# Elitzur–Vaidman bomb tester

Bomb-testing problem diagram. A - photon emitter, B - bomb to be tested, C,D - photon detectors. Mirrors in the lower left and upper right corners are half-silvered.

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.[1] 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.[2] It employs a Mach–Zehnder interferometer for ascertaining whether a measurement has taken place.

## Problem

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.[3] Thus, the dud bomb will not detect the photon and will not detonate. Is it possible to detect if 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?

## Solution

A bomb is placed on one path of a Mach–Zehnder interferometer with a single-photon light source; if the bomb is live then the photon is absorbed and triggers the bomb, else the photon will pass through the dud bomb unaffected. When a photon passes through the half-silvered plane mirror of the interferometer, the photon exists in a quantum superposition containing all its possible outcomes, which interact with each other. In this case the photon is both transmitted and reflected through both paths of the interferometer. The interference from both routes will alter the probability of detection at either detector (C and D). This continues until an observer (the detector) causes the wave function to collapse and the photon takes a single one of the states.

If the interferometer is aligned so the interference is constructive at C and destructive at D, then photons will only ever be detected at C. If a bomb is now placed in the lower (transmitted) path then it will block this route and so destroy the interference pattern i.e. the photon will have a 50% chance of being detected in either (but never both) detectors. Thus if a photon is detected in D there must be a live, photon-absorbing bomb. If a photon is detected at C then the bomb may be either live or dud.

However once a detection has been made the superposition is destroyed and the photon path becomes certain. Since there is a 50% chance the photon was transmitted through the lower path, there is a 50% chance a detection will trigger any live bombs. With this process 25% of live bombs can be identified without being detonated,[1] 50% will be detonated and 25% remain uncertain. By repeating the process with the unknowns, the ratio of identified, non-detonated live bombs approaches 33% of the initial population. See Experiments section below for a modified experiment that can identify the usable bombs with a yield rate approaching 100%.

## Experiments

In 1994, Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog actually performed an equivalent of the above experiment, proving interaction-free measurements are indeed possible.[2]

In 1996, Kwiat et al. devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one. The key idea is to split a fraction of the photon beam into a large number of beams of very small amplitude, and reflect all of them off the mirror, recombining them with the original beam afterwards.[4] ( See also http://www.nature.com/nature/journal/v439/n7079/full/nature04523.html#B1 .) It can also be argued that this revised construction is simply equivalent to a resonant cavity and the result looks much less shocking in this language. See Watanabe and Inoue (2000).