Polynomial-Time Algorithms for Weaver's Discrepancy Problem in a Dense Regime

Ben Jourdan, Peter Macgregor, He Sun

Given $v_1,\dots ,v_m\in {\mathbb{C}}^d$ with $\Vert v_i{\Vert }^2=\alpha$ for all $i\in [m]$ as input and suppose ${\sum }_{i=1}^m|⟨u,v_i⟩{|}^2=1$ for every unit vector $u\in\mathbb…