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Robin
and I have been thinking a bit about the following problem. Consider an
irrep of a group that is a unitary 1-design (and isn't also a unitary
2-design). For example, take a d-dimensional irrep of the
Weyl-Heisenberg group mod d. We know that the action of this irrep on
some vector will also produce a state 1-design. By analogy with
SICPOVMs, we can imagine that the action could also produce a
higher-order state design. We have taken to calling these vectors
"voodoo states", since it seems to involve black magic to construct
them. Robin and I are currently thinking about voodoo states for other
groups, which might lead to some insight into SICs. More will be
forthcoming.
Older stuff: Have a look at that:
http://arxiv.org/abs/quant-ph/0605050
Comment from
David:
Steve refers to two papers:
[37] A. Nobs, Comment. Math. Helv. 51, (4) 46589 (German) (1976)
[38] A. Nobs and J. Wolfart, Comment. Math. Helv. 51, (4) 491526
(German) (1976)
which detail the structure of SL(2,Z_d). It's a very good and
complete paper. I'm prepared to translate paragraphs should there be
some interest. Look at the tables to get a rough idea of what you might
want to know about. :-)
Last modified:
Monday, October 26, 2015 - 17:56
