# Orbits of mutually unbiased bases

@article{Blanchfield2014OrbitsOM, title={Orbits of mutually unbiased bases}, author={Kate Blanchfield}, journal={Journal of Physics A}, year={2014}, volume={47}, pages={135303} }

We express Alltop?s construction of mutually unbiased bases as orbits under the Weyl?Heisenberg group in prime dimensions and find a related construction in dimensions 2 and 4. We reproduce Alltop?s mutually unbiased bases using abelian subgroups of the Clifford group in prime dimensions, in direct analogy to the well-known construction of mutually unbiased bases using abelian subgroups of the Weyl?Heisenberg group. Finally, we prove three theorems relating to the distances and linear…

## 13 Citations

Order 3 symmetry in the Clifford hierarchy

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We investigate the action of the first three levels of the Clifford hierarchy on sets of mutually unbiased bases comprising the Ivanovic mutually unbiased base (MUB) and the Alltop MUBs. Vectors in…

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