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

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The quantum state of a d-dimensional system can be represented by the d² probabilities corresponding to a SIC-POVM, and then this distribution of probability can be represented by a vector of ᵈ²⁻¹ in a simplex, we will call this set of vectors Q. Other way of represent a d-dimensional system is by the corresponding Bloch vector also in ᵈ²⁻¹, we will call this set of vectors B. In this paper it is proved that with the adequate scaling B=Q. Also we indicate some features of the shape of Q.