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- W1860134631 abstract "Mutually unbiased bases (MUBs) are interesting for various reasons. The most attractive example of (a complete set of) MUBs is the one constructed by Ivanoviifmmode acute{c}else '{c}fi{} as well as Wootters and Fields, which is referred to as the canonical MUB. Nevertheless, little is known about anything that is unique to this MUB. We show that the canonical MUB in any prime power dimension is uniquely determined by an extremal orbit of the (restricted) Clifford group except in dimension 3, in which case the orbit defines a special symmetric informationally complete measurement (SIC), known as the Hesse SIC. Here the extremal orbit is the orbit with the smallest number of pure states. Quite surprisingly, this characterization does not rely on any concept that is related to bases or unbiasedness. As a corollary, the canonical MUB is the unique minimal 2-design covariant with respect to the Clifford group except in dimension 3. In addition, these MUBs provide an infinite family of highly symmetric frames and positive-operator-valued measures (POVMs), which are of independent interest." @default.
- W1860134631 created "2016-06-24" @default.
- W1860134631 creator A5041994729 @default.
- W1860134631 date "2015-06-30" @default.
- W1860134631 modified "2023-10-07" @default.
- W1860134631 title "Mutually unbiased bases as minimal Clifford covariant 2-designs" @default.
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- W1860134631 doi "https://doi.org/10.1103/physreva.91.060301" @default.
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