= 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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