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arXiv · 1310.4684

Orbits of mutually unbiased bases

Kate Blanchfield
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Abstract

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 dependencies among different sets of mutually unbiased bases.

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Kate Blanchfield. 2013-10-17. Orbits of mutually unbiased bases. https://doi.org/10.1088/1751-8113%2F47%2F13%2F135303

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