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Extension of the necromancy method to r-SICs (r>1)

Develop and analyze an extension of the numerical "necromancy" procedure for reconstructing SIC fiducials so that it efficiently and reliably applies to r-SICs with rank r>1, including algorithmic guarantees and complexity bounds.

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Background

The authors present a heuristic necromancy method for 1-SICs, discuss practicalities, and note that extending the method to higher-rank SICs is likely possible but not yet attempted. They explicitly leave this case to future work.

References

It is likely that the methods here extend to r-SICs for r>1, but we have not attempted to systematically approach numerical computation for r>1, so we leave this case for future work and focus on 1-SICs for the rest of this section.

— A Constructive Approach to Zauner's Conjecture via the Stark Conjectures (2501.03970 - Appleby et al., 7 Jan 2025) in Section 6.1 (Numerical calculations)