2013/10/31 by Kate Blanchfield
Mathematics · Physics and Astronomy · #Abelian group #Algebraic and Geometric Analysis #Analogy #Group (periodic table) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mutually unbiased bases #Prime (order theory) #quant-ph
paper · pdf · doi:10.1088/1751-8113/47/13/135303
published as J. Phys. A: Math. Theor. 47 (2014) 135303 · 21 pages
openalex publication_date 2014/03/14 · arxiv created 2014/03/25 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.