; Martin, William J; Owens, William
Publisher(s):
Elsevier BV
Tags:
Mathematics; Discrete Mathematics and Combinatorics
article description
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.