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At first, I'm not a physicist, I'm a programmer, and English is not my native language, that's why something in my text might sound not quite right.

While researching various quantum entanglement experiments (just a hobby) I found one great article written by supposedly acknowledged physicist Nick Herbert. I don't know much about him, thus if his article is entirely wrong, tell me and I'll close the topic and be done with it.

Here you go:

http://quantumtantra.com/bell2.html

At first I tried to implement his so called SPOT detector in a simple C# program to simulate how it would work with normal "local" behavior. I'm using a random generator and it seems sufficient to achieve statistically meaningful results, which match my expectations. But still there are some things which I'm not sure about and I'd like to ask for help.

Here are my questions:

1) the SPOT is built the way that it detects if a photon is polarized vertically (result is 1) or horizontally (result is 0). Now, if we detect a stream of vertically polarized photons with the SPOT detector and then turn it 45 degrees, we should detect no photons at all because all of them are vertically polarized and there should be no 45 degrees polarized photons. In this case, the SPOT should just completely ignore the photon, and it goes by undetected at all. But Nick Herbert says:

It seems to me, Nick forgot some important details. I have a vague guess what it might be but it would be great if someone could confirm my suspicions with a definite and simple answer: We calibrate SPOT by aiming it at a source of Vertically polarized light, turning the tube till one detector fires all the time, calling that detector "1" and moving SPOT's little red arrow so that it points vertically. ... If we turn SPOT by 90 degrees while viewing the same Vertically polarized light beam, its output will look like this: ...0, 0, 0, 0, 0, 0, 0... which we interpret to mean that SPOT is looking at a beam of photons that are polarized exactly orthogonal to the direction SPOT's arrow is pointing.If we turn SPOT so its arrow points at 45 degrees--half-way between Vertical and Horizontal, his output will look like this: ...0, 1, 1, 0, 1, 0, 0, 0, 1... a seemingly random 50/50 sequence of zeros and ones.

How does the SPOT detector decide whether a photon is vertically or horizontally polarized and how can it detect any of the vertically polarized photons if the SPOT is turned by 45 degrees?

For example, I have the SPOT turned 0 degrees. In what range of degrees a photon will be detected as being horizontally polarized and in what range it will be detected if vertically polarized?

2) To go on with his simplified experiment, Nick says:

What exactly is polarization of these phase-entangled photons in the scope of this particular experiment? Do I understand correctly, that they are both polarized completely randomly so we don't know the polarization beforehand? In operation the Kansas City light source emits pairs of phase-entangled photons, sending one photon of the pair to Anaheim and the other photon to Baltimore.

3) There is a nice graph with values for non-local results of the experiment in Nick's article and he explains it as follows:

But he does not explain one important detail - Zero angle = 100% Match.

Right angle = 0% Match.

Angle between Zero and Right angle = Cosine Squared (Angle) Match.why the value is Cosine Squared (Angle)?

Can this formula be demonstrated using simple math example and statistics without referring to quantum mechanics formulas? If we assume that (in a simplified understanding of quantum mechanics) the rotation of Alice's SPOT has effect on results detected by Bob's SPOT (and vice versa - who ever of them manages to detect the entangled photon first), then how the difference

turns out to be Cosine Squared (Angle)?

For example, Alice has her SPOT at 0 degrees, and Bob has at 30 degrees. Then there comes a photon and Alice's detector gets it first. From the idea of quantum entanglement we know that at this very moment the polarization state of the other twin photon becomes determined. Then Bob receives this entangled photon. Now if they both continue receiving their photons with their detector difference of 30 degrees, how then Cosine Squared (Angle) formula relates to their results?

4) Is Nick's simplified experiment with measuring the difference just between two detectors set to 0 and 60 degree angles really good enough to prove Bell's theorem and "non-locality" of quantum entanglement? If used in real life, will it give close enough results to the values mentioned by Nick (25% mismatch at 30 degrees and 75% mismatch at 60 degrees)?

Nick's example seems much simpler than all the others I see around because other experiments often talk about three various detector positions or about spins instead of polarization, thus making things more confusing than they are presented by Nick Herbert.

Thank you in advance for your help.

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# Help me understand a simplified CHSH (Bell's) experiment

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