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.

 

[DrChinese]

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

Ahhh, not so fast. Basic operational quantum theory DOES reproduce the statistics of these experiments. It is completely silent regarding retrocausality, instantaneous action at a distance, etc.

 

[Morbert]

Ahhh, not so fast. Basic operational quantum theory DOES reproduce the statistics of these experiments. It is completely silent regarding retrocausality, instantaneous action at a distance, etc.

Yep. If you want to read the calculations in a retrocausal way, you can, but you don't have to.

 

[DrChinese]

1. 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, ...


2. ... 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.


3. 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'."


4. In light of this, it is obvious that what @martinbn says is correct.


5. 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 [of photons 1 and 4] into subsets that each have a different meaning and interpretation. This formation of subsets is independent of the temporal order of the measurements."


6. ...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)...


7. but there will be no "preparation" that allows them to be distinguished beforehand.

Lucas.

1. Fine.


2. If you consider the preparation to be after/during the overlap at the Beam Splitter: then yes, I agree.


3. There is no such thing as "future preparation" in this context. You are just making this up. There is an initial preparation (either 1. or 2. as we agreed). There is an independent variable - to swap or not. My entire point - which really doesn't matter to a discussion of Bohmian Mechanics - is that there is no initial connection between photons 2 & 3 and/or any other photon in the entire universe. From an earlier post of mine:

---

Now, a little thought will explain why I vehemently reject Morbert's expansion as meaningless - even if it appears to be sound from an algebraic point of view. There is initially no connection between the 1&2 pair and the 3&4 pair. So they cannot be in a combined Bell state. And in fact, they are no more in a Bell state with each other than any other entangled photon pairs in the entire universe. We could just as easily start with another pair, photons 5&6, prepared as the others. This experimental permutation is experimentally realizable. Then we get (all unquestionably and simultaneously true by your own logic per 1.):

|Ψ〉1234 = |Ψ−〉12⨂|Ψ−〉34
|Ψ〉1256 = |Ψ−〉12⨂|Ψ−〉56
|Ψ〉5634 = |Ψ−〉56⨂|Ψ−〉34

and end up with the following using Morbert's expansion on each of these:

i) |Ψ〉1234 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23)
ii) |Ψ〉1256 = 1/2(|Ψ+〉16⨂|Ψ+〉25 − |Ψ−〉16⨂|Ψ−〉25 − |Φ+〉16⨂|Φ+〉25 + |Φ−〉16⨂|Φ−〉25)
iii) |Ψ〉5634 = 1/2(|Ψ+〉54⨂|Ψ+〉63 − |Ψ−〉54⨂|Ψ−〉63 − |Φ+〉54⨂|Φ+〉63 + |Φ−〉54⨂|Φ−〉63)

None of these last 3 have any physical significance. And they cannot be physically simultaneously true. (Hopefully that is obvious by MoE and needs no further explanation.) You need to first overlap photons in a BSM apparatus to give it physical significance.

---

4. What @martinbn says that is 100% wrong: There are no defined subsets (4-fold) in the Product State (Separable) results that exhibit non-classical correlations. This is not really a serious point of debate. This was demonstrated experimentally in the references. If there were such a subset, it would be news to a lot of experimenters around the world. If you want to see a paper that attempts - unsuccessfully - to locate hidden correlations in Bell test data sets, try this one from Huw Price (2024).


5. This is, of course, precisely correct. It's everything I have been saying.


6. This doesn't even make sense as a statement... "show"? You are assuming that which cannot be proved. The only subsets that you can "show" from 2 fold coincidences of photons 1 and 4 are |HH>, |VV>, |HV>, |VH>. You can make of those 4 subsets whatever you like, but non-classical correlations is not one of those things. They do not represent any connection whatsoever between the initial pairs 1&2 and 3&4. I can take any 2 lists of random numbers and group them by odd and even, and I will get 4 subsets too. Similarly, they don't "show" us anything meaningful.

Importantly: Just as the BSM changes the state of photons 2 & 3 (agreeing with you on this point): We cannot actually make a convincing statement that it does not also change the state of photons 1 & 4. You can, of course, make any assumption you like either way. There's no experimental proof. But the fact is:

Initially: |Ψ〉14 = |Ψ〉1⨂|Ψ〉4
After a detection of photons 2 and 3 as |Ψ−〉23: |Ψ〉12 = |Ψ-〉14
To the untrained eye, one might conclude that photons 1 and 4 changed states due to the BSM. Note that I am not making an assertion about what "really" happens. I don't know.


7. That's true whether or not there is a BSM. Only 4-fold coincidences are reported as meaningful. And the results are conditioned on the experimenter's choice of BSM/SSM, and nothing else.


Can we please return to a discussion of Bohmian Mechanics...

 

[DrChinese]

Yep. If you want to read the calculations in a retrocausal way, you can, but you don't have to.

Woo hoo! We see totally eye to eye!!

 

[DrChinese]

1. There is no objective criteria, but such _________ exist.

2. 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.

1. I replaced your word "subsets" with a blank for anyone to fill in something they believe in. Possible alternatives: tooth fairy, Santa Claus, leprechauns... you get the idea. Exactly as you say, and with which I agree: There is no objective criteria to support your statement.


2. And here we agree as well: "There are no such papers." Obviously correct.


Can we return to Bohmian Mechanics?

 

[Sambuco]

Can we please return to a discussion of Bohmian Mechanics...

I am addressing your points because I think they are indeed relevant to how Bohmian mechanics explains the DCES experiment. I will focus on the disagreements that I believe are the most important.

We could just as easily start with another pair, photons 5&6, prepared as the others. This experimental permutation is experimentally realizable. Then we get (all unquestionably and simultaneously true by your own logic per 1.):

|Ψ〉1234 = |Ψ−〉12⨂|Ψ−〉34
|Ψ〉1256 = |Ψ−〉12⨂|Ψ−〉56
|Ψ〉5634 = |Ψ−〉56⨂|Ψ−〉34

and end up with the following using Morbert's expansion on each of these:

i) |Ψ〉1234 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23)
ii) |Ψ〉1256 = 1/2(|Ψ+〉16⨂|Ψ+〉25 − |Ψ−〉16⨂|Ψ−〉25 − |Φ+〉16⨂|Φ+〉25 + |Φ−〉16⨂|Φ−〉25)
iii) |Ψ〉5634 = 1/2(|Ψ+〉54⨂|Ψ+〉63 − |Ψ−〉54⨂|Ψ−〉63 − |Φ+〉54⨂|Φ+〉63 + |Φ−〉54⨂|Φ−〉63)

None of these last 3 have any physical significance. And they cannot be physically simultaneously true. (Hopefully that is obvious by MoE and needs no further explanation.)

Your statement regarding the monogamy of entanglement is just wrong. Any of the three states you wrote is correct, not only from an algebraic point of view but also from a physical one. None of those states exhibits entanglement between the photons of pair (1, 2) and photons from other pairs. In the past, I have shared several references with you on how to handle entangled states, including textbooks such as Zweibach’s (specifically chapter 18) so, given that your claim regarding entanglement between photons in the pair (1, 2) and photons from other pairs is wrong and contradicts what is stated in textbooks, I ask that you provide a reference to support your assertion. Since you are so certain that what you say is true, it should be very easy for you to find a reference demonstrating that type of entanglement. Until you do so, your claim will remain incorrect because it contradicts what is written in the references I have previously provided.

Just as the BSM changes the state of photons 2 & 3 (agreeing with you on this point): We cannot actually make a convincing statement that it does not also change the state of photons 1 & 4.

This is not true! All the interpretations I am aware of (many-worlds, bohmian mechanics, QBism, RQM, Copenhagen and so on) agree that the swap involving photons 2 and 3 does not physically change the state of photons 1 and 4. Indeed, as said 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'."

This doesn't even make sense as a statement... "show"? You are assuming that which cannot be proved. The only subsets that you can "show" from 2 fold coincidences of photons 1 and 4 are |HH>, |VV>, |HV>, |VH>. You can make of those 4 subsets whatever you like, but non-classical correlations is not one of those things.

This is also wrong. As I have cited, Ma's paper states that the measurement results for photons 1 and 4 have been "irrevocably recorded". What distinguishes the swap case from the case where no swap takes place is that, only in the swap scenario, we possess the information needed to reorder the data into four sets that demonstrate a violation of Bell's inequalities. The swap does not magically generate those results. One more time: those results have been "already irrevocably recorded", just as Ma's paper states. There is no debate on this point unless you wish to dispute what Ma's paper says, in which case you would need to provide a reference to support your claim.

All of this is highly relevant to the Bohmian interpretation of the experiments, given that you seem to believe that after the swap, the physical state of the photon pair (1, 4) changes due to the swap, which is wrong, as said by the authors in Ma's paper. Indeed, as I have mentioned in previous posts, in Bohmian mechanics there is a single wave function guiding the particles, and it evolves only forward in time. Consequently, the entanglement between photons 1 and 4 is as experimentally observed (violation of Bell inequalities) real, yet not ontic, since that wave function is not the one guiding the particles from the source to the detectors.

Lucas.