they are widely believed to [@Fuchs:2017a] and have even been experimentally demonstrated in some low dimensions [@Durt:2008; @Medendorp:2011; @Bent:2015; @Hou:2018]. The *SIC projectors* associated with a SIC are the pure states $\rho_i=dH_i$. In dimension 2, a SIC can be represented as a regular tetrahedron inscribed in the Bloch sphere. (States defining a qubit SIC can be extracted from Feynman’s 1987 essay “Negative probabilities” [@Feynman:1987].) In higher dimensions, they are, of course, harder to visualize. When there is no chance of confusion, we will refer to the set of projectors as SICs as well. Prior work has given special attention to the reference procedure where the measurement and post-measurement states are the same SIC [@Fuchs:2013; @Fuchs:2017b; @Appleby:2017b]. In this case we denote $\Phi$ by $\Phi_{\rm SIC}$ and Eq.  takes the particularly simple form $$Q(D_j)=\sum_{i=1}^{d^2}\left[(d+1)P(H_i)-\frac{1}{d}\right]\! P(D_j|H_i)\;.
    \label{urgleichung}$$

Recall that the LTP expresses the simple consistency relation between the probabilities one assigns to the second of a sequence of measurements, the probabilities one assigns to the first, and the conditional probabilities for the second given the outcome of the first. Written in vector notation, this is $$\label{ltp}
    P(D)=P(D|H)P(H)\;.$$ We write $P(D)$ as opposed to $Q(D)$ to indicate that it is the probability vector 