= Repeated weak-rotation bomb-test efficiency
{title2=$P_N=\frac{q}{1+q}(1-q^{2N}),\quad q=1-p$}
For an <Elitzur-Vaidman bomb tester> using a <rotation> and its inverse, let $p$ be the <probability> of entering the absorbing path and $q=1-p$. Conditional on a live absorber, one trial has explosion <probability> $p$, successful safe identification <probability> $pq$, and inconclusive <probability> $q^2$. The inconclusive <projective measurement> resets the input, so summing a <geometric series> gives the displayed success <probability> after at most $N$ trials. Its limit is $q/(1+q)$, approaching one half as $p$ tends to zero through positive values. Exactly zero coupling produces no information.
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