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minkwe derives no mututal information between the outcomes. However the analysis appears incorrect. Consider the case that the settings are 0 and pi/8. Then we have from QM (minkwe gives 1/4 for all of these):

P-- = 0.5 * cos^2(pi/8) = 0.42678

P++ = 0.5 * cos^2(pi/8) = 0.42678

P-+ = 0.5 * sin^2(pi/8) = 0.07322

P+- = 0.5 * sin^2(pi/8) = 0.07322

These produce a non-zero mutual information between the outcomes. All the other angle combinations also yield non-zero mutual information.

I wrote a simulation to prove this. I implemented the quantum joint solution with the standard angle sets, and produced settings (chosen randomly) and outcome sequences (by sampling the distributions with 10000000 samples). I verified that the CHSH is violated and calculated the mutual informations. Here is the result (S means setting, O means outcome, A and B are the two sides):

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Generate sequences using the quantum joint prediction.

Calculate the expectation values and the CHSH metric.

S greater than 2 is a violation of the CHSH inequality.

e1 = 0.707306, e2 = -0.707511, e3 = 0.706807, e4 = 0.707812

S = 2.829437

MI SB-OA 0.000000

MI SA-OB 0.000000

MI SA-SB 0.000000

MI OA-OB 0.092227

MI SA-OA 0.000000

MI SB-OB 0.000000

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It's intuitively obvious to me that the two outcome streams will have a non-zero mutual information. After all, the streams are correlated, otherwise CHSH would not be violated.

Perhaps minkwe goes wrong by averaging together the results for different angle combinations.

The interesting thing for me is that there is no mutual information involving settings despite published claims that setting and outcome dependence are needed for violating CHSH. What's going on? Thinking simply, the outcomes at B depend on the angle difference, and hence depend on each setting, however, we do not see mutual information between SA and OB. I have an idea about this and will report further if it pans out.