Entanglement swapping and Bohmian mechanics

[Morbert]

I understand them just fine. Mjelva’s paper opened my eyes to some of the conflicts between experiment and various interpretations. Your arguments essentially follow the same line as his. Of course, he also makes several other critical mistakes, not directly present in your mathematical development.

And you think there are these conflicts because you don't understand basic operational quantum theory, which readily reproduces the statistics of these experiments without recourse to retrocausal entanglement swapping.

 

[martinbn]

1. Your understanding of Entanglement Swapping is incorrect. When Swapping is enabled via BSM on photons 2/3, each and every 1/4 pair becomes entangled in one of 4 Bell states. Using current technology: Only half (or so) can be identified as belonging to a specific subset, and those (and only those) demonstrate Entangled State correlations. Those subsets are identified using specific criteria chosen in advance.

I agree with this. But you don't understand that the full ensemble is not entangled and shows no non-classical correlations. Only when you look at the subensembles determined by those four Bell state outcomes you see non-c;assical correlations.

2. When Swapping is NOT enabled on photons 2/3, there is no entanglement of any 1/4 pairs. Using the same criteria as for identifying the Entangled subsets, there is no correlation at all.

No, there isn't entanglement of the 1/4 pairs, just like in the swap case. I am not sayning that there is. You still fail to grasp that you need to look at subsets.

3. Also when Swapping is NOT enabled on photons 2/3 : There is absolutely no objective criteria under which non-classical correlations will appear. Product State experiments produce Product State statistics. I.e. there are no identifiable subsets of the type you are attempting to describe.

There is no objective criteria, but such subsets exist.

You keep posting as if what you say is so obvious, it needs no support. If you are correct, a suitable quote should be easy to locate. OTOH: Megidish: "The first and last photons, that did not share between them any correlations, become entangled." See their Fig. 3. "In order to fully characterize the first and last photons’ state, a quantum state tomography (QST) procedure is required."

Yes, what I post is obviously correct. No, I cannot give you a quote from a paper that shows that you have a misunderstanding. There are no such papers. Any QM text book explains how QM works. Any paper on swapping assumes basic knowledge of QM, none will explain what you want me to quote.

 

[Sambuco]

When Swapping is enabled via BSM on photons 2/3, each and every 1/4 pair becomes entangled in one of 4 Bell states.

This is obviously true, but we must remember that there is no quantum state we can assign to a system unless we know how it was prepared. In the case of photons 1 and 4, if we consider their initial preparation at the start of the experiment, each pair is in a non-entangled (product) state, whereas if we take the swap performed on photons 2 and 3 as the "preparation", then each pair of photons 1 and 4 is in an entangled state corresponding to the Bell state measured on photons 2 and 3. Both statements are true simultaneously. The fact that we can treat the swap performed on photons 2 and 3 as a form of "future preparation" for photons 1 and 4, thereby assigning them an entangled state, does not in any way mean that the swap physically affects photons 1 and 4. As clearly stated in Ma's paper:

"If one viewed the quantum state as a real physical object, one could get the paradoxical situation that future actions seem to have an influence on past and already irrevocably recorded events. However, there is never a paradox if the quantum state is viewed as no more than a `catalogue of our knowledge'."

In light of this, it is obvious that what @martinbn says is correct. As also noted in Ma's paper, the initial quantum state can be rewritten (in the Bell state basis) as:

$\ket{\psi}_{1234} = \frac{1}{2} (\ket{\psi^+}_{14} \otimes \ket{\psi^+}_{23} - \ket{\psi^-}_{14} \otimes \ket{\psi^-}_{23} - \ket{\phi^+}_{14} \otimes \ket{\phi^+}_{23} + \ket{\phi^-}_{14} \otimes \ket{\phi^-}_{23})$

which means that the outcomes obtained by Alice and Bob on photons 1 and 4, respectively, can be separated into four sets exhibiting Bell's inequalities violations. Victor's decision to perform the swap on photons 2 and 3 physically changes the state of photons 2 and 3, allowing us to identify (postselect) the subsets of photons 1 and 4 that will show violation of Bell's inequalities. The authors are very clear about this point:

"What, however, is important is to relate the lists of Alice, Bob and Victor's measurement results. On the basis of Victor's measurement settings and results, Alice and Bob can group their earlier and locally totally random results into subsets that each have a different meaning and interpretation. This formation of subsets is independent of the temporal order of the measurements."

As @martinbn said, if Víctor does not perform the swap, the measurement results for photons 1 and 4 will continue to show subsets that violate Bell's inequalities (as concluded from the equation I wrote above), but there will be no "preparation" that allows them to be distinguished beforehand.

Lucas.