Algebraic Graph Theory Seminar - Chris Godsil

Title: Mutually unbiased bases

Abstract:

A pair of d x d unitary matrices is unbiased if M*N is at, i.e., all its entries have the same absolute value. A relatively simple argument shows that a set of pairwise unbiased unitary matrices has size at most d + 1. Constructions of sets that meet this bound are known only if d is a prime power, and the constructions are combinatorial (distance-regular graphs, finite geometry, difference sets). I will present an introduction to the topic.