Zauner’s Conjecture (existence of 1-SICs in all dimensions)
Establish the existence of 1-SICs (symmetric informationally complete POVMs) in complex dimension d for every positive integer d.
References
In 1999, Zauner made the following conjecture regarding $1$-SICs. \begin{conj}[Zauner's Conjecture] \label{conj:zauner} 1-SICs exist for all $d$. \end{conj}
— A Constructive Approach to Zauner's Conjecture via the Stark Conjectures
(Appleby et al., 7 Jan 2025) in Section 1 (Introduction)