= Depolarizing noise weight above one
{title2=$\Phi_q(\rho)=(1-q)\rho+qI/2,\quad0\leq q\leq4/3$}
The displayed qubit <quantum channel> is completely positive for $0\leq q\leq4/3$. Indeed its <Pauli channel> probabilities are $1-3q/4$ for the identity and $q/4$ for each nonidentity Pauli operator. In the range $q>1$ the coefficient $1-q$ is negative, so the displayed expression is not a convex mixture of the unchanged and maximally mixed states, even though the Pauli representation is a valid <random unitary channel>. Its <Bloch vector> is contracted and reversed by the factor $1-q$. The <Holevo capacity of a qubit depolarizing channel> remains $1-h_2(q/2)$ throughout this interval.
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