# Elitzur–Vaidman bomb tester

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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

Start with a Mach–Zehnder interferometer and a light source which emits single photons. When a photon emitted by the light source reaches a half-silvered plane mirror, it has equal chances of passing through or reflecting.[4] On one path, place a bomb (B) for the photon to encounter. If the bomb has a sensor, then the photon is absorbed and triggers the bomb. If the bomb has no sensor, the photon will pass through the dud bomb unaffected.

When a photon's state is non-deterministically altered, such as interacting with a half-silvered mirror where it non-deterministically passes through or is reflected, the photon undergoes quantum superposition, whereby it takes on all possible states and can interact with itself. This phenomenon continues until an 'observer' (detector) interacts with it, causing the wave function to collapse and returning the photon to a deterministic state.

### Step-by-step explanation

• After being emitted, the photon 'probability' wave will both pass through the first 50% reflecting mirror (take the lower-route) and be reflected (take the upper-route). Both waves are reflected/transmitted again in the second 50% reflecting mirror (upper-right), so both detectors receive 50% of the 'lower' and 'upper' wave. The interferometer is aligned so the interference of both waves is destructive for detector C and constructive for detector D, when no bomb is placed. Then all photons will be detected by D and none by C. Now a bomb is placed:

If the bomb is a dud:

• The situation is as described above, without a bomb. Detector C will not detect photons.

If the bomb is usable:

• If the photon particle takes the lower route:
• Because the bomb is usable, the photon is absorbed and triggers the bomb, which explodes.
• If the photon particle takes the upper route:
• The bomb blocks the 'lower' wave, so there is no interference effect anymore at the second 50% reflecting mirror. Now there is a 50% chance of detecting the photon in detector C and D (but not both).

Thus we can state that if a photon is detected in C, there must have been a working detector at B.

With this process, 25% of the usable bombs can be identified as usable without being consumed.[1] whilst 50% of the usable bombs will be consumed and 25% remain 'unknown'. By repeating the process with the 'unknowns', the ratio of surviving, identified, usable bombs approaches 33% of the initial population of usable bombs. 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.[5] ( 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).

## References

1. ^ a b Elitzur, Avshalom C.; Lev Vaidman (1993). "Quantum mechanical interaction-free measurements". Foundations of Physics 23 (7): 987–997. arXiv:hep-th/9305002. Bibcode:1993FoPh...23..987E. doi:10.1007/BF00736012. Retrieved 2014-04-01.
2. ^ a b Paul G. Kwiat; H. Weinfurter; T. Herzog; A. Zeilinger; M. Kasevich (1994). "Experimental realization of "interaction-free" measurements" (pdf). Retrieved 2012-05-07.
3. ^ Keith Bowden (1997-03-15). "Can Schrodinger's Cat Collapse the Wavefunction?". Retrieved 2007-12-08.
4. ^ David M. Harrison (2005-08-17). "Mach–Zehnder Interferometer". Retrieved 2007-12-08.
5. ^ Tao of Interaction-Free Measurements, Paul Kwiat