Equiangular lines, mutually unbiased bases, and spin models

Details Equiangular lines, mutually unbiased bases, and spin models Equiangular lines, mutually unbiased bases, and spin models

2005-11-01

arxiv.org/abs/quant-ph/0511004v3

European Journal of Combinatorics 30 (2009), pp. 246--262

Physics

Quantum Physics

23 pages; no figures. Minor correction as pointed out in arxiv.org:1104.3370

Scientific paper

10.1016/j.ejc.2008.01.002

We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters (k,n,k,l) we construct sets of n+1 mutually unbiased bases in C^k. We show how to construct these difference sets from commutative semifields and that several known maximal sets of mutually unbiased bases can be obtained in this way, resolving a conjecture about the monomiality of maximal sets. We also relate mutually unbiased bases to spin models.

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