 There are also technical problems with Equation \((\ref{ex2})\), which assumes the existence of SICs in the relevant Hilbert space. But infinite as well as finite-dimensional Hilbert spaces are used in quantum theory, and SICs have not (yet) been shown to exist in every finite  dimension.[4]  Informationally-complete (but not necessarily symmetric) POVMs do exist in all finite dimensional spaces. Fuchs and Schack (2015) give a schematic alternative to Equation \((\ref{ex2})\) that does not require symmetry of an informationally-complete POVM representing a hypothetical fiducial measurement.