= Bloch-vector map of amplitude damping
{c}
{title2=$\mathbf s\mapsto(\sqrt{1-p}s_x,\sqrt{1-p}s_y,p+(1-p)s_z)$}
Applying the <amplitude damping channel> to the <Bloch vector> form of a qubit <density operator> gives an affine map. Transverse components contract by $\sqrt{1-p}$; the longitudinal component contracts by $1-p$ and shifts toward the ground-state north pole. Reading the entries of the output <density operator> proves the map. The displacement distinguishes this channel from centered depolarization.
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