Elitzur–Vaidman bomb-testing problem

In physics, the Elitzur–Vaidman bomb-testing problem is a thought experiment in quantum mechanics, first proposed by Avshalom Elitzur and Lev Vaidman in 1993. An actual experiment demonstrating the solution was constructed and successfully tested by Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog from the University of Innsbruck, Austria and Mark A. Kasevich of Stanford University in 1994. It employs a Mach–Zehnder interferometer to check whether a measurement has taken place.

Consider a collection of bombs, of which some are duds. Suppose each usable (non-dud) bomb has a photon-triggered sensor, which will absorb an incident photon and detonate the bomb. Dud bombs have no sensor, so do not interact with the photons. Thus, the dud bomb will not detect the photon and will not detonate. Is it possible to detect whether a bomb is a non-dud without detonating it? Is it possible to determine that some bombs are non-duds without detonating all of them?

A bomb is placed on the lower path of a Mach–Zehnder interferometer with a single-photon light source. If the photon takes the lower path and the bomb is live, then the photon is absorbed and triggers the bomb; otherwise, if the bomb is a dud, the photon will pass through unaffected.

When a photon passes through a semi-transparent plane mirror, it enters a quantum superposition of all possible outcomes, which interact with each other. The photon is both transmitted and reflected, and takes both paths through the interferometer. The interference from the two routes determines the probability of detection at each detector (C and D). The photon remains in the superposition state until an observer (the bomb's photon sensor, if present, and later the detector at C or D) causes the wave function to collapse and the photon assumes a single one of the states.

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