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 .

翻译：我们给出了一个关于重叠变量的全纯四次多项式，其在环面上的零点恰好对应于Weyl-Heisenberg对称信息完备测量（对称信息完备正算子值测度）。作为对比，所有其他已知的确定Weyl-Heisenberg对称信息完备测量的方程组都涉及变量及其复共轭。我们还给出了关于群G = Z d x Z d的投影傅里叶变换幂次的一个相关有趣结果。