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# Elitzur-Vaidman bomb-tester

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 bomb-tester was constructed and successfully tested by Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog in 1994.Paul Kwiat 1994] 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, some of which are duds. The bombs are triggered by a single photon. Usable bombs will absorb the photon and detonate. Dud bombs will not absorb the photon. 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.Keith Bowden (k.bowden@physics.bbk.ac.uk)]

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.David Harrison] On one path, place a bomb (B) for the photon to encounter. If the bomb is working, then the photon is absorbed and triggers the bomb. If the bomb is non-functional, 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 interacts with it, causing the wave function to collapse and returning the photon to a deterministic state.

One conceptual way to understand this phenomenon is through the Everett many-worlds interpretation. The superposition behavior is analogous to having parallel worlds for all possible states of the photon. Therefore, when a photon encounters a half-silvered mirror, in one world it passes through, and in another world it reflects off the mirror. These two worlds are completely separate except for the particle in superposition. The photon that passes through the mirror in one world may interact with the photon that reflected off the mirror in the other world. The photons may continue to interact with each other until an observer from one world measures the photon's state.

A step-by-step explanation of what happens:

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.
* Upon meeting the observer (the bomb), the wave function collapses and the photon must be either on the lower route or on the upper route, but not both.
* 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 lower route is not taken, there will be no interference effect at the 2nd half-silvered mirror.
** The photon on the upper route now both (i) passes through the 2nd half-silvered mirror and (ii) is reflected.
** Upon meeting further observers (detector C and D), the wave function collapses again and the photon must be either at detector C or at detector D, but not both.

Therefore, there are only three observable results:

# The bomb explodes.
# The bomb does not explode and only detector (C) detects the photon. The bomb must be usable.
# 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. On average, this will identify all of the dud bombs, explode two thirds of the usable bombs, and identify one third of the usable bombs without detonating them.

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.

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. [Kwiat: Tao of Interaction-Free Measurements] (This reference is not currently available. Try http://www.nature.com/nature/journal/v439/n7079/full/nature04523.html#B1instead.) 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.

This experiment is philosophically significant because it determines the answer to a counterfactual question: "What would happen were the photon to pass through the bomb sensor?". The answer is either: "the bomb works, the photon was observed, and the bomb will explode", or "the bomb is a dud, the photon was not observed, and the photon passes through unimpeded".

If we were actually to perform the measurement, any bomb would actually explode. But here the answer to the question "what would happen" is determined "without" the bomb going off. This provides an example of an experimental method to answer a counterfactual question.

To determine the answer to a counterfactual had long been assumed to be impossible in philosophy.

ee also

*Counterfactual definiteness
*Interaction-free measurement

Notes

References

*cite journal|author=P. G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich|title=Interaction-free Measurement|journal=Phys. Rev. Lett.|volume=74|pages=4763|year=1995|doi=10.1103/PhysRevLett.74.4763
*cite web| url=http://www.quantum.univie.ac.at/publications/pdffiles/1994-08.pdf
author=Paul G. Kwiat
coauthors=H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich
title=Experimental realization of "interaction-free" measurements
format=pdf
accessdate=2007-12-08

*cite web| url=http://www.p23.lanl.gov/Quantum/kwiat/ifm-folder/ifmtext.html
archiveurl=http://web.archive.org/web/19990222174102/www.p23.lanl.gov/Quantum/kwiat/ifm-folder/ifmtext.html
archivedate=1999-02-21
author=Paul G. Kwiat
title=Tao of Interaction-Free Measurements
format=html
accessdate=2007-12-08

*cite web| url=http://nonlocal.com/quantum-d/v2/kbowden_03-15-97.html
author=Keith Bowden
title=Can Schrodinger's Cat Collapse the Wavefunction?
accessdate=2007-12-08
date=1997-03-15

*cite web| url=http://www.upscale.utoronto.ca/GeneralInterest/Harrison/MachZehnder/MachZehnder.html
author=David M. Harrison
title=Mach-Zehnder Interferometer
accessdate=2007-12-08
date=2005-08-17

*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.
*cite journal|author=G.S. Paraoanu|title=Interaction-free Measurement|journal=Phys. Rev. Lett.|volume=97|pages=180406|year=2006|doi=10.1103/PhysRevLett.97.180406

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