Codes and Expansions (CodEx) Seminar

Ingemar Bengtsson (Stockholm University):
Pythagorean SICs

So far we are able to prove existence of SICs (maximal equiangular tight frames in complex vector spaces) only by explicit construction, dimension by dimension. Still, number theoretic connections between SICs in different dimensions have been observed. I will sketch how they arise. Then I will focus on a special infinite sequence of dimensions for which I conjecture that there are SIC vectors that take a very simple form relative to a suitable basis. All the phase factors that occur in their components should be formed from Pythagorean triples of integers.