= Bloch ball
{c}
{title2=$\{\mathbf s\in\mathbb R^3:|\mathbf s|\leq1\}$}
The qubit <density operators> $\rho=(I+\mathbf s\cdot\boldsymbol\sigma)/2$ correspond exactly to the closed unit ball: their <eigenvalues> are $(1\pm|\mathbf s|)/2$, so positivity is equivalent to $|\mathbf s|\leq1$. 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.
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