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This talk presents a construction of symmetric informationally complete POVMs (SIC-POVMs), a special class of quantum measurements conjectured to exist in all dimensions by Zauner in 1999. Explore the concept of "ghost SICs," explicit mathematical objects built from number-theoretic properties of special modular functions, and learn how they relate to actual SICs through Galois conjugation. The presentation demonstrates how, assuming Stark's conjecture from algebraic number theory and a special value identity for a modular function, this construction produces valid SICs in every dimension. Discover a simplified special case that still implies Zauner's conjecture, and learn about Zauner.jl, a free open-source software package used to verify results against known solutions and identify new SICs, including previously undiscovered examples in dimension 100. The talk also covers higher-rank generalizations called r-SICs, revealing deep connections between SIC existence and abelian field extensions in algebraic number theory.
