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What is Mutually Unbiased Bases as 2-Designs about?

Mutually unbiased bases (MUBs) are sets of bases in a quantum system where the bases are maximally incompatible. This paper shows that maximal sets of MUBs have a rich combinatorial structure by demonstrating they are equivalent to complex projective 2-designs with angle set {0, 1/d}. It also provides a new proof that symmetric informationally complete POVMs are complex projective 2-designs with angle set {1/(d+1)}. Several known constructions of MUBs are described, though their existence is only proven for

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