I Photon Bell Experiment, what happens in a single case?

[KeesDeVries]

TL;DR Summary

I am wondering what happens in the case of two engangled photons with a polarization angle of 0 degrees that interact with Alice at 22,5 degrees and Bob at 45 degrees.

I am wondering what happens in the case of 100 entangled photons with a polarization angle of 0 degrees (or 0 and 90) that interact with Alice at 22,5 degrees and Bob at 45 degrees in a Bell Experiment.

Do I get a count of 85 for Alice and 50 for Bob, which means a maximum coincidence count of 65 (50+15).
Or do I get a much higher coincidence count, which means that either Bob's 50 singles count or Alice's 85 singles count or both singles count must differ.

Can anybody point me to research about such an experiment?

 

[DrChinese]

Summary:: I am wondering what happens in the case of two engangled photons with a polarization angle of 0 degrees that interact with Alice at 22,5 degrees and Bob at 45 degrees.

I am wondering what happens in the case of 100 entangled photons with a polarization angle of 0 degrees (or 0 and 90) that interact with Alice at 22,5 degrees and Bob at 45 degrees in a Bell Experiment.

Do I get a count of 85 for Alice and 50 for Bob, which means a maximum coincidence count of 65 (50+15).
Or do I get a much higher coincidence count, which means that either Bob's 50 singles count or Alice's 85 singles count or both singles count must differ.

Can anybody point me to research about such an experiment?

Polarization entangled photons do not work that way.

First, they are not initially polarized at a specific angle. They are in what is called a "superposition".

Second, the Alice stream of 100 photons - by itself - will be a series of + and - (or 0/1) that is random. It will be about 50% + and 50% -. Same for Bob's stream, completely random. This assumes you measure each stream using a polarizing beam splitter (PBS).

Finally, when Alice and Bob match up their results, they will see a coincidence count that is dependent on the angle difference between Alice and Bob's settings. That angle is usually called "theta". The estimate for theta is usually the 1-cos^2(theta) for Type II PDC photons. For a difference of 22.5 degrees, you would see a match rate of 14.6%. For Type I PDC, it would be 85.4%.

 

[KeesDeVries]

Many thanks for your answer.

If I understand your answer correctly, after the beam splitter, the entangled photons are randomly polarized in a superposition of two ( perpendicular ) states? Or there is no polarization, only superposition with the same response to each angle, meaning 50%.

So there is no experiment where they, after the Beam splitter, put a polarizer at 0 degrees for both Bob And Alice, where 50% would pass and after that do the 22,5 and 45 degree test? Or is the entanglement lost after the first polarizer?

 

[vanhees71]

If you have a polarization entangled photon pair (in a Bell state), the single photons are not in a superposition but in a mixture. That's what makes entanglement so interesting and very different from any classical correlation.

 

[KeesDeVries]

Tnx, I think I get it know. For the case I describe Bob wil always get a singles count of 50*0,5 + 50*0,5 =50. Alice wil get 85*0,5 + 15*0,5 = also 50. Now it makes sense to me.