Elitzur-Vaidman bomb tester

A photon in a quantum superposition of a safe path and an absorbing path can sometimes certify a live absorber without being absorbed. Recombination is chosen so that one output is impossible if the absorber is absent. A detection at that output is then an unambiguous successful test. The measurement back-action of a surviving live-absorber trial changes the interference pattern.

In 1993, Avshalom Elitzur and Lev Vaidman asked how to identify a working bomb whose sensor would be triggered by even one photon. Their theoretical proposal places the sensor in one arm of a Mach-Zehnder interferometer, adjusted so that destructive interference keeps one detector dark when both arms are unobstructed. A click there can identify a working bomb while leaving it unexploded. The motivation is to obtain information about a fragile object without destroying it; the bomb makes that operational claim explicit without committing to an interpretation of quantum mechanics.^[ref]

With two Hadamard gates as mixers, an unobstructed zero-phase arm gives only port 0 for upper-port incidence. An ideal absorber in arm 1 acts on the intermediate superposition $(|0⟩+|1⟩)/\sqrt{2}$. It absorbs with probability $1/2$; its no-absorption branch is the unnormalized state $|0⟩/\sqrt{2}$. Recombination gives amplitude $1/2$ at each surviving output, so the dark-port success probability is $1/4$. The result assumes a calibrated transparent alternative and an ideal absorber; a dark-port event alone does not establish those apparatus assumptions.

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.