minkwe wrote:We will proceed as follows:
* Generate pairs of particles as done previously.
* Instead of measuring at just "alice" and "bob", we will add two more "ghost" stations called "cindy" and "dave". We will send an exact copy of Alice's particle to Cindy and an exact copy of Bob's particle to Dave. This way we will have counterfactual results for Alice's particle at Cindy, and the same for Bob at Dave.
* We will do the data analysis in two steps. In the first step, we will ignore Cindy and Dave and simply use Alice and Bob as we have been doing until now. This scenario is equivalent to substituting actual results on different sets of particles for counterfactual results on a single set.
* The next step of data analysis will involve using all 4 outcomes for calculating the correlations. So that we use Alice and Bob to calculate C(a,b), Cindy and Bob to calculate C(a',b), Alice and Dave to calculate C(a,b') and Cindy and Dave to calculate C(a',b'). This step is equivalent to using counter-factual correlations just as is intended in the CHSH.
* We will then compare the results between the two scenarios and be able to answer our main question.
So here are quick results I've done using my python version for the above:
===== Using only the ('alice', 'bob') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.391, QM: 2.389
===== Using only the ('alice', 'dave') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.390, QM: 2.389
===== Using only the ('cindy', 'bob') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.389, QM: 2.389
===== Using only the ('cindy', 'dave') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.41, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.386, QM: 2.389
==== USING ALL FOUR COUNTERFACTUAL ===
E(0, 22.5), AB=-0.90, QM=-0.92
E(0, 67.5), AB=-0.69, QM=-0.38
E(45, 22.5), AB=-0.90, QM=-0.92
E(45, 67.5), AB=-0.90, QM=-0.92
CHSH: < 2.0, Sim: 2.00, QM: 2.39
Notice anything?