New Insights into the SIC-POVM Fiducials

Symmetric, Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) hold a central role in Quantum Foundations, particularly for QBism. SIC-POVMs offer an optimal way to represent quantum states and have intrigued researchers due to their potential in quantum state tomography and foundational quantum theories. All known SIC-POVMs can be generated by acting with the Weyl-Heisenberg group on a starting vector, known as the SIC fiducial. In this presentation, we will explore recently uncovered relationships among the elements of these SIC fiducials, which may provide crucial insights into the long-standing open question of whether SIC-POVMs exist in all dimensions.