DrChinese
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PeterDonis said:Of course not, because you're looking at the formula for states where all of the amplitudes of the terms are equal so their ratios drop out of the formulas.
If you want to see what happens when the amplitudes of the terms are not equal, try doing a similar analysis to the one that predicts violations of the CHSH inequality, but for this state:
$$
\ket{\Psi} = \sqrt{\frac{1}{3}} \ket{H}_1 \ket{V}_2 + \sqrt{\frac{2}{3}} e^{i \varphi} \ket{V}_1 \ket{H}_2
$$
Yes, you COULD run an experiment where there is a mismatch between the terms and the outcomes are not balanced (more likely to be V than H or vice versa). So what? This has absolutely nothing to do with what is being discussed in this thread - nor anything to do with attempting to isolate what contributes to the theoretical quantum expectation value. What you are doing is going in the opposite direction from actual tests: we wish to factor out things like outside noise, source or detector inefficiency, distinguishability, any contribution other than the purest of entangled states; so we have the opportunity to locate any hypothetical deeper explanation for observed statistics.
As we do that, the settings of Alice and Bob are all that remain as inputs. Nothing else seems to matter, and we get that from theory as well as experiment. Again: every individual entangled pair used in a Bell test is 100% identical in all respects to every other pair (as far as we know, and as far as QM predicts). There is no suspected difference that satisfactorily accounts for, contributes to, or otherwise explains the outcomes of one trial run versus any other. Alice's individual results appear completely random, as do Bob's. And yet when Alice and Bob compare results when observing at identical settings, their results are perfectly synchronized. I have no idea why you would debate this point. This is all standard, we should be in complete agreement.
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