Measurement of the state of polarization of single photons and a beam of light How is the the state of polarization of a beam of light measured?
How is the state of polarization of a single photon measured?
 A: The answer is essentially the same regardless of whether you have a classical light beam or an ensemble of beams all of which contain a single photon with the same pure quantum state of polarization. (If you only had a single such photon, then you would be provably unable to find its polarization state.)
The field of polarimetry can have lots of complicated stuff in it, particularly if you want to have a reliable black-box imaging polarimeter, but the basics are simple enough: they reduce to measuring the Stokes parameters of the beam. To do this in full, you require six independent measurements: you measure the intensity of the beam, after it is put through


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*a linear polarizer, at 0° to some reference axis,

*a linear polarizer, at 90° to the reference axis,

*a linear polarizer, at 45° to the reference axis,

*a linear polarizer, at 135° to the reference axis,

*a quarter-wave plate with its slow axis at 0° to the reference axis, plus a linear polarizer at 45° to the reference axis, and

*a quarter-wave plate with its slow axis at 0° to the reference axis, plus a linear polarizer at 135° to the reference axis. (If this and the above one sound complicated, just get a pair of 3D glasses from your nearest cinema.)


This provides enough information to figure out the polarization state of the light. There are then multiple ways to piece it back together, depending on what form you need, which are explained in the Wikipedia page linked above or in any optics textbook.
For the single-photon ensemble, the above lets you determine the wave mode that the photon is in. Photons are, fundamentally, levels of excitation of those modes, i.e. states of how excited each mode is, so the single-photon nature of a beam comes out in its counting statistics and similar observables. As such, the polarimetry itself can be performed with the same method as a classical beam (which just has different counting statistics over the same mode).
A: Light is a type of electromagnetic radiation. The simplest form to understand is $E_0\cos(\omega t) \hat{p}$. Where  $\hat{p}$ is the polarization of the light, and $\omega$ is the frequency of the light. Visible light is classified as light that are the frequencies in which $\omega$ 430–770 THz. If you put such a light-field in a photodetector, you will not be able to see the time dynamics, because (typically) photodetectors are not fast enough to see these fast oscillations (and instead average out to a DC term, since detectors measure the intensity of the light, which is $\cos^2(\omega t) = \frac{1}{2}$). Therefore, if you want to see the direction in which our light wiggles, we have to resort to something else. 
The easiest way experimentally to measure the polarization of light is with a polarizer. A polarizer is a type of material in which the output intensity of the light is: $I = I_0 cos^2 \theta$.  By putting a photo-detector after a polarizer, we can choose an angle such that the photo-detector's measured value is the highest. If all of the light goes through, then your light is linear along the axis associated with the polarizer. If there does not exist such an angle, then your light is circular or elliptical. If you can find an angle on a quarter wave plate such that all of the light emits out of the polarizer, then your light was circular. If this does not exist, then your light is elliptical (which is a fancy way of saying that there's some non-quarter-wave-long phase shift between your polarizations). 
For single photons, simply perform the same experiment as before, but replace a photo-diode with a single-photon-detector. The angle that gives the most "clicks" is the correct polarization of the input photon source. 
