 Bloch ball

The qubit density operators $\rho =(I+\mathbf{s}\cdot \mathbf{\sigma })/2$ correspond exactly to the closed unit ball: their eigenvalues are $(1\pm |\mathbf{s}|)/2$, so positivity is equivalent to $|\mathbf{s}|\le 1$. The boundary is the Bloch sphere of pure states, and the centre is $I/2$. A depolarizing channel scales this ball isotropically, possibly with a sign reversal in the larger completely positive parameter interval.