Unbiased complex Hadamard matrices and bases

Authors:
Darcy Best;Hadi Kharaghani
Affiliations:
Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Canada T1K 3M4;Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Canada T1K 3M4
Venue:
Cryptography and Communications
Year:
2010

Citing 4
Cited 0

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Abstract

We introduce mutually unbiased complex Hadamard (MUCH) matrices and show that the number of MUCH matrices of order 2n, n odd, is at most 2 and the bound is attained for n驴=驴1, 5, 9. Furthermore, we prove that certain pairs of mutually unbiased complex Hadamard matrices of order m can be used to construct pairs of unbiased real Hadamard matrices of order 2m. As a consequence we generate a new pair of unbiased real Hadamard matrices of order 36.