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This is a Quantitative Study study.

October 16, 2025Open Access

Asymmetric SICs over finite fields

Key Points

New SICs were constructed over finite fields, showing properties distinct from previously known systems.
While known SICs exhibit Weyl--Heisenberg symmetry, the discovered SICs have trivial automorphism groups.
The study proposes that totally asymmetric SICs may exist in infinitely many dimensions within finite fields.
This research expands the understanding of equiangular lines and their applications in quantum mechanics.

Abstract

Zauner's conjecture concerns the existence of d² equiangular lines in Cᵈ; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl--Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such totally asymmetric SICs exist in infinitely many dimensions in the finite field setting.

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Cite This Study

Iverson et al. (Wed,) studied this question.

synapsesocial.com/papers/68f04918e559138a1a06d456 https://doi.org/https://doi.org/10.48550/arxiv.2506.20778

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