Linear to Circular Polarisation Questions

[StevieTNZ]

I have some questions referring to wave plates.

We have an entangled pair of photons as |H>|V> - |V>|H> and both go through 22.5 degree orientated half-wave plates. |H> is converted to |45> and |V> is converted to |135> (so the description is now |45>|135> - |135>|45>). So inputting the polarisation |H> (regardless if the photon is in the possibility being |H> polarised, or if the photon is actually |H> polarised) into the half wave plate does not produce the output |45>-|135> (a superposition)? Are those two statements correct?

However I am a bit confused when converting photons, either in superposition or in definite polarisation, to the |R> and |L> axis. If we inputted a definite |H> polarised photon into a quarter wave plate orientated at 45 degrees (if that is the correct orientation and wave plate to convert from |H> or |V> to circular polarisation), would the output be a superposed state of |R> +|L>? With |V> polarised photon it would be –i|R>-|L> [the same would apply if the photon was in a superposition of being either |H> or |V>, and one of the superposition terms, |V>, would produce the same wave plate output -i|R>-|L>].

Likewise, if we measure (using wave plates and PBS orientated in the H/V basis) the entangled state |H>|V> - |V>|H> in the R/L basis, would the output of wave plates be for the first |H> be |R> + |L>, the
|V> = -i|R>-|L>, then for the 2nd half of the entangled state (starting with -|V>), - -i|R>-|L> and the |H> =|R>+|L>. If we expanded over these terms, could we only find one photon as |R> and the other as |L>, or would it be both |R>|R> or |L>|L>, or both of those possibilities?

I hope the above questions are clear. If not, please let me know.

 

[kith]

Maybe this helps. In the Jones formalism, the only difference between linear polarization vectors and circular (or elliptical) polarization vectors is that the latter include complex components. So if you know how optical elements act on linear polarization you should be able to deduce their effect also on other polarizations.