I can see why you might get that impression from the text you quoted, but that text comes from the introduction of the paper. Details given later in the article, not to mention the actual quantum theory the experiment is based on, contradict your interpretation.This makes it clear that Alice and Bob should be able to compare their measurements and decide whether or not their respective photons are entangled or separable with no information from Victor; they should be able to deduce Victor's choice of whether or not to entangle the photon pairs.

Specifically: if you work in this retrocausal "picture" of the experiment, then an important detail is that when Victor performs an entangling measurement, he effectively retroactively projects the state shared by Alice and Bob randomly onto one of

*four different*entangled states, only one of which Alice and Bob are actually interested in. So to see correlations they need to know which of the photons they receive are in the entangled state they're interested in, and they can only get that information from Victor.

This kind of detail is clear if you're already familiar with the theory behind this sort of experiment, but it is also stated in a few places in the paper. For instance, near the beginning of page 4:

Here they explain that their implementation of the Bell state (entangling) measurement only distinguishes two of the four Bell states. So their Bell state measurement returns $$\Phi^{+}$$ a quarter of the time, $$\Phi^{-}$$ a quarter of the time, and an inconclusive result half the time. On the next page, they say:When used for a BSM, our BiSA can project onto two of the four Bell states, namely onto $$| \Phi^{+} \rangle_{23} \,=\, ( | HH \rangle \,+\, | VV \rangle ) / \sqrt{2}$$ (both detectors in b'' firing or both detectors in c'' firing) and $$| \Phi^{-} \rangle_{23} \,=\, ( | HH \rangle_{23} \,-\, | VV \rangle_{23} ) / \sqrt{2}$$ (one photon in b'' and one in c'' with the same polarization).

Here they say that their correlation function for the entangling measurement cases is also conditioned on Victor getting the $$\Phi^{-}$$ result.For each pair of photons 1&4, we record the chosen measurement configurations and the 4-fold coincidence detection events. All raw data are sorted into four subensembles in real time according to Victor’s choice and measurement results. After all the data had been taken, we calculated the polarization correlation function of photons 1 and 4. It is derived from their coincidence counts of photons 1 and 4 conditional on projecting photons 2 and 3 to $$| \Phi^{-} \rangle \,=\, (| HH \rangle_{23} \,-\,| VV \rangle_{23}) / \sqrt{2}$$ when the Bell-state measurement was performed, and to $$| HH \rangle_{23}$$ or $$| VV \rangle_{23}$$ when the separable state measurement was performed.

That depends. If Victor always sends the same entangled state, then yes. If Victor sends a random stream of the four different entangled Bell states, then no. They just see completely uncorrelated results in that case, and they need information from Victor to filter out the three entangled states they're not interested in.Let me ask it another way, putting Victor's choice ahead of Alice and Bob's measurements: if Victor produces a stream of entangled photon pairs and sends one each to Alice and Bob, you agree that they should be able to measure them, compare their results, and after sufficient iterations determine whether or not the stream is correlated WITHOUT asking Victor, yes?

This is an aside, but the experiment described in the paper doesn't actually perform a Bell test (though they could have, and there's not much doubt about the result they'd have obtained if they had).That's the whole point of Bell's experiment!

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