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Mean king’s problem with mutually unbiased bases and orthogonal Latin squares
The mean king's problem with maximal mutually unbiased bases (MUB's) in general dimension $d$ is investigated. It is shown that a solution of the problem exists if and only if the maximal number $(d+1)$ of orthogonal Latin squares exists. This implies that there is no solution in $d=6$ or $d=10$ …