Elitzur-Vaidman bomb-testing problem

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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. It employs a Mach-Zehnder interferometer for ascertaining whether a measurement has taken place.

The following example illustrates the bomb-testing problem: Consider a collection of bombs which contains some duds. The problem is how to separate the usable bombs from the duds. A bomb sorter could accumulate dud bombs by attempting to detonate each one. Unfortunately, this process destroys all the usable bombs.

A solution is for the sorter to use a mode of observation known as counterfactual measurement, which relies on principles of quantum mechanics.

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. On one path, place a bomb (B) for the photon to encounter. If the bomb is working, then the photon gets absorbed, else the photon will pass through the dud bomb unaffected.

Due to the effects of quantum superposition, the interference effects of all possible paths taken are still noticed by the photon, even though only one path is actually taken.

If the bomb is a dud:

• The photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected.
• The bomb will not absorb a photon, and so the lower route is a possible path to the point of interference.
• The system reduces to the basic Mach-Zehnder apparatus with no sample, in which constructive interference occurs along the path horizontally exiting towards (D) and destructive interference occurs along the path vertically exiting towards (C).
• Therefore, the detector at (D) will detect a photon, and the detector at (C) will not.

If the bomb is usable:

• The photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected.
• If the photon actually takes the lower route:
  • Because the bomb is usable, this photon triggers the bomb and it explodes.
• If the photon actually takes the upper route:
  • Since the bomb would absorb any photon which took the lower route, the lower route is not a possible path to the point of interference. Thus, there will be no interference effect.
  • The photon on the upper-route now either passes through the 2nd half-silvered mirror or is reflected.
  • If the photon is reflected:
    • The detector at (C) will detect a photon, and the detector at (D) will not.
  • If the photon passes through:
    • The detector at (D) will detect a photon, and the detector at (C) will not.

Therefore, there are only three observable results:

1. The bomb explodes.
2. The bomb does not explode and only detector (C) detects the photon. The bomb must be usable.
3. The bomb does not explode and only detector (D) detects the photon. It is possible that the bomb is usable or that it is a dud.

In the case of the third observation, the experiment may be repeated to see if the bomb will explode or if detector (C) will detect a photon.

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 [1]. In 1996, Kwiat et al have devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one.

[edit] Further reading

• Elitzur A. C. and Vaidman L. (1993). Quantum mechanical interaction-free measurements. Found. Phys. 23, 987-97.

• Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of Physics. Jonathan Cape, London.

[edit] See also

• Interaction-free measurement
• Can Schrodinger's Cat Collapse the Wavefunction?