= Iterated phase-flip channel
{title2=$\epsilon_n=[1-(1-2\epsilon)^n]/2$}
Independent successive applications of the <phase-flip channel> $D_\epsilon(\rho)=(1-\epsilon)\rho+\epsilon Z\rho Z$ preserve diagonal entries and multiply off-diagonal entries by $(1-2\epsilon)^n$. Hence $D_\epsilon^n=D_{\epsilon_n}$ with the displayed parameter, for nonnegative integers $n$. If $0<\epsilon<1/2$, the limit is the <completely dephasing channel>, equivalently a <nonselective projective measurement> in the <computational basis>. A time-interval law can be iterated this way only under the memoryless composition assumption.
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