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Existence of additional sporadic SICs

Determine whether there exist additional "sporadic" 1-SICs (symmetric informationally complete POVMs) that are not Weyl–Heisenberg covariant beyond those currently known.

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Background

The authors focus exclusively on WH-covariant r-SICs and dimensions d>3. They note that known 1-SICs excluded under this restriction are exceptional and often termed "sporadic SICs." The existence of further examples of non-WH-covariant 1-SICs remains an open question.

References

The known 1-SICs thus excluded are all in some ways exceptional and are called sporadic SICs by Stacey. It is open whether more such examples exist.

— A Constructive Approach to Zauner's Conjecture via the Stark Conjectures (2501.03970 - Appleby et al., 7 Jan 2025) in Remark after Definition 2.9 (WH-covariant r-SIC), Section 2.1