Physics – Quantum Physics
Scientific paper
2007-01-17
Physics
Quantum Physics
4 pages, 2 figures, some minor changes made
Scientific paper
10.1016/j.physleta.2007.04.059
The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper we move away from the traditional analytic approach and use a numerical approach to attempt to determine this number. We numerically minimise a non-negative function of a set of N+1 orthonormal bases in dimension d which only evaluates to zero if the bases are mutually unbiased. As a result we find strong evidence that (as has been conjectured elsewhere) there are no more than three mutually unbiased bases in dimension six.
Butterley Paul
Hall William
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