How does this relate to the MIC-POVM representation of states?
In the QuantumFramework, we have a transformation that turns a quantum state into a probability distribution in a minimal d^2 dimension, not of order d^3, like in your paper. Then, the Schrodinger equation (technically Liouville–von Neumann equation) can also be written in probability vector form.
We've made this a special case for evolution in phase space. For example, given random Hamiltonian and initial state, you can inspect what equations it generates for NDSolve:
equations = Normal @ QuantumEvolve[QuantumOperator["RandomHermitian"],
QuantumWignerMICTransform[QuantumState["RandomMixed"]], {t, 0, 1},
"ReturnEquations" -> True]
For a qubit, the initial vector would be a 4-dimension probability distribution.
Of course, not every 4-dimension probability distribution would correspond to a valid qubit.
