Thursday February 28, 2008

From an entry today at the weblog of Lieven Le Bruyn (U. of Antwerp):

“MUBs (for Mutually Unbiased Bases) are quite popular at the moment. Kea is running a mini-series Mutual Unbias….”

The link to Kea (Marni Dee Sheppeard (pdf) of New Zealand) and a link in her Mutual Unbias III (Feb. 13) lead to the following illustration, from a talk, “Discrete phase space based on finite fields,” by William Wootters at the Perimeter Institute in 2005:

This illustration makes clear the
close relationship of MUB’s to the
finite geometry of the 4×4 square.

See also “Reflections on Symmetry,”

“Quantum Information Theory Related to Finite Geometry,”

and a comment at The n-Category Cafe,

On Spekkens’ toy system and finite geometry.

The Wootters talk was on July 20, 2005. For related material from that July which some will find more entertaining, see “Steven Cullinane is a Crank,” conveniently reproduced as a five-page thread in the Mathematics Forum at groupsrv.com.