$\rho$ implies that she assigns the Born Rule probabilities $Q(D_j)=\tr \rho D_j$ for the outcomes of her measurement. In this way, any quantum state $\rho$ may be regarded as a compilation of probability distributions for all possible measurements. However, one does not have to consider all possible measurements to completely specify $\rho$. In fact, there exist measurements which are informationally complete (IC) in the sense that $\rho$ is uniquely specified by the agent’s expectations for the outcomes of that single measurement [@Prugovecki:1977]. With respect to an IC measurement, any quantum state, pure or mixed, is equivalent to a single probability distribution. In this paper, we consider minimal informationally-complete POVMs (MICs) for finite dimensional quantum systems. These sets of operators form bases for the vector space of Hermitian operators and lead to probability distributions with the fewest number of entries necessary for reconstructing the quantum state. MICs furnish a convenient way to bypass the language of quantum states, making quantum theory analogous to classical stochastic process theory, in which one puts probabilities in and gets probabilities out.

One can eliminate the need to use the operators $\rho$ and $D_j$ in the Born Rule by reexpressing it as a relation between an 