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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.

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.

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