Bloch Sphere

A Bloch Sphere is a representation of a Qubit. Any Density Operator can be represented as in the shape $\rho =\frac{1}{2}(I+\overrightarrow{r}\cdot \sigma )$, where $\overrightarrow{r}=[r_x,r_y,r_z]\in {\mathbb{C}}^3$ and $\sigma =[{\sigma }_x,{\sigma }_y,{\sigma }_z]$ are the Pauli Matrixes.