Mutually Unbiased Equiangular Tight Frames

Authors

Matthew C. Fickus, Air Force Institute of TechnologyFollow
Benjamin R. Mayo

Document Type

Article

Publication Date

3-2021

Abstract

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.

Comments

The "Link to Full Text" on this page will open or load the arXiv e-print version as hosted at the arXiv repository. arXiv:2001.02055

The version of record (published version) is available from IEEE, and is cited below.

DOI

10.1109/TIT.2020.3042735

Source Publication

IEEE Transactions on Information Theory

Recommended Citation

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]