= Repeated amplitude damping limit
{title2=$\mathbf s^{(n)}=((1-p)^{n/2}s_x,(1-p)^{n/2}s_y,1-(1-p)^n(1-s_z))$}
Under repeated identical <amplitude damping channels>, all excited population eventually relaxes to the ground state for any fixed $0<p\leq1$. The <Bloch vector> approaches $(0,0,1)$. For $p=1$ the limit is reached in one action, while $p=0$ is the identity channel and preserves every input. Keeping the zero-damping endpoint separate prevents an incorrect universal relaxation claim.
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