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Zauner’s Conjecture

Prove the existence of symmetric informationally complete sets of d^2 complex equiangular lines in C^d (1-SICs) for every integer dimension d.

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Background

Zauner’s conjecture asserts universal existence of 1-SICs, which are maximal complex equiangular tight frames achieving d2 lines in dimension d. The paper develops a conditional constructive framework showing that this conjecture follows from the Stark Conjecture together with a special function identity (the Twisted Convolution Conjecture).

References

In 1999, Zauner made the following conjecture regarding 1-SICs. 1-SICs exist for all d.

— A Constructive Approach to Zauner's Conjecture via the Stark Conjectures (2501.03970 - Appleby et al., 7 Jan 2025) in Conjecture 1.1 (Zauner’s Conjecture), Section 1 (Introduction)