Representation of quantum states as points in a probability simplex associated to a SIC-POVM

Understand

The quantum state of a $d$-dimensional system can be represented by the $d^2$ probabilities corresponding to a SIC-POVM, and then this distribution of probability can be represented by a vector of $\R^{d^2-1}$ in a simplex, we will call this set of vectors $\mathcal{Q}$.

• Other way of represent a $d$-dimensional system is by the corresponding Bloch vector also in $\R^{d^2-1}$, we will call this set of vectors $\mathcal{B}$.
• In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$.
• Also we indicate some features of the shape of $\mathcal{Q}$.