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From what I have understood, if a physical system may be in one of many configurations then the most general state is a combination of all of these possibilities. However, when you measure that physical system, you will get one of these possible states.

I have also read that a photon polarized along the direction $\alpha$ can be written as a superposition of the two states 1) polarization along the x direction and 2) polarization along the y direction. When you measure the photon polarization, you can get a combination of these 2 states (x and y), not only one of the states (x or y). It seems like this explanation of the photon polarization goes against the concept of quantum polarization.

If the explanation is that when you measure, you can also get the superimposed, then how can, say, an electron be in the superimposed state of spin up and down, if you can't measure that electron and get a state of spin up and down at the same time?

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  • $\begingroup$ When the polarization measuring a single photon you have the freedom to choose the axis along which to measure (or more generally the basis, you can for example measure whether the photon is left- or right-handed circularly polarized). But when you do this measurement, you only get one of the answers: along that direction or opposite to that direction and exactly that is the nature of quantum measurement you describe. Where is the discrepancy? $\endgroup$ – Sebastian Riese Jun 8 '18 at 18:24
  • $\begingroup$ but what if the photon polarized along the direction α is written as a superposition of the 2 states: polarization along the x and y direction, the answers are not along that direction or opposite to that direction $\endgroup$ – forpointing Jun 8 '18 at 19:00
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    $\begingroup$ Suppose the y-axis is 0 degrees and the x-axis is 90 degrees. Now suppose your photon is at $\alpha = 45 \text{degrees}$. Now suppose you have a polarizer. You're going to allow the photon to hit the polarizer, and you're going to see whether or not the photon gets through. If you align the polarizer along the x or y axes, then you'll have a 1/2 probability of the photon getting through. If you align the polarizer along the $\alpha$ axis, then the photon will always get through. $\endgroup$ – DanielSank Jun 8 '18 at 20:05
  • $\begingroup$ As @SebastianRiese correctly stated, individual photons are circularly polarized by spin that points forward or backward. Your error is in thinking that photons are linearly polarized in a direction perpendicular to their movement. This is incorrect. A linear polarization of light is created by an equal number of photons circularly polarized in both directions. $\endgroup$ – safesphere Jun 8 '18 at 21:37
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    $\begingroup$ It is a pure state (in the usual sense of the word) that the density matrix is of the form $\rho = \left|\psi\right>\left<\psi\right|$. There is nothing that makes the helicity eigenstates of the photon more real or pure than any other state of the photon. It is just one of the possible bases to measure the polarization in. $\endgroup$ – Sebastian Riese Jun 8 '18 at 22:10

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