Photon Polarization I'm having some issues to understand some concepts related with the polarization of photons, especifically the 'pratical' diference between a superposition of two polarizations (let's say $|H\rangle + |V\rangle$) and a single polarization ($|H\rangle$ or $|V\rangle$). I've read a topic similiar (Can we determine whether a photon's polarization is fixed or in a superposition), but this is not exactly what I'm trying to understand. My question: it's possible to create a experimental arrangement capable of making a diference between a superposition state or a single polarized state? Would it be diferent if I had a source who provides me with both $|H\rangle$ and $|V\rangle$ in a known rate? That is: can we use a arrangement of polarizers, mirrors, beam spliters and detectores to find out wether a source is providing these states? My original idea is to use two ortogonal polarizers in 45 degrees but I'm having some issues to understand the principles behind the situation.
 A: The basic idea is you will have to have multiple photons prepared identically, and make multiple polarization measurements (using a polarization filter) to be able to distinguish between $|H\rangle$ and $|H\rangle+|V\rangle$. One way I can do it would be to get a polarization filter and only allow vertically polarized light through. So I'm looking for the presence of a $|V\rangle$ state. If I make 10,000 measurements and I find no component $|V\rangle$ (all my results come back negative, i.e. no photons were let through the polarizer) then I am relatively certain the state was $|H\rangle$ to begin with and not $|H\rangle+|V\rangle$. If the original state was the latter, I would expect 50% of my measurements to come back positive. (If the original state was $|V\rangle$ then all 10,000 of my results should have come back positive). By building out these probabilities, I can figure out what state the photon was in originally. 
This answers the question of "the photon was known to be in some pure state, how can I determine what that pure state was?". Interestingly though, when one does measure the vertical polarization, for photons which do pass through the polarizer, their state is now changed to be exactly $|V\rangle$. So say a photon starts in state $|H\rangle+|V\rangle$ and you measure $V$, then for photons that pass through your polarizer, their state is now $|V\rangle$ and NOT $|H\rangle+|V\rangle$. By measuring the state, you have changed the state (see the joke in Futurama about a "quantum finish" in a horse race). So, if one wants a bunch of $|V\rangle$ state photons, one can merely pass a bunch of randomly prepared photons through an (idealized) vertical polarizer and they will end up in that state. If one wants a bunch of $|H\rangle+|V\rangle$ photons, one can pass it through a (45$^\circ$) diagonally polarized filter to accomplish that.     
