Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM

@article{Rosado2011RepresentationOQ,
  title={Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM},
  author={Jos{\'e} Ignacio Rosado},
  journal={Foundations of Physics},
  year={2011},
  volume={41},
  pages={1200-1213}
}
  • J. Rosado
  • Published 5 July 2010
  • Mathematics
  • Foundations of Physics
The quantum state of a d-dimensional system can be represented by a probability distribution over the d2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d2−1)-dimensional 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 $\mathbb {R}^{d^{2}-1}$, we… 
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