So I’ve been quite busy which I why I haven’t yet responded to the comments on my previous post, but now it’s Saturday! Realizing that not everyone knows the Elitzur-Vaidman bomb test, I’ll give a full description to further discussion along!

Imagine a simplified Mach-Zender interferometer in which a beam of light passes through a beamsplitter (usually some kind of crystal) becoming two beams of light. The two beams bounce off a couple of mirrors and meet again at a second beamsplitter, each splitting again with some from each merging. Thus, in the diagram below, the yellow beams are each a mixture of the green and red beams (sort of).

If you set up the beamsplitter’s properly, you can create interference such that detector D0 always registers photons and D1 never does. In other words, the probability that D0 detects a photon is 1 and the probability that D1 does is 0. This is because we have set it up such that we have constructive interference leading to D0 and destructive interference leading to D1.

Suppose now that we stick our hand in the path of the green beam such that the photons are absorbed by our hand. This destroys any interference effects. Any single photon entering the device at the beginning, then, has a 50-50 chance of hitting our hand. If it doesn’t, it goes through the red beam and then has an equal chance of hitting D0 or D1. So the probabilities are

- Photon reaches D0 = 1/4
- Photon reaches D1 = 1/4
- Photon reaches hand = 1/2

Notice that by blocking the green beam with a hand, we have actually *increased* the probability that the photon reaches D1.

Now suppose there is a factory that produces bombs triggered by a single photon of light. Because of manufacturing defects, though, some come off the assembly line without working triggers. Photons passing through these wouldn’t do anything and the bombs would be labeled as duds. How do the factory managers, however, tell if some of the bombs are in working order without triggering them? They want at least *some* working bombs when they’re done otherwise the Army won’t be too pleased.

They do it using the above Mach-Zender interferometer that is preset to always produce constructive interference at D0 and destructive at D1. Instead of placing a hand in the green beam, a bomb (actually its trigger) is placed there. The trigger acts like a photon detector and the results will be

Bomb is a dud

- Photon reaches D0 = 1
- Photon reaches D1 = 0
- Bomb explodes = 0

Bomb is working

- Photon reaches D0 = 1/4
- Photon reaches D1 = 1/4
- Bomb explodes = 1/2

Now put a bomb fresh off the assembly line into the device (and back away – far, far away). If the bomb explodes, it was in working order but has now been wasted (the cost of quality control under such conditions is losing a few bombs). If the photon is detected by D0, the test is inconclusive and can be run again (if, after many repeated trials, the photon keeps showing up at D0, the bomb is probably a dud). But if the photon *ever* reaches D1 – which is should do 25% of the time – then the managers know that the unexploded bomb is in working order *even though the bomb never detects the passage of the photon*!

Presumably someone out there has done a calculation to figure out the maximum percentage of usable bombs one can hope to get out of this by repeating the D0 tests. I don’t know what the answer is but it’s not quite as simple as it looks since it is not clear exactly what percentage of *total* photons is detected at D0 (remember, it’s only 1/4 if the bombs are all working!).