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 infinite families of them arise from some type of combinatorial design. In this paper, 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.
IEEE Transactions on Information Theory
M. Fickus and B. R. Mayo, "Mutually Unbiased Equiangular Tight Frames," in IEEE Transactions on Information Theory, vol. 67, no. 3, pp. 1656-1667, March 2021, doi: 10.1109/TIT.2020.3042735. arXiv:2001.02055 [math.FA]