Codes and Expansions (CodEx) Seminar

Matt Fickus (Air Force Institute of Technology)
Mutually Unbiased Equiangular Tight Frames

An equiangular tight frame (ETF) yields a type of optimal packing of lines in a Euclidean space. ETFs seem to be rare, and all known nontrivial infinite families of them arise from some type of combinatorial design. We introduce a new method for constructing ETFs. We begin by showing that it is sometimes possible to construct multiple ETFs for the same space that are mutually unbiased in a way that is analogous to the quantum-information-theoretic concept of mutually unbiased bases. We then show that taking certain tensor products of these mutually unbiased ETFs with other ETFs sometimes yields infinite families of new complex ETFs.