Another example of confusion about what QM calculations mean. Confusion about individual particles and the meaning of probabilities.
This paper does not raise any questions about our assumptions about nature. It raises serious questions about our assumptions of what QM is all about, and the language we use to describe our calculations. That is the sole source of the paradox.
This paragraph may ring a bell to those who ave been following the Bell debates in these forums:
What the above discussion shows is that there is a significant difference between correlations that can be observed when we measure particles separately and when we measure them jointly.This difference can be observed only when we consider pre- and post- selected ensembles, but it is always there, as an intrinsic part of quantum mechanics. Indeed, one may not be familiar with the idea of pre and post-selection but it fact it is something that we encounter routinely: Everytime when we have a sequence of measurements we can split the original ensemble into a number of different pre and post-selected sub-ensembles according to the result of the final measurement, and in each such sub-ensemble we can observe a similar effect.
The authors should have studied probability theory more carefully. The difference between individual probabilities and joint or conditional probabilities is precisely the same effect they just "discovered" in QM, and the post- processing required to calculate joint probabilities is precisely the post processing they are talking about.
This is why P(AB) = P(A)P(B|A) = P(B)P(A|B)
P(B|A) and P(A|B) are post selected terms. They cannot be calculated empirically except by post selection.