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Do you agree that the statistics of the A&D system is fully described by its reduced density matrix? Do you agree that the local operations at B&C don't change the reduced density matrix of A&D and therefore don't change the statistics of A&D? If you answer yes to these questions, then the full ensemble of A&D (before or after, it doesn't matter) already contains all the subensembles and they only need to be singled out by post-selection. Do you agree with that as well? Do you agree that singling out a sublist of a full list of already performed measurements is a perfectly classical thing to do? In that case, we're now in a completely classical statistical situation and the only thing left to understand is that singling out such a sublist may introduce a bias (new correlations) in the statistics of the resulting subensemble. This is what is explained in the book I referenced (in particular, what's interesting here is the collider bias).gentzen said:Honestly, I guess that entanglement swapping adds something to the mystery of entanglement. I have read your reference, and it didn't convince me otherwise. But as I said, it doesn't even mention entanglement, so this is no real surprise.
Entanglement is always a statistical property of an ensemble, it only appears in the statistics of many measurements. In order to violate Bell's inequality, one needs to collect data of many pairs and compute the empirical correlations.gentzen said:Maybe. What about the difference between an individual pair, and an ensemble of pairs? If he just takes one individual pair from anyone of the subensembles, couldn't he rightfully claim that this "resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities"? Or maybe the language used by Gisin et al here is misleading, and only ensembles of pairs can violate Bell inequalities?