Interpreting photon correlations from independent sources

[DrChinese]

@DrChinese As the holidays are now over for me I will have to reduce my posting frequency but over the next couple days I will read your post and formulate a reply. I suspect this statement by Ma will be relevant but I will know for sure in my response.

No problem on timing, take all the time you need

But please don’t over focus on the Ma quote. Don’t forget that the Megadish paper demonstrates the same results. But it’s mechanism for stopping a swap is such that the issues you have been raising are not a factor.

 

[DrChinese]

I ask to understand better, if "swap yes" or "swap no" affects the results, doesn't that mean that the swap is also a form of measurement that breaks the entanglement between (1&4)?

The swap doesn’t break the entanglement, it creates the entanglement between 1 & 4. The swamp breaks the entanglement between 1 & 2 though (and between 3 & 4)

 

[javisot20]

The swamp breaks the entanglement between 1 & 2 though (and between 3 & 4)

It breaks them to entangled 1&4 and 2&3 (not mutually), right?

 

[gentzen]

All: I think this deep dive into the statistics missed numerous important points ...

4). These are mutually unbiased bases, and any correlation would violate the Uncertainty principle. Because there is no such correlation, it is impossible to select* any subset of entangled 1 & 2 pairs and 3 & 4 pairs that would produce correlation between 1 & 4 - unless you select on the SAME basis.

*And of course I mean by some specific criteria, and not by hand. But I really didn't need to say this, did I?

I a post started with "All:"? Of course you need to say this! I would even go further: since the meaning of "by hand" is not obvious, you should specify a spacetime point (relative to each individual run) where the selection of the subsets is possible if a swap was performed, but impossible if not.
Alternatively, you could specify explicitly which information is allowed to be used for the selection of the subsets.

 

[DrChinese]

I a post started with "All:"? Of course you need to say this! I would even go further: since the meaning of "by hand" is not obvious, you should specify a spacetime point (relative to each individual run) where the selection of the subsets is possible if a swap was performed, but impossible if not.
Alternatively, you could specify explicitly which information is allowed to be used for the selection of the subsets.

What I am saying is simple: there is no such criteria. Suppose you execute/record a 4 hour run of 4 fold coincidences without executing a swap and look for a pattern in the data that indicates correlations. You won’t find one. It’s canonically impossible.

Do the same with physical overlap of the 2 & 3 photons, and voila: a pattern jumps out that did not appear previously. This is predicted by QM.

If there was correlation hidden in the data: why is it predicted not to exist when there is no swap? And why does it appear as predicted when there is a swap?

“Something” changed! How is this not obvious? We already agreed that to see the pattern when there is a swap, look for the HH/VV signatures. So if the swap does not change anything, where does this “impossible” pattern come from?

 

[DrChinese]

It breaks them to entangled 1&4 and 2&3 (not mutually), right?

Yes, the new pairs are in the same Bell state but there is no other relationship remaining.

 

[gentzen]

What I am saying is simple: there is no such criteria. Suppose you execute/record a 4 hour run of 4 fold coincidences without executing a swap and look for a pattern in the data that indicates correlations. You won’t find one. It’s canonically impossible.

It is only impossible from your point of view, because you interpret "by hand" in a specific way. But this is a losing battle for anyone trying to argue against you. Whichever counterexample to your claim they would present, you would just say that it doesn't count.

I am sorry, but I will not play this game with you. Feel free to give whoever tries to play this game with you his medicine:

And for the Nth time: Where is the slightest theoretical support for what you assert in opposition to peer reviewed published papers by top researchers?

I don't care who is right or wrong here. But I am out. I have said my thing now, will unwatch this thread, and ignore any reactions in this thread.

 

[DrChinese]

1. It is only impossible from your point of view, because you interpret "by hand" in a specific way.

I am sorry, but I will not play this game with you.

2. I don't care who is right or wrong here. But I am out. I have said my thing now, will unwatch this thread, and ignore any reactions in this thread.

1. I’m only asking for someone - who thinks there are correlations hidden in data when there are no swaps - to present ANY hidden pattern. Easy to make such claim, but again this is canonically impossible per QM.

And I'm not sure how "by hand" can be interpreted other than one way.


2. As always, you are the best judge of how to allocate your time.

 

[lodbrok]

1. I’m only asking for someone - who thinks there are correlations hidden in data when there are no swaps - to present ANY hidden pattern. Easy to make such claim, but again this is canonically impossible per QM.

What do you mean by "data"? Please be precise. Are you referring to

1. the complete data from 1 & 4 pairs without any selection based on the 2 & 3 measurement?
2. Just the subset of 1 & 4 pairs for which a BSM measurement was performed irrespective of the BSM outcome?
3. Just the subset of 1 & 4 pairs for which an SSM measurement was performed regardless of the SSM outcome?
4. a subset of 1 & 4 data for which a particular BSM outcome was observed (i.e., selected based on |Φ+〉23, or |Φ−〉23)
5. a subset of 1 & 4 data for which a specific SSM outcome was observed (i.e., selected based on |𝐻𝐻〉23 or |𝑉𝑉〉23)

Secondly, what "data" do you claim "changed" as a result of the "swap"? Please answer based on the same categories above.

 

[PeterDonis]

what "data" do you claim "changed" as a result of the "swap"?

This is an ill-formed question. Each set of data is what it is; it can't be "changed". When we test a scientific theory, we don't ask "how does the data change when we do X?"

What we do ask is, what does the theory predict the data will look like when we do X, and when we do not do X? If the theory predicts that the data will look different when we do X vs. when we do not do X, then we say the theory predicts that doing X affects the data--or, in more colloquial language, that doing X "does something" to whatever thing we are measuring to obtain the data. That is how we test scientific theories.

In this case, the theory we are testing is QM, or more specifically QM's predictions about the correlations between measurements on entangled systems and about what the swap operation does when it is performed. The theory predicts that the data will look different when we do the swap operation vs. when we don't. The theory even tells us specifically how the data will look different: when we pick out subsets of the data according to the four possible photon 2 & 3 measurement results (HH, HV, VH, VV), the photon 1 & 4 measurement results in each subset will show Bell state correlations if we do the swap, but will show no correlations if we don't. Experiment bears out these predictions.

What more do you want?

As for your 1. through 5., as far as I can tell, none of them are picking out the correct subsets of data that the QM predictions I described above apply to. So they are all irrelevant.

 

[PeterDonis]

What you are missing is that the same BSM signature appears in the reported cases - the only difference being whether the swap is executed or not. Forget the subsets other than what they report on (the other 3 Bell states), they only report on the single Bell state |Φ->. For that state, the 2 & 3 signature is HH or VV. That same signature is reported on for both entangled (3a) and separable (3b) cases.

Just to re-emphasize this point, and maybe help to focus the discussion: in my previous posts, I've been talking about an idealized experiment where it's somehow possible to set things up so that each of the four possible 2 & 3 signatures (HH, HV, VH, VV) corresponds to one of the four Bell states. But AFAIK no actual experiment has actually done that. What actual experiments have done is what is described in the quote above, so let me restate the point I've made in multiple earlier posts (and which @DrChinese makes in the quote above) as clearly as I can for that specific scenario:

We do a bunch of runs, and for each run, we measure the polarization of the photons in the two output channels of the "BSM" beam splitter. In some runs, we don't get a signal at all in one of those output channels (because both photons, 2 & 3, went into the other one); we discard those runs. For runs where we do get a signal in both output channels, we pick out only those runs where the polarization measurement outcomes in both channels were the same: HH or VV.

Then we separate those runs into those where a swap was done by the experimenter, and those where no swap was done. QM predicts that, for the runs where a swap was done, the photon 1 & 4 measurements will show correlations indicating the Bell state $\ket{\Phi -}$; and QM predicts that, for the runs where no swap was done, the photon 1 & 4 measurements will show no correlation.

 

[DrChinese]

A. What do you mean by "data"? Please be precise. Are you referring to

1. the complete data from 1 & 4 pairs without any selection based on the 2 & 3 measurement?
2. Just the subset of 1 & 4 pairs for which a BSM measurement was performed irrespective of the BSM outcome?
3. Just the subset of 1 & 4 pairs for which an SSM measurement was performed regardless of the SSM outcome?
4. a subset of 1 & 4 data for which a particular BSM outcome was observed (i.e., selected based on |Φ+〉23, or |Φ−〉23)
5. a subset of 1 & 4 data for which a specific SSM outcome was observed (i.e., selected based on |𝐻𝐻〉23 or |𝑉𝑉〉23)

B. Secondly, what "data" do you claim "changed" as a result of the "swap"? Please answer based on the same categories above.

A. If you perform a continuous series of swap=OFF runs, say 1000 4 fold coincidences, the full data will include timing information (used to determine the 4 fold coincidences) along with information regarding the 4 photons' measurements. The 1 & 4 photons will be measured on L/R basis, and the 2 & 3 photons will be measured on the H/V basis.

I say the correlation between the 1 & 4 photons will be close to 0.0 for any criteria you might specify to filter those down to less than 1000, other than looking at the 1 & 4 photons' values themselves. You can look at the 2 & 3 outcomes, the time of day, the geographical location, or whatever else you think might help you establish a significant correlation.

On the other hand: I claim it is canonically impossible for there to exist any such criteria. Because LL and RR outcomes for 1 & 4 photons bear no known mathematical relationship to H/V outcomes for 2 & 3 photons. I hope there is no question about this statement, it's nothing more than a version of the uncertainty relations.

On the other hand: if you obtain a similar dataset of 1000 4 fold coincidences with swap-ON, you can easily filter down to a subset with high correlation. Simply look at the data points with the 2 and 3 photons measured as HH or VV and you will see that the LL and RR outcomes (photons 1 & 4) show high correlations - approaching 1.0 in the ideal case. That's because after a swap resulting in the Φ- Bell state, there is a mathematical relationship between the L/R polarization of the 1 & 4 photons. So all you do is look for that signature in the 2 & 3 data.

So how is it possible to do this "trick" if something wasn't different about the two full datasets? After all, it has been claimed that since there is no "nonlocal influence" (or whatever you choose to label it): There is nothing material that changed.


B. I can't say for a fact what specific things "change", if anything at all. I am not specifying that there is a counterfactual outcome. I just know that the population shows no correlation in one case (no swap), and strong correlation in the other (swap). And the only difference is physical overlap in a beam splitter, resulting in Entangled State statistics between photons that have never interacted nor have existed in a common light cone.

You tell me why that happens, that's what I am asking. Because I don't think there are any explanations that DON'T involve some kind of "nonlocal influence". But if you agree that the swap=OFF data cannot contain any markers that might allow us to filter down to a correlated subset; and you agree that the swap=ON dataset does: there really isn't much left as an option, is there?

 

[DrChinese]

Just to re-emphasize this point, and maybe help to focus the discussion: in my previous posts, I've been talking about an idealized experiment where it's somehow possible to set things up so that each of the four possible 2 & 3 signatures (HH, HV, VH, VV) corresponds to one of the four Bell states. But AFAIK no actual experiment has actually done that. ...

First, I think your entire post is concise.

Second, there is hope that one day there will be sufficient improvements to technology so as to allow all 4 Bell states to be identified in a single experiment. I am not aware of specific theoretical issues to prohibit this (but I am not an expert).

But that wouldn't really change our conclusion (whatever that is). Un-swapped 1 & 4 pairs are not entangled in any way, and show no mathematical relationship that can be determined from examining 2 & 3 pairs. Swapped pairs do show such a relationship when their Bell state is known. If that can be determined for even 1 Bell state, an experiment demonstrating such is valid and important.

 

[javisot20]

The entanglement between 1&4 was not "there waiting" in the initial state. Rather, it is created by the measurement of 2&3, which redistributes the correlations of the system according to quantum rules. The non-locality of 1&4 emerges because the measurement in 2&3 reconfigures the global state of the system. Quantum correlations are not limited to locally measured particles, but affect the entire system.

If the swap of 2&3 affects 1&4, aren't we violating MoE? (I understand that 2&3 is not maximally entangled with 1&4, but swapping or not swapping 2&3 affects 1&4, is that allowed without violating MoE?)

 

[DrChinese]

1. The entanglement between 1&4 was not "there waiting" in the initial state. Rather, it is created by the measurement of 2&3, which redistributes the correlations of the system according to quantum rules. The non-locality of 1&4 emerges because the measurement in 2&3 reconfigures the global state of the system. Quantum correlations are not limited to locally measured particles, but affect the entire system.

2. If the swap of 2&3 affects 1&4, aren't we violating MoE? (I understand that 2&3 is not maximally entangled with 1&4, but swapping or not swapping 2&3 affects 1&4, is that allowed without violating MoE?)

1. Yes.

2. Photon 1 (or any photon) can only be maximally entangled (the type we are working with here) to one other quantum system (particle in our case) at a time*. That's the MoE. So when the swap occurs, 1 is no longer entangled with 2 - and is now entangled with 4.


*There aren't words or terms to properly describe "when" the swap itself occurs. About all you can say is: Before it was X, later it was Y.

 

[PeterDonis]

there is hope that one day there will be sufficient improvements to technology so as to allow all 4 Bell states to be identified in a single experiment. I am not aware of specific theoretical issues to prohibit this (but I am not an expert).

I'm not aware of any theoretical issues that would absolutely prohibit it, but the standard configuration where the swap operation is done at a single beam splitter has the obvious drawback that both photons can come out in the same output channel instead of separate ones. I don't know if anyone has actually investigated how one would have to change the experimental design to ensure that both output photons can always be separated.

that wouldn't really change our conclusion

I agree, but I think doing the experiment such that all 4 Bell states can be identified will help in closing apparent loopholes that various critics bring up--just as all the refinements in how experiments testing the Bell inequalities are done have helped to close lots of apparent loopholes, without actually changing the conclusion.

 

[DrChinese]

1. I'm not aware of any theoretical issues that would absolutely prohibit it, but the standard configuration where the swap operation is done at a single beam splitter has the obvious drawback that both photons can come out in the same output channel instead of separate ones. I don't know if anyone has actually investigated how one would have to change the experimental design to ensure that both output photons can always be separated.


2. I agree, but I think doing the experiment such that all 4 Bell states can be identified will help in closing apparent loopholes that various critics bring up--just as all the refinements in how experiments testing the Bell inequalities are done have helped to close lots of apparent loopholes, without actually changing the conclusion.

1. Well, by my count there are 16 permutations of 2 photons into 4 detectors. But only 4 of those involve both photons going to the same detector. Those currently cannot be properly identified, because only 1 is detected and you need 2 clicks to be sure it is a 4 fold event. The avalanche detectors don't operate fast enough.

So it seems like we should be able to identify more Bell states than actually is done (with the remaining 12 permutations). I'll admit I haven't done sufficient homework to understand this apparent discrepancy (which I'm sure is actually due to my ignorance).

[I do have an idea how to separate 2 going simultaneously to a single detector, but that's a subject for a different thread. ]


2. Given the number of papers I see each year by authors continuing to push some variation on Local Realism, defying/dismissing Bell: I'm not sure the ongoing improvements are satisfying dedicated critics. Although I will say, from looking at the dates of such papers, there are fewer new writers doing that in recent years than previously. So maybe these ongoing experiments, such as Hensen et al, are having an effect.

I don't see too many theory papers denying Local Realism from experimentalists, that's for sure. Most any experimental paper uses the term "nonlocality" or equivalent to describe what they are reporting. Maybe seeing is believing.

 

[PeterDonis]

by my count there are 16 permutations of 2 photons into 4 detectors.

The beam splitter where the swap takes place has two output channels. Either the two photons come out one in each channel, or they both come out in the same channel. Only in the former case can the two photons have their polarizations measured separately, which is necessary in order to determine what you have been calling the "signature" (HH, HV, VH, or VV)--and, as we have already agreed, only the HH and VV outcomes are usable for testing the QM predictions. The fact that 4 detectors total are necessary to make those two polarization measurements, one in each channel, is not the relevant fact for determining how many meaningfully different outcomes there are. At least, that's my understanding of why the current setup has the limitation it has.

 

[lodbrok]

A. If you perform a continuous series of swap=OFF runs, say 1000 4 fold coincidences, the full data will include timing information (used to determine the 4 fold coincidences) along with information regarding the 4 photons' measurements. The 1 & 4 photons will be measured on L/R basis, and the 2 & 3 photons will be measured on the H/V basis.

Since there's nothing like "swap=OFF" or "swap=ON" in the Ma paper. Remembering that they randomly switched between BSM and SSM. Are you referring to the SSM data (3) when you say "swap=OFF"? Or are you referring to the complete 1 & 4 data (1)? (numbers in parenthesis are the dataset numbers in my question)

Also, please clarify precisely what you think "swap" means according to the Ma experiment. It might help to state the steps you believe they take to accomplish the "swap". It will also help if you limit your answer to actual experimental steps done in that experiment, as it will help us relate it to the datasets. Thus, will you say a swap has been done if the BSM measurement was performed, but we are analyzing data set (1), i.e. the complete 1 & 4 data without filtering according to the 2 & 3 results?

I say the correlation between the 1 & 4 photons will be close to 0.0 for any criteria you might specify to filter those down to less than 1000, other than looking at the 1 & 4 photons' values themselves.
You can look at the 2 & 3 outcomes, the time of day, the geographical location, or whatever else you think might help you establish a significant correlation.

On the other hand: I claim it is canonically impossible for there to exist any such criteria. Because LL and RR outcomes for 1 & 4 photons bear no known mathematical relationship to H/V outcomes for 2 & 3 photons. I hope there is no question about this statement, it's nothing more than a version of the uncertainty relations.

To clarify, are you claiming here that datasets dataset (2) and dataset (3) are materially different and that while subsets of dataset (2) can be found that are correlated, it is impossible to find subsets of (3) that are correlated? I'm using my dataset numbers for precision. Since the BSM and the SSM were switched randomly, (2) corresponds to the runs where BSM was active, and (3) corresponds to the runs where SSM was active. For this reason, I want you to clarify what you think "swap" means. Because it appears you think there is something experimentally more to swapping than the fact that BSM was measured.

That's because after a swap resulting in the Φ- Bell state, there is a mathematical relationship between the L/R polarization of the 1 & 4 photons. So all you do is look for that signature in the 2 & 3 data.

So how is it possible to do this "trick" if something wasn't different about the two full datasets? After all, it has been claimed that since there is no "nonlocal influence" (or whatever you choose to label it): There is nothing material that changed.

Then, my questions should help clarify your claim and the disagreement. At the moment, it appears you are claiming there is a material difference between datasets (2) and (3) that goes beyond the fact that for dataset (2), we have additional information from the 2 & 3 BSM measurement about how to sort them.

B. I can't say for a fact what specific things "change", if anything at all. I am not specifying that there is a counterfactual outcome. I just know that the population shows no correlation in one case (no swap), and strong correlation in the other (swap). And the only difference is physical overlap in a beam splitter, resulting in Entangled State statistics between photons that have never interacted nor have existed in a common light cone.

I think you've answered this somewhat. You imply that dataset (2) is materially different from dataset (3), meaning something changed.

The point of all this is that since the data from the Ma experiment is available or can be obtained, it is relatively easy to verify any claims about the actual data.

 

[PeterDonis]

they randomly switched between BSM and SSM

Yes, but for each run, they know which setting was in effect for that run. That's all that's necessary. All the runs with the setting "BSM" are "swap=ON" runs; all the runs with the setting "SSM" are "swap=OFF" runs. That is sufficient to analyze the data the way I described in post #116, which in turn is sufficient to test the QM predictions. Note that in post #116 there is nothing whatever about whether the "BSM" outcomes HH and VV are "the same" as the "SSM" outcomes HH and VV; such a question is simply irrelevant (I would also say it's meaningless, for reasons I gave in an earlier post, but "irrelevant" is sufficient for this discussion).

 

[Morbert]

@Morbert

I have been trying to understand where you are getting your ideas about the |HH⟩ = (|Φ+⟩ + |Φ-⟩)/√2 from. I think I can identify now and describe our point of departure.

Let's consider the Ma experiment specifically, and not the Megadish experiment for the time being. They both demonstrate essentially the same idea, and come to the exact same conclusion. And both of them agree with the predictions of QM. But there is a nuance of difference between their implementations that may be leading you astray. (Of course I say it's you, not me. )

In the Ma experiment, the "switch" being flipped (swap vs no swap) is a beam splitter (BS) which alternates between normal BS operation and full reflective operation (like a mirror). Normal BS being 50:50, the other being 0:100 (transmit:reflect).

Suppose we run 100 iterations and record 4 fold coincidences with the swap switch ON. In the ideal case, we'd expect 25 |Φ-⟩ outcomes (signatures being |HH⟩ and |VV⟩ for photons 2 and 3). After all, there are 4 Bell states and they occur randomly and equally often. I think you agree with this.

Suppose we run 100 iterations and record 4 fold coincidences with the swap switch OFF. In the ideal case, we'd expect 25 |HH⟩ outcomes (photons 2 and 3). After all, there are 4 Product state permutations of H and V (2 * 2) and they occur randomly and equally often. Similarly, there would be 25 |VV⟩ outcomes too. I think you agree with this.

Yes, agreed so far.

Now, for the Ma sorting purposes, they would combine the |HH⟩ and |VV⟩ outcomes together for their reporting. That would be 50 results for swap=OFF, compared to only 25 results for swap=ON. Whoa, what gives? Those bad experimenters are trying to trick us somehow! Clearly, they are combining result subsets for the swap=OFF that have the effect of canceling out (and therefore hiding) correlations that would blow the entire experiment.

Of course I am kidding with that last bit. Obviously, no one pulling anything over on anybody. This situation is strictly an artifact of the specific method by which the swap/no swap switch operates in the Ma experiment. As long as we use the same criteria for comparison (3a vs 3b), all is good and the scientific method is preserved. And in fact, the Ma paper points this exact situation out explicitly:

Ma et al, page 5, text below (3): "Note that the reason why we use one specific entangled state [|Φ-⟩] but both separable states [|HH⟩ and |VV⟩] to compute the correlation function is that the measurement solely depends on the settings of the EOMs in the BiSA."

First let me say that I agree the combination of |HH⟩ and |VV⟩ SSM outcomes is not a trick. Even if we limit this subset to |HH⟩ or to |VV⟩, no L/R or +/- correlation will be observed. Combining these subsets is proper as |Φ-⟩ = (|HH⟩ - |VV⟩)/√2.

The problem is not the mixing of |HH⟩ and |VV⟩ results. It's that 4-fold coincidence condition does not filter out |Φ+⟩ when swap=off. I.e. The SSM subset |HH⟩ is akin to mixing runs from the |Φ+⟩ and |Φ-⟩ BSM subsets. Indeed, if we have swap=on and combine the |Φ+⟩ and |Φ-⟩ subsets, we will get correlations like Fig 3b.

The loophole Ma is closing with this experiment is by moving Victor's choice outside the past light cones of Alice and Bob, Victor's choice cannot locally influence Alice's or Bob's outcomes.

For each successful run (a 4-fold coincidence count), not only Victor’s measurement event happens 485 ns later than Alice and Bob’s measurement events, but Victor’s choice happens in an interval of 14 ns to 313 ns later than Alice and Bob’s measurement events. Therefore, independent of the reference frame, Victor’s choice and measurement are in the future light cones of Alice and Bob’s measurements. Given the causal structure of special relativity, i.e. that past events can influence (time-like) future events but not vice versa, we explicitly implemented the delayed-choice scenario as described by Peres. Only after Victor’s measurement, we can assert the quantum states shared by Alice and Bob.

But to conclude Victor's choice nonlocally influences Alice's and Bob's results, a stronger loophole needs to be closed. The same 4-fold coincidence condition will give rise to a different selection criterion depending on whether a BSM or SSM is made. This allows a "localist" to suppose that the observed correlation is not induced by the BSM or the SSM, but by Victor's choice of which runs to discard.

PS We can move to Megidish, but I would first like to exhaust the Ma experiment.

 

[Morbert]

I agree, but I think doing the experiment such that all 4 Bell states can be identified will help in closing apparent loopholes that various critics bring up--just as all the refinements in how experiments testing the Bell inequalities are done have helped to close lots of apparent loopholes, without actually changing the conclusion.

A perfect BSM would not overcome the issue, which is more fundamental. Namely, the complementary relation between {|Φ+⟩,|Φ-⟩,|Ψ+⟩,|Ψ-⟩} and {|HH⟩,|VV⟩,|VH⟩,|HV⟩}. What would be needed (and is impossible in my understanding), is swap vs no-swap measurements that are not complementary.

 

[lodbrok]

Yes, but for each run, they know which setting was in effect for that run. That's all that's necessary. All the runs with the setting "BSM" are "swap=ON" runs; all the runs with the setting "SSM" are "swap=OFF" runs. That is sufficient to analyze the data the way I described in post #116, which in turn is sufficient to test the QM predictions. Note that in post #116 there is nothing whatever about whether the "BSM" outcomes HH and VV are "the same" as the "SSM" outcomes HH and VV; such a question is simply irrelevant (I would also say it's meaningless, for reasons I gave in an earlier post, but "irrelevant" is sufficient for this discussion).

Here are the datasets:
(2) Just the subset of 1 & 4 pairs for which a BSM measurement was performed irrespective of the BSM outcome?
(3) Just the subset of 1 & 4 pairs for which an SSM measurement was performed regardless of the SSM outcome?
DrC implies that these two datasets are materially different from each other. Do you agree?

 

[PeterDonis]

Here are the datasets:
(2) Just the subset of 1 & 4 pairs for which a BSM measurement was performed irrespective of the BSM outcome?
(3) Just the subset of 1 & 4 pairs for which an SSM measurement was performed regardless of the SSM outcome?
DrC implies that these two datasets are materially different from each other. Do you agree?

I agree with @DrChinese, yes. What you seem to be getting hung up on is that to see the difference in these two datasets, you have to partition them into subsets by the particular outcomes. I fail to see why that is even an issue. As I have already pointed out in other posts, in any other area of science, it is commonplace to use this sort of evidence to demonstrate the existence of a physical effect.

 

[DrChinese]

1. Since there's nothing like "swap=OFF" or "swap=ON" in the Ma paper. Remembering that they randomly switched between BSM and SSM. Are you referring to the SSM data (3) when you say "swap=OFF"? Or are you referring to the complete 1 & 4 data (1)? (numbers in parenthesis are the dataset numbers in my question)

2. Also, please clarify precisely what you think "swap" means according to the Ma experiment. It might help to state the steps you believe they take to accomplish the "swap". It will also help if you limit your answer to actual experimental steps done in that experiment, as it will help us relate it to the datasets. Thus, will you say a swap has been done if the BSM measurement was performed, but we are analyzing data set (1), i.e. the complete 1 & 4 data without filtering according to the 2 & 3 results?

3. To clarify, are you claiming here that datasets dataset (2) and dataset (3) are materially different and that while subsets of dataset (2) can be found that are correlated, it is impossible to find subsets of (3) that are correlated?
I'm using my dataset numbers for precision. Since the BSM and the SSM were switched randomly, (2) corresponds to the runs where BSM was active, and (3) corresponds to the runs where SSM was active. For this reason, I want you to clarify what you think "swap" means. Because it appears you think there is something experimentally more to swapping than the fact that BSM was measured.

4. Then, my questions should help clarify your claim and the disagreement. At the moment, it appears you are claiming there is a material difference between datasets (2) and (3) that goes beyond the fact that for dataset (2), we have additional information from the 2 & 3 BSM measurement about how to sort them.

I think you've answered this somewhat. You imply that dataset (2) is materially different from dataset (3), meaning something changed.

1. Yes. A Bell State Measurement (BSM) is essentially synonymous with creating a swap, and I have been using swap=ON sometimes to denote that. A Separable State Measurement (SSM) won't create a swap, and I have been using swap=OFF sometimes to denote that. I think that has been pretty clear.


2. What I mean by a swap is the same thing described in every single paper I have cited. When there is a swap, photons 2&3 become entangled at the beam splitter when indistinguishable. The Bell state they evolve to, also becomes the same Bell state that remotely 1 & 4 evolve to. I think that has been pretty clear too.


3. Assuming your (2) is when a BSM (swap=ON) occurs and (3) is when an SSM occurs (swap=OFF):

Everything you describe represents my position. A swap occurs with physical overlap of the 2 & 3 photons in the beam splitter (BS) within a narrow time window such that the output photons of the BS are indistinguishable upon exiting. The subsequent polarization measurement of those output photons allows the identification of their resulting Bell state in some cases. All this together is a BSM.

If the outputs of the BS are identifiable as to being photon 2 or photon 3 individually, there is no entanglement swap. All of this is exactly as described by every one of the papers I cite, although their labels vary from paper to paper.


4. You are correct that I think there is a material difference when there is an identified BSM. The difference is that 1 & 4 become entangled. When there is any SSM, there is no entanglement whatsoever between 1 & 4 and certainly no correlation if 1 & 4 are measured on an unbiased basis (for example, L/R polarization when 2 & 3 are measured for H/V polarization). This is exactly as each paper represents their results. I have already quoted them many times, but here is another:

"When Victor performs a Bell-state measurement and finds photons 2 and 3 in the state |Φ−〉23 = (|𝐻𝐻〉23 − |𝑉𝑉〉23)/√2, entanglement is swapped to photons 1 and 4. ... When Victor performs a separable-state measurement and finds photons 2and 3 in either the state |𝐻𝐻〉23 or |𝑉𝑉〉23, entanglement is not swapped."

In one case there is a remote swap. In the other, no swap. That is a physically measurable difference, as reported. I call that material, but I guess each person can evaluate for themselves.

But... You are completely incorrect that the BSM dataset contains any more data elements per 4 fold event. There are 4 in either case (2) or (3): a polarization outcome for all 4 photons. Please reference figure 1 of the Ma paper, in which all 4 data elements are presented in a set of examples, with an added indicator to tell us whether there was a swap or not. Note that that indicator is implied in their diagram, it is the presence of |Φ−〉 or |Φ+〉 in Victor's column. (Their diagram would be a little improved if they did not display a |Φ+〉 event in their examples, as they did not report on it. It also hides the fact that there were specific HH/VV/etc outcomes associated with the Bell state, and those are not detailed. They probably assumed their audience would understand that detail is unnecessary to their experimental results and conclusion.)

 

[DrChinese]

1. Yes, agreed so far.

First let me say that I agree the combination of |HH⟩ and |VV⟩ SSM outcomes is not a trick. Even if we limit this subset to |HH⟩ or to |VV⟩, no L/R or +/- correlation will be observed. Combining these subsets is proper as |Φ-⟩ = (|HH⟩ - |VV⟩)/√2.

2. The problem is not the mixing of |HH⟩ and |VV⟩ results. It's that 4-fold coincidence condition does not filter out |Φ+⟩ when swap=off. I.e. The SSM subset |HH⟩ is akin to mixing runs from the |Φ+⟩ and |Φ-⟩ BSM subsets.

3. Indeed, if we have swap=on and combine the |Φ+⟩ and |Φ-⟩ subsets, we will get correlations like Fig 3b.

4. The loophole Ma is closing with this experiment is by moving Victor's choice outside the past light cones of Alice and Bob, Victor's choice cannot locally influence Alice's or Bob's outcomes.
But to conclude Victor's choice nonlocally influences Alice's and Bob's results, a stronger loophole needs to be closed.

5. The same 4-fold coincidence condition will give rise to a different selection criterion depending on whether a BSM or SSM is made. This allows a "localist" to suppose that the observed correlation is not induced by the BSM or the SSM, but by Victor's choice of which runs to discard.

1. Good.


2. No, this makes no sense at all. As @PeterDonis and I have been trying to tell you: The SSM subsets |HH⟩ and |VV⟩ have no connection to |Φ-⟩ OTHER THAN having the same signature for polarization measurements on photons 2 & 3. The difference: SSM is not entangled, BSM are entangled. On the other hand: |Φ+⟩ is associated with SSM subsets |HV⟩ and |VH⟩ as to signature. Those aren't reported on.


3. This may come as a surprise, but the |Φ+⟩ subsets would show correlation of -1.0 (in principle). If you combine |Φ-⟩ with correlation of 1.0 with |Φ+⟩ with correlation of -1.0, you get... zero. Note that you can distinguish these two cases experimentally (they simply discarded the |Φ+⟩ results for various reasons that don't matter.

Again: There cannot be any identifiable subset of SSM events that produce any correlation at all. That is canonically impossible. That can only happen when an identifiable swap occurs.


4. You have mixed modes here. Alice and Bob make remote, nonlocal measurements outside of each other's light cones. There is nothing local going on in this experiment, Victor is elsewhere in spacetime as well.


5. When all selection criteria are held constant in any scientific experiment, and a single variable changes statistical outcomes: we normally conclude that variable is the cause of the change. That is Science 101.

The ONLY change occurring between the BSM results and the SSM results is that there is physical overlap that leads to the swap. That is the exact variable identified, it is physical, the experiment is thoughtfully performed, the results are statistically significant, and the experiment has been repeated and confirmed with variations by other top teams.

I'm not sure what you are waiting to see.

---

Suppose I had a drug call ES that I could choose to give to two groups of patients suffering from a terrible disease that kills half the patients that get it. If I give the drug to one group, call it the BSM group: they all survive and get well. I don't give it to any the other group, call it the SSM group: half live and half die.

Your friend's mother gets the disease. Do you mention the ES drug to your friend? You see, the issues you raise don't really matter. The ES drug is the cause of the cure. You are going to tell your friend.

Well, I'm your friend... and I'm telling you.

 

[lodbrok]

3. Assuming your (2) is when a BSM (swap=ON) occurs and (3) is when an SSM occurs (swap=OFF):

Everything you describe represents my position.

Ok, do you have any evidence from this experiment that the two are different? Or is it just your hypothesis?

A swap occurs with physical overlap of the 2 & 3 photons in the beam splitter (BS) within a narrow time window such that the output photons of the BS are indistinguishable upon exiting. The subsequent polarization measurement of those output photons allows the identification of their resulting Bell state in some cases. All this together is a BSM.

If the outputs of the BS are identifiable as to being photon 2 or photon 3 individually, there is no entanglement swap. All of this is exactly as described by every one of the papers I cite, although their labels vary from paper to paper.

Clear as a bell!

4. You are correct that I think there is a material difference when there is an identified BSM.

I'm waiting to hear your evidence for this claim.

The difference is that 1 & 4 become entangled. When there is any SSM, there is no entanglement whatsoever between 1 & 4

No, if you are still talking about the same dataset (2), 1&4 are not entangled. *Subsets* of dataset (2) appear correlated as if they are entangled. Now you have switched the meaning of dataset to my dataset (4).

"When Victor performs a Bell-state measurement and finds photons 2 and 3 in the state |Φ−〉23 = (|𝐻𝐻〉23 − |𝑉𝑉〉23)/√2, entanglement is swapped to photons 1 and 4. ... When Victor performs a separable-state measurement and finds photons 2and 3 in either the state |𝐻𝐻〉23 or |𝑉𝑉〉23, entanglement is not swapped."

In one case there is a remote swap.

What you described so far as "swap" is a local process, at 2 & 3, where did you get "remote" from?

But... You are completely incorrect that the BSM dataset contains any more data elements per 4 fold event.

Huh? Where did I claim this?

There are 4 in either case (2) or (3): a polarization outcome for all 4 photons.

Correct! Figure 1 is clear.

.Note that that indicator is implied in their diagram, it is the presence of |Φ−〉 or |Φ+〉 in Victor's column. (Their diagram would be a little improved if they did not display a |Φ+〉 event in their examples, as they did not report on it. It also hides the fact that there were specific HH/VV/etc outcomes associated with the Bell state, and those are not detailed.

I understand that your position is that the 1 & 4 data corresponding to |Φ−〉 or |Φ+〉 in Victor's column are materially different than the 1 & 4 data corresponding to |HH〉 or |VV〉 in Victor's column.
What is the evidence for that?

Note the following from the paper:
When Victor performs a BSM, photons 1 and 4 are only entangled if there exists the information necessary for Victor to specify into which subensembles the data are to be sorted. In our case the subensembles correspond to |Φ−〉23 or |Φ+〉23. Without the ability for this specification, he would have to assign a mixture of these two Bell states to his output state which is separable, and thus he could not correctly sort Alice's and Bob's data into subensembles. This is confirmed by evaluating the experimental data obtained in a BSM but without discriminating between |Φ−〉23 and |Φ+〉23. Then there exists a correlation only in the |𝐻〉/|𝑉〉 basis (0.55 ± 0.06) and no correlations in the |+〉/|−〉 (0.02 ± 0.05) and |𝑅〉/|𝐿〉 (0.01 ± 0.05) bases, similar to the situation when Victor performs a separable-state measurement.

 

[javisot20]

What you described so far as "swap" is a local process, at 2 & 3, where did you get "remote" from?

The swap not only creates the entanglement between 2&3 (locally), it also creates the entanglement between 1&4 (no-locally, remotely)

This allows a "localist" to suppose that the observed correlation is not induced by the BSM or the SSM, but by Victor's choice of which runs to discard.

Being strict, not only "swap" or "no swap" produces changes predicted by QM, also here the standard understanding of MoE that we take is tested. If we leave everything the same except MoE there will be changes. I find it increasingly difficult for a "localist" to explain everything by accepting the standard understanding of MoE.

 

[Morbert]

2. No, this makes no sense at all. As @PeterDonis and I have been trying to tell you: The SSM subsets |HH⟩ and |VV⟩ have no connection to |Φ-⟩ OTHER THAN having the same signature for polarization measurements on photons 2 & 3. The difference: SSM is not entangled, BSM are entangled. On the other hand: |Φ+⟩ is associated with SSM subsets |HV⟩ and |VH⟩ as to signature. Those aren't reported on.

You'e mixing up spatial modes here. These are the relevant relations:\begin{eqnarray*}|\Phi^+\rangle_{bc} &=& \frac{1}{\sqrt{2}}(|HH\rangle_{bc} + |VV\rangle_{bc})\\ U^\mathrm{(BSM)}\ket{\Phi^+}_{bc} &=& \frac{i}{\sqrt{2}}(\ket{HV}_{b''b''} - \ket{HV}_{c''c''})\end{eqnarray*}The SSM results are in the b and c spatial modes, not b'' and c''. E.g. When an SSM is carried out, the signature (HH, b"c") implies the result $\ket{HH}_{bc}$ and it is clear that $$\ket{HV}\bra{HV}_{bc}\ket{\Phi^+}\bra{\Phi^+}_{bc} = \ket{VH}\bra{VH}_{bc}\ket{\Phi^+}\bra{\Phi^+}_{bc} = 0$$

3. This may come as a surprise, but the |Φ+⟩ subsets would show correlation of -1.0 (in principle). If you combine |Φ-⟩ with correlation of 1.0 with |Φ+⟩ with correlation of -1.0, you get... zero. Note that you can distinguish these two cases experimentally (they simply discarded the |Φ+⟩ results for various reasons that don't matter.

How does this not directly contradict Ma?

When Victor performs a BSM, photons 1 and 4 are only entangled if there exists the information necessary for Victor to specify into which subensembles the data are to be sorted. In our case the subensembles correspond to |Φ − 〉 23 or |Φ + 〉 23. Without the ability for this specification, he would have to assign a mixture of these two Bell states to his output state which is separable, and thus he could not correctly sort Alice's and Bob's data into subensembles. This is confirmed by evaluating the experimental data obtained in a BSM but without discriminating between |Φ− 〉 23 and |Φ+ 〉 23. Then there exists a correlation only in the |𝐻〉/|𝑉〉 basis (0.55 ± 0.06) and no correlations in the |+〉/|−〉 (0.02 ± 0.05) and 𝑅〉/|𝐿〉 (0.01 ± 0.05) bases, similar to the situation when Victor performs a separable-state measurement.

4. You have mixed modes here. Alice and Bob make remote, nonlocal measurements outside of each other's light cones. There is nothing local going on in this experiment, Victor is elsewhere in spacetime as well.

I (and Ma) said the loophole this experiment closes is the one where Victor's choice locally influences Alice's and Bob's results, as Victor's choice has been moved to the future light cones of Alice and Bob. Both the localist and the nonlocalist can agree that Victor's choice does not locally influence Alice's or Bob's results. Both agree that this experiment successfully closes a loophole. Where they disagree is the nonlocalist says "Therefore, Victor's choice must nonlocally influence Alice's and Bob's results" while the localist says "Therefore, Victor's choice is not influencing Alice's and Bob's results, locally or nonlocally".

5. When all selection criteria are held constant in any scientific experiment, and a single variable changes statistical outcomes: we normally conclude that variable is the cause of the change. That is Science 101.

The ONLY change occurring between the BSM results and the SSM results is that there is physical overlap that leads to the swap. That is the exact variable identified, it is physical, the experiment is thoughtfully performed, the results are statistically significant, and the experiment has been repeated and confirmed with variations by other top teams.

I'm not sure what you are waiting to see.

The bit in bold what is being argued over: Is the selection criteria actually being held constant?

This exercise might be useful: Consider Victor's apparatus and 4-fold coincidence condition away from the entanglement swapping experiment, and consider photons entering the apparatus, prepared in the state $|HH\rangle_{bc}$. When Victor has the quarter-wave plate off (SSM), the observed signature will always be (HH, b"c"). Every run will be selected.

Now say Victor turns the quarter-wave plate on and uses the same 4-fold coincidence condition (HH, b"c") or (VV, b"c"). Do you believe every run will still be selected?

 

[javisot20]

Where they disagree is the nonlocalist says "Therefore, Victor's choice must nonlocally influence Alice's and Bob's results" while the localist says "Therefore, Victor's choice is not influencing Alice's and Bob's results, locally or nonlocally".

Two photons can only be entangled through some local or non-local interaction having to respect the standard MoE description?

This is what I was referring to when I asked if two photon that show maximum correlation can do so by chance, without local or non-local interaction, simply chance. Nothing differentiates non-local entanglement from entanglement by chance (neither local nor non-local), in both cases there is correlation. In this supposed random entanglement, there is no swap that explains this correlation either, this is true.

 

[DrChinese]

1. Ok, do you have any evidence from this experiment that the two are different? Or is it just your hypothesis?

2. Clear as a bell!

3. I'm waiting to hear your evidence for this claim.

4. No, if you are still talking about the same dataset (2), 1&4 are not entangled. *Subsets* of dataset (2) appear correlated as if they are entangled. Now you have switched the meaning of dataset to my dataset (4).

5. What you described so far as "swap" is a local process, at 2 & 3, where did you get "remote" from?

6. Huh? Where did I claim this?

7. Correct! Figure 1 is clear.

8. I understand that your position is that the 1 & 4 data corresponding to |Φ−〉 or |Φ+〉 in Victor's column are materially different than the 1 & 4 data corresponding to |HH〉 or |VV〉 in Victor's column.
What is the evidence for that?

9. Note the following from the paper:
When Victor performs a BSM, photons 1 and 4 are only entangled if there exists the information necessary for Victor to specify into which subensembles the data are to be sorted. In our case the subensembles correspond to |Φ−〉23 or |Φ+〉23. Without the ability for this specification, he would have to assign a mixture of these two Bell states to his output state which is separable, and thus he could not correctly sort Alice's and Bob's data into subensembles. This is confirmed by evaluating the experimental data obtained in a BSM but without discriminating between |Φ−〉23 and |Φ+〉23. Then there exists a correlation only in the |𝐻〉/|𝑉〉 basis (0.55 ± 0.06) and no correlations in the |+〉/|−〉 (0.02 ± 0.05) and |𝑅〉/|𝐿〉 (0.01 ± 0.05) bases, similar to the situation when Victor performs a separable-state measurement.

1., 3., 4., 8. The Ma paper reports the following results, and it is evidence exactly as I say - big difference in the datasets:

"Fig. 3A shows that when Victor performs the Bell-state measurement [BSM] and projects photons 2 and 3 onto |Φ−〉23, this swaps the entanglement, which is confirmed by significant correlations of photons 1 and 4 in all three bases. ... On the other hand, when Victor performs the separable-state measurement on photons 2 and 3 and does not swap entanglement, the correlation only exists in the |𝐻〉/|𝑉〉 basis and vanishes in the |+〉/|−〉 and |𝑅〉/|𝐿〉 bases, as shown in Fig. 3B. This is a signature that photons 1 and 4 are not entangled but in a separable state."

Note yet again: This experiment reports on one Bell state, |Φ−〉 and nothing else. They have the information to report on the |Φ+〉 case but don't, for various reasons. They don't have sufficient information to report on the |Ψ−〉 or |Ψ+〉 cases. How you map that to your numbered cases is not relevant (you are saying I have switched from (2) to your (4). But that's their experiment and what we are debating. There is no requirement in science that an experiment's selection criteria include things that cannot be properly tracked.

If you want to assert that the |Φ+〉, |Ψ−〉 or |Ψ+〉 cases would produce contradictory results to the |Φ-〉, that would have a degree of scientific merit. Fine, go ahead, although those cases are encompassed by the same theoretical foundation. But that does not change the fact that the |Φ-〉 case is properly documented and presented in accordance with scientific standards.

On the other hand: Other experiments have demonstrated that all 4 Bell states DO produce Entangled State statistics. So that would be a problem. For example, here is the CHSH results from the Kaltenbaek et al paper (where S>2 indicates Entangled States):

S(ψ−) = 2.40 ± 0.09
S(ψ+) = 2.38 ± 0.09


2., 7. Yay!


5. The swap that occurs is remote/nonlocal because 1 & 4 are not local (or need not be) to the beam splitter. They are now entangled. We must look at the full context.


6. Well, you said: "... for dataset (2), we have additional information from the 2 & 3 BSM measurement about how to sort them." Nope, same data elements for both. There is no "additional information" as you describe.


9. As I have said previously: this experiment reports on |Φ-〉 which produces an ideal correlation of 1.0. The |Φ+〉 produces an ideal correlation of -1.0. When you add those two, you do get zero. Not exactly a shocker, but there is no purpose to adding these together except to demonstrate more agreement with prediction.

---

You keep missing the forest for the trees. Take a single Bell state, |Φ-〉 and analyze that. Let's vary a single parameter - physical overlap of 2 photons within a beam splitter. How do you get strong correlation/anti-correlation in the |Φ-〉 and |Φ+〉 states individually, but none in any variation of L/R or +/- bases for separable states? This is the crux of the issue here, and these results should not occur if your strict locality hypothesis is applied. And yet again: All of this - as reported - is completely in accordance with quantum theory. And you are saying it doesn't happen in the first place.

I'm not sure why you don't tackle this directly. You have asked me a number of direct questions, and I have responded by answering to the best of my ability. So here's a direct one for you to answer. Do you deny the following statement:

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.

 

[Morbert]

Not addressed to me but:

Do you deny the following statement:

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.

I completely accept it. It is a concrete fact. It's not the site of disagreement for us.

 

[Morbert]

Two photons can only be entangled through some local or non-local interaction having to respect the standard MoE description?

This is what I was referring to when I asked if two photon that show maximum correlation can do so by chance, without local or non-local interaction, simply chance. Nothing differentiates non-local entanglement from entanglement by chance (neither local nor non-local), in both cases there is correlation. In this supposed random entanglement, there is no swap that explains this correlation either, this is true.

So long as your sample is large enough, you don't have to worry about fluke events. There is no danger of the subset identified by the SSM coincidentally exhibiting correlation in unbiased bases.

 

[DrChinese]

1. You'e mixing up spatial modes here. ...

2. How does this not directly contradict Ma?

3. Both the localist and the nonlocalist can agree that Victor's choice does not locally influence Alice's or Bob's results.

4. The bit in bold what is being argued over: Is the selection criteria actually being held constant?

5. This exercise might be useful: Consider Victor's apparatus and 4-fold coincidence condition away from the entanglement swapping experiment, and consider photons entering the apparatus, prepared in the state $|HH\rangle_{bc}$. When Victor has the quarter-wave plate off (SSM), the observed signature will always be (HH, b"c"). Every run will be selected.

Now say Victor turns the quarter-wave plate on and uses the same 4-fold coincidence condition (HH, b"c") or (VV, b"c"). Do you believe every run will still be selected?

1. No, you are. b and c are not varied during the experiment. b" and c" are not varied during the experiment. But b" and c" do report as H or V, so using that added label is relevant. But not b or c.

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.
What you are saying skips over what's being discussed: Why do correlations appear that are canonically impossible according to you? Because in your book, no entanglement swaps occur at all! You believe everything is a separable measurement.

2. I don't see where there is a disagreement with Ma.

3. First, the use of the word "locally" in your sentence makes no sense in an experiment testing nonlocality. Strike that.

Second, of course the "nonlocalist" would not agree with your statement. It might be true, it might not. But the evidence is that it is true. To quote from the Ma paper: "This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as 'quantum steering into the past'."

So...no.

4. Who cares whether the SSM matches the BSM selection criteria? Yes, we have specified we are only changing a single controllable variable - so you would think (as @PeterDonis has said), this is a standard scientific experiment with proper controls. OK, but let's forget that for a second.

Let's just focus on the basic assertion you are making: There is no remote physical swap, nothing nonlocal occurring, and nothing changing to the past. In that view, all events are Separable State events, right? Hopefully we agree that the Uncertainty Principle dictates:

There is no mathematical relationship between L/R polarization and H/V polarization and +/- polarization of any photon.

Ergo:

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.
And yet: Numerous papers have located precisely such subsets. You don't need to compare those results to anything, because theory says they can't exist at all UNLESS a (magical?) remote physical swap occurs. The simple existence of a single counterexample to your assertion (that there is no swap and therefore all measured events are actually separable) is sufficient to reject it.
Further, the Ma experiment points out a very critical experimental counterexample to the idea that there can be apparent 1 & 4 entanglement between some pairs 1&2 and 3&4, depending on some kind of selection criteria. Pairs 1&2 and 3&4 must always be perfectly anti-correlated when all are measured on the H/V basis. (This is a result of using Type II PDC.) Ma reports that when a swap occurs, there is no such entanglement. In other words: When the 1&2 photons' H/V polarization is analyzed, it is fully anti-correlated when a SSM is performed. But it has no correlation at all when a BSM is performed. Again, that result is diametrically opposite of any assertion that the initial 1 & 2 entanglement survives a swap. From Ma, Table 1:

BSM cases: Photons 1&2 are as antisymmetric: 0.301 ± 0.039 (very low correlation)
SSM cases: Photons 1&2 are as antisymmetric: 0.908 ± 0.016 (very high correlation)

For your assertion/hypothesis to be correct (that there is no physical swap): there should be high correlation in all cases. After all, the 1&2 initial entanglement features "perfect" correlation. Instead, the initial 1&2 correlation disappears, precisely as predicted by Entanglement theory. Entanglement Swaps physically change the results from SSM to BSM statistics on all levels - eliminating 1&2 entanglement (when creating 1&4 entanglement). This result has absolute NOTHING to do with selection of subsets, as should be obvious.


5. This is incorrect: "the observed signature will always be (HH, b"c")". It will be either (HH, b"c") OR (VV, b"c").

It will certainly not select every event. You can also have (HV, b"c") or (VH, b"c").

And as pointed out in 4. above: you ideas about selection criteria are a red herring because your premise about subsets is demonstrably wrong via experiment. The loss of 1&2 entanglement for any BSMs at all is a direct counterexample.

 

[Morbert]

1. No, you are. b and c are not varied during the experiment. b" and c" are not varied during the experiment. But b" and c" do report as H or V, so using that added label is relevant. But not b or c.

No, I am not. The b and c labels are not irrelevant. They are vital. The BSM projects onto |Φ-〉 in the spatial modes b and c even though the H/V signatures are registered in b" and c". Careful, precise tracking of these modes makes clear the complementary relation between the BSM and the SSM, and why they cannot be interpreted as the same selection criteria even when the same 4-fold coincidence condition is used, as the time-evolution of the photons through the apparatus is different depending on the configuration of the quarter-wave plate.

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.
What you are saying skips over what's being discussed: Why do correlations appear that are canonically impossible according to you? Because in your book, no entanglement swaps occur at all! You believe everything is a separable measurement.

No correlations appear that are canonically impossible according to me. You must have wires crossed. The BSM result that projects photons 2&3 onto the state |Φ-〉 in the spatial modes b and c will identify a subset of 1&4 measurements that exhibit correlations in all three mutually unbiased bases, without the need to insist on nonlocal influence. This is the entanglement swap.

3. First, the use of the word "locally" in your sentence makes no sense in an experiment testing nonlocality. Strike that.

Second, of course the "nonlocalist" would not agree with your statement. It might be true, it might not. But the evidence is that it is true. To quote from the Ma paper: "This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as 'quantum steering into the past'."

So...no.

You're not addressing what I carefully said about the loophole and its relation to a local interpretation of events so I am dropping this point digression for now.

4. Who cares whether the SSM matches the BSM selection criteria?

A local interpretation of events is possible if the SSM and BSM choices amount to different selection criteria, as we can say the BSM or SSM themselves are not responsible for any of the correlations seen in 1&4. Instead, the identification of alternative subsets is what is responsible.

Let's just focus on the basic assertion you are making: There is no remote physical swap, nothing nonlocal occurring, and nothing changing to the past. In that view, all events are Separable State events, right? Hopefully we agree that the Uncertainty Principle dictates:

There is no mathematical relationship between L/R polarization and H/V polarization and +/- polarization of any photon.

Ergo:

There cannot exist any identifiable subset of SSM events that produce any correlation at all (on mutually unbiased bases L/R or +/-). That is canonically impossible.
And yet: Numerous papers have located precisely such subsets. You don't need to compare those results to anything, because theory says they can't exist at all UNLESS a (magical?) remote physical swap occurs. The simple existence of a single counterexample to your assertion (that there is no swap and therefore all measured events are actually separable) is sufficient to reject it.
Further, the Ma experiment points out a very critical experimental counterexample to the idea that there can be apparent 1 & 4 entanglement between some pairs 1&2 and 3&4, depending on some kind of selection criteria. Pairs 1&2 and 3&4 must always be perfectly anti-correlated when all are measured on the H/V basis. (This is a result of using Type II PDC.) Ma reports that when a swap occurs, there is no such entanglement. In other words: When the 1&2 photons' H/V polarization is analyzed, it is fully anti-correlated when a SSM is performed. But it has no correlation at all when a BSM is performed. Again, that result is diametrically opposite of any assertion that the initial 1 & 2 entanglement survives a swap. From Ma, Table 1:

BSM cases: Photons 1&2 are as antisymmetric: 0.301 ± 0.039 (very low correlation)
SSM cases: Photons 1&2 are as antisymmetric: 0.908 ± 0.016 (very high correlation)

For your assertion/hypothesis to be correct (that there is no physical swap): there should be high correlation in all cases. After all, the 1&2 initial entanglement features "perfect" correlation. Instead, the initial 1&2 correlation disappears, precisely as predicted by Entanglement theory. Entanglement Swaps physically change the results from SSM to BSM statistics on all levels - eliminating 1&2 entanglement (when creating 1&4 entanglement). This result has absolute NOTHING to do with selection of subsets, as should be obvious.

All of this is premised on a position that isn't anyone's.

There is absolutely a swap when the quarter-wave plate is on and the appropriate coincidences are observed. Nobody is claiming there is no swap. Nobody is claiming MoE is invalid. While the subsets identified by the SSM don't exhibit correlation in mutually unbiased bases, BSM subsets do.

It is the physical significance of this swap, and the MoE that is being argued over. (You say it is a nonlocal effect, I say it is a selection effect). The data presented by the paper is agreed upon by everyone.

If you cannot understand how a local interpretation is consistent will all data then you cannot hope to refute it surely.

5. This is incorrect: "the observed signature will always be (HH, b"c")". It will be either (HH, b"c") OR (VV, b"c").

It will certainly not select every event. You can also have (HV, b"c") or (VH, b"c").

And as pointed out in 4. above: you ideas about selection criteria are a red herring because your premise about subsets is demonstrably wrong via experiment. The loss of 1&2 entanglement for any BSMs at all is a direct counterexample.

Here you're not understanding the alternative scenario I was posing and it's not going to be useful so I will table it for now.