Elitzur-Vaidman bomb-testing problem

From Wikipedia, the free encyclopedia

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 bomb-testing problem is illustrated by use of the following analogy: Consider a collection of bombs from some dubious source, so that it is not certain which, and indeed how many, of the bombs are duds. Say we need to know which are usable bombs. Clearly we can accumulate dud bombs by throwing the bombs, one by one, at a wall, and collecting the ones that do not explode. Unfortunately this process does not work in reverse; the only way of finding out which bombs are usable destroys them. Just to make the problem a little harder we will specify that the trigger of each bomb is sensitive to a single photon. Specifically, the bombs either absorb the photon and explode, or transmit the photon and are duds. It is, in principle, impossible to identify usable bombs by any nondestructive classical process. However, through a mode of observation known as counterfactual measurement which relies on quantum mechanics, we can solve this problem.

We set up the following experiment: We start with a Mach-Zehnder interferometer and modify the light source (A) so it emits a single photon. When this photon reaches a half-silvered plane mirror, it can pass through or can be reflected, with an equal chance at either. Under quantum mechanics, the interference effects of all possible paths taken are still noticed by this photon, even though only one path is physically taken. Thus, we have quantum superposition whereby the photon has both passed through the half-silvered mirror and been reflected at an angle, but we still have only one photon. On one path, we 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. The rest of the system is set up exactly like a Mach-Zehnder interferometer.

• If the bomb is a dud:
  • The photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected.
  • Because the bomb is a dud, the photon traveling in the lower route is not absorbed.
  • The system thus reduces to the basic Mach-Zehnder apparatus with no sample, which guarantees that constructive interference occurs between the paths horizontally exiting towards (D) and destructive interference occurs between the paths vertically exiting towards (C).
  • Therefore, whichever intermediate path the photon actually took is irrelevant, the only exiting path is horizontal and the detector at (D) notices the photon, and the one at (C) does not.
• Otherwise:
  • Logically, the bomb is real.
  • The photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected
  • If the photon really took the lower route:
    • Because the bomb is real, this photon triggers the bomb and it explodes.
  • Otherwise:
    • Logically, the photon really took the upper route.
    • The effects of the photon taking the lower route are not noticed because it's not possible for a photon on the lower route to pass through a real bomb without being absorbed, hence the lower route photon could not possibly continue to interfere with the one traveling on the upper route.
    • The photon on the upper-route now both (i) passes through the 2nd half-silvered mirror and (ii) is reflected.
    • If the photon really was reflected:
      • The detector at (C) notices, the one at (D) does not.
    • Otherwise:
      • Logically, the photon passed through.
      • The detector at (D) notices, and the one at (C) does not.

Therefore, with the above theoretical behavior, we can conclude which If-branch/branches was/were taken, ultimately revealing whether the bomb was real or not, based on the observed effects which must be one of the following:

1. The bomb exploded. Obviously it was real.
2. The bomb does not explode and only (C) received anything. Logically, the bomb must be real.
3. The bomb does not explode and only (D) received anything. No information was learned. Either the bomb is a dud, or it is real.

We run the experiment many times if the ambiguous 3rd observation is made. Sometimes good bombs explode, but at other times we are guaranteed of finding a good bomb without wasting it.

In 1994, Zeilinger actually performed an equivalent of the above experiment. 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?