Equations for the overlaps of a SIC

Len Bos; Shayne Waldron

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arXiv · 2405.14123

Equations for the overlaps of a SIC

Len Bos·Shayne Waldron

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Abstract

We give a holomorphic quartic polynomial in the overlap variables whose zeros on the torus are precisely the Weyl-Heisenberg SICs (symmetric informationally complete positive operator valued measures). By way of comparison, all the other known systems of equations that determine a Weyl-Heisenberg SIC involve variables and their complex conjugates. We also give a related interesting result about the powers of the projective Fourier transform of the group G = Z d x Z d .

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Len Bos, Shayne Waldron. 2024-05-23. Equations for the overlaps of a SIC. https://arxiv.org/abs/2405.14123

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