What is the Difference Between Locality and Separability in Quantum Mechanics?

[DrChinese]

Photons from entangled photon source are transported to three sites where measurements are made via optical fibre. ... If we want to be careful we should check that rotating polarizers in the same direction (clockwise) by the same amount still gives us maximum (to see that our choice of clockwise for all three sites is correct).

You are switching between contexts, and that is making the discussion difficult to follow.

The 3 photon case, as I mentioned earlier, is DIFFERENT than the 2 photon case. ALL STANDARD BELL TESTS are actually performed with 2 photons - Alice and Bob. The fair sampling assumption relates to the universe of Alice+Bob pairs. Your scenario - as described - does not match theory or experiment I am familiar with.

Yes, you can entangle 3 photons and send them to 3 detectors. Yes, you can calibrate them for maximum correlation. But they will not follow the cos^2 theta rule you describe, and the reason for that has nothing to do with fair sampling. As I mentioned, the 3 photon case is more complicated than the 2 photon case.

For example: there is the GHZ scenario (groups of 3 photons), which is actually a separate theoretical proof than the Bell inequality (groups of 2 photons).

 

[DrChinese]

If we have signal from A, B and C we record A-B, B-C and C-A coincidences.

So we do not record A-B-C coincidences you was referring to but nonetheless we find correlations in all three detectors.

These seem contradictory. Are you imagining 3 detectors, and sometimes all three fire due to 3 entangled photons? Because this is not what is referred to as the Bell state.

And how is any of this related to fair sampling? As has been mentioned, fair sampling critics assert that detectors are MORE likely to detect photons that will violate Bell's Inequality than those that will not. That being an experimental issue that is rapidly disappearing as technology improves - and guess what? As experimental detection effeciency increases, violation of the Inequalities do NOT decrease as the critics propose. (Of course, those same critics assert that there would be NO violation if all pairs were sampled.)

 

[zonde]

Yes, you can entangle 3 photons and send them to 3 detectors. Yes, you can calibrate them for maximum correlation. But they will not follow the cos^2 theta rule you describe, and the reason for that has nothing to do with fair sampling.

Are you saying that in this case picking arbitrary two detectors and finding out correlation between them it will differ from cos^2(theta) value?

These seem contradictory. Are you imagining 3 detectors, and sometimes all three fire due to 3 entangled photons?

I don't get it. Where do you see contradiction?

As experimental detection effeciency increases, violation of the Inequalities do NOT decrease as the critics propose. (Of course, those same critics assert that there would be NO violation if all pairs were sampled.)

Do you speak about photon polarization experiments or about completely different experiments? Because as far as I know photon polarization experiments are carried out using the same 10% efficiency even if technology allows higher detection rates with reduced noise.