Properties of the Probability Current in Purely Probabilistic Representations of Quantum Theory

Braasch and Wootters have recently explored properties of the quasi-probability current for discrete Wigner-function (quasi-probability) representations of finite dimensional quantum theory. In this talk, I will consider analogous properties for a purely probabilistic representation of the same setting, i.e., one with true-blue probabilities. Of most interest is a representation induced by the Symmetric Informationally Complete Positive Operator-Valued Measure (SIC-POVMs), which is particularly important for QBism. I will then generalize the findings there to any Informationally Complete (IC) POVM representation and motivate a notion of gauge invariance for the von Neumann equation.