On the existence of algebraic equiangular lines
Year: 2026
Type: article
Abstract: In this paper, we consider real and complex equiangular lines, generated by unit vectors. We show that, for an arbitrary dimension [Formula: see text], if there exists a set of [Formula: see text] equiangular unit vectors in [Formula: see text], then there must exist a set of [Formula: see text] equiangular unit vectors with all of their coefficients in a number field. This result is motivated by the question of constructing SIC-POVMs in quantum physics and conjectures around them. We discuss applications of our techniques to the case of real equiangular lines, mutually unbiased bases, and consequences of the above results.
Authors: Igor Van Loo, Frédérique Oggier
Institutions: Nanyang Technological University, University of Birmingham
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208780980
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