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Avshalom Elitzur and Lev Vaidman proposed detecting an absorbing object through a Mach-Zehnder interferometer adjusted so that destructive interference makes one output dark. Blocking one arm permits a photon to reach that previously dark output. In that successful outcome the photon is detected rather than absorbed by the object, yet its detection establishes that the arm was obstructed. For the balanced arrangement, the success probability is $1/4$ per trial; absorption still occurs with probability $1/2$.^[ref]

David Albert, Yakir Aharonov and Lev Vaidman introduced the weak value associated with preparing $|i⟩$ and selecting a later outcome $|f⟩$: $A_w=⟨f|A|i⟩/⟨f|i⟩$ when the denominator is nonzero. A sufficiently weak coupling followed by this selection can produce a conditional average pointer shift outside the eigenvalue range of the measured observable. This concerns the statistics of selected weak measurements; it does not assert that a single projective quantum measurement returns an otherwise forbidden eigenvalue.^[ref]

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 Avshalom Elitzur, Lev Vaidman showed how an obstructed arm changes the possible outputs of a Mach-Zehnder interferometer. A click in an output forbidden by destructive interference when both arms are open can reveal the obstruction even though the detected photon was not absorbed there. The proposal makes the distinction between a successful conditional quantum measurement and an entire procedure particularly clear: other trials can absorb the photon or give an inconclusive result.^[ref]

Published in Foundations of Physics 23, pp. 987–997 (July 1993). Author byline: Avshalom C. Elitzur and Lev Vaidman. Public author preprint: arxiv.org/abs/hep-th/9305002v2; full text: arxiv.org/pdf/hep-th/9305002v2.