The paper by Renes et al. explores the existence of symmetric, informationally complete positive operator-valued measures (SIC-POVMs) in arbitrary finite dimensions. SIC-POVMs are sets of rank-one operators in a Hilbert space \(\mathbb{C}^d\) where all pairwise inner products are equal, and they are equivalent to sets of \(d^2\) equiangular lines. These measurements are crucial in quantum state tomography, quantum cryptography, and foundational studies in quantum mechanics. The authors conjecture that SIC-POVMs exist in all finite dimensions and that there is a group-covariant SIC-POVM for any dimension \(d\). They provide analytic solutions for dimensions 2, 3, and 4 and numerical solutions up to dimension 45, supporting their conjecture. The paper also discusses the connection between SIC-POVMs and spherical \(t\)-designs, and the use of group theory to simplify the search for these measurements. Despite the strong numerical evidence, a rigorous proof of the conjecture remains elusive.The paper by Renes et al. explores the existence of symmetric, informationally complete positive operator-valued measures (SIC-POVMs) in arbitrary finite dimensions. SIC-POVMs are sets of rank-one operators in a Hilbert space \(\mathbb{C}^d\) where all pairwise inner products are equal, and they are equivalent to sets of \(d^2\) equiangular lines. These measurements are crucial in quantum state tomography, quantum cryptography, and foundational studies in quantum mechanics. The authors conjecture that SIC-POVMs exist in all finite dimensions and that there is a group-covariant SIC-POVM for any dimension \(d\). They provide analytic solutions for dimensions 2, 3, and 4 and numerical solutions up to dimension 45, supporting their conjecture. The paper also discusses the connection between SIC-POVMs and spherical \(t\)-designs, and the use of group theory to simplify the search for these measurements. Despite the strong numerical evidence, a rigorous proof of the conjecture remains elusive.