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

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Abstract: 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 ofprobability can be represented by a vector of $\R^{d^2-1}$ in a simplex, wewill 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 itis proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$. Also weindicate some features of the shape of $\mathcal{Q}$.

Author: ** Jose Ignacio Rosado**

Source: https://arxiv.org/