Peres, p47 has an thought experiment where:(adsbygoogle = window.adsbygoogle || []).push({});

1 million linearly polarized photons in the x-direction and another million polarized in the y-direction are placed in a box where they travel in the +- z direction with no change in the polarizations. No record is kept of the order in which they are introduced, only the total numbers are recorded. A second box repeats this but with circularly polarized photons - a million clockwise and a million counter-clockwise. You are given one of the boxes at random and test each photon with a perfect detector. what is the probability of making a wrong guess?

The author lists it as approximately [itex](4\pi * 10^6)^{-1/2}[/itex]

My thinking is that testing for linear vs. circular polarization are non-complementary, pure states so if you get the linear box and set up a test for circular polarization, then you will get a random answer - a 50/50 chance of being either clockwise or counterclockwise. If you test for linear polarization on the linear box with a perfect detector you will recover the original polarization.

So I get the probability of making a wrong guess of which box you received is just smidgen under 50% : the prob of getting the right box less the prob of getting the wrong box and getting a random outcome where exactly 1,000,000 photons are detected in one of the polarized states.

Obviously, I am way off in my thinking - where am I going wrong here?

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# Photon Polarization

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