For a single photon, its polarization can be a superposition of two orthogonal bases (e.g. horizontal or vertical). However, as I understand, once it has been measured, it must collapse into one of the possible bases. So does that mean that once a photon hits a polarizing beam splitter its wave function collapses? After all, there are only two options: either the photon goes through or it does not. Assuming the original polarization was 45 degrees the, the probability for both events is 50%. Or, if we do not measure which path it takes, does it simply exist in a superposition of the two possible paths, meaning that we have not affected the wave function.
Secondly, I am a bit confused by the idea that once we make a measurement the photon must collapse into one of the possible base states. For example, if we measure that the photon was reflected by the beam splitter, we might conclude that it is either horizontally or vertically polarized (depending on the configuration of the beam splitter) but it could very well be simply 45 degrees of polarization.