Interpreting photon correlations from independent sources

  • #1
DrChinese
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I'd like to discuss 3 different examples of photon polarization correlations where we have 2 different, independent sources S1 and S2, each sufficiently distant to each other that the sources themselves are not directly responsible for the correlations. (Refer to this for an experimental realization of examples III and IV.)



I. 2 lasers S1 and S2 both have V polarizing filters over their output streams, which are not entangled in any way. We will label the stream of photons from S1 as being P1, and the stream from S2 as being P4 (the reason for labeling like this should become clear).

a. We measure the V polarization of P1 and P4, and they are each vertically polarized of course: |VV>. The correlation of P1 & P4 is 1.00 in principle.

b. Question: What is the correlation of the polarizations of P1 & P4 at other angles?

c. Answer: on same mutually biased bases to V, they will have various correlations between 0 and 1.


II. 2 lasers each drive a PDC crystal S1, S2 producing the entangled Bell state |VV>+|HH>. We will label the stream of photon pairs from S1 as being P1&P2, and will label the stream of photon pairs from S2 as being P3&P4. P1&P2 are entangled, P3&P4 are entangled, but there is nothing in particular that connects P1&P2 to P3 or P4, and vice versa. No swapping occurs.

a. We measure the polarization of P2 and P3, and it happens they are each vertically polarized: |VV>. The correlation of P1 & P4 is 1.00 in principle.

b. Question: What is the correlation of the polarizations of P1 & P4 at other angles?

c. Answer: on same mutually biased bases to V, they will have various correlations between 0 and 1.


III. Same setup as example II, but there is swapping of entanglement via a Bell State Measurement (BSM) on P2 and P3 - this done as a delayed choice by the experimenter. After the swap, P1 & P4 are entangled in a Bell state as revealed by the BSM.

a. We measure the polarization of P2 and P3, and it happens they are each vertically polarized: |VV>. The correlation of P1 & P4 is 1.00 in principle.

Note that although we know both are V, we cannot distinguish between them as to which is P2 and which is P3. This is required for a successful swap.

b. Question: What is the correlation of the polarizations of P1 & P4 at other angles?

c. Answer: on ALL SAME BASES, the correlation of P1 & P4 is 1.00 in principle. Perfect correlations!


IV. Just like III, but what if it becomes possible to distinguish the P2 and P3 photons, perhaps by some kind of intentional tagging by the experimenter? In this case, there is no swap.

b. Question: What is the correlation of the polarizations of P1 & P4 at other angles?

c. Answer: on same mutually biased bases to V, they will have various correlations between 0 and 1.

The statistics look exactly the same as Example II. This is the case because 1 & 4 are not entangled, and corresponds to Figure 3b in the cited paper.



It should be clear that there can be correlations of varying types according to which type (per the examples) of streams we are comparing. But only 1 of the 4 examples above produces "perfect" correlations. Of course, real-world correlations are not "perfect". And even though in the ideal case, QM does make an exact (not statistical) predictions for Example III: you need to accumulate a sufficiently large dataset to be sure of what you've got. This is as @PeterDonis has correctly pointed out on a number of occasions.

Assuming you follow the above examples:
i) We know entanglement swaps (via a BSM on P2 & P3) can be executed after P1 and P4 cease to exist. (This is the delayed choice scenario.)
ii) We know entanglement swaps can be performed such that P1 & P4 have never interacted, and have never interacted with any common 3rd system in the past. (This is the strict locality test.)
iii) We know that the entanglement swap fails if there is distinguishability of the P2 & P3 photons. (As demonstrated in various experimental realizations such as THIS).
iv) We know Einsteinian causality should not allow a later choice (to execute a swap or not) to create correlations after the fact.

Something's gotta give! What gives? That's my question.
 
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  • #2
Are you seeing an apparent retro causation from P23 measurements back to P12 measurements? If so, do you mind pointing it out more specifically? I'm not seeing it at first, looks like the usual explanation of delayed choice type experiments could be applied here, no?
 
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  • #3
msumm21 said:
Are you seeing an apparent retro causation from P23 measurements back to P12 measurements? If so, do you mind pointing it out more specifically? I'm not seeing it at first, looks like the usual explanation of delayed choice type experiments could be applied here, no?
I’m not saying there is retro causation. But there could be, especially since that is the most intuitive deduction.

If I entangled something after the fact, you might deduce that something was changed in the past. The correlated statistics of the entangled states versus the separable states in the cited Ma experiment are pretty clear that might actually occur. The after the fact swap seemingly changes the earlier, Alice/Bob results from uncorrelated to correlated. Emphasis on the word “seemingly”.

I haven’t really seen any standard “usual” explanations of delayed choice experiments. Unless you refer to the act of bringing all of the information together in one place as some kind of action intimately tied to the swap. Is that what you mean?

Personally, I call any explanation up that alley as being completely circular. After all, any attempt to demonstrate action at a distance, necessarily requires bringing the information from distant points together at a later time. If that is your explanation, then obviously you will never believe in an FTL influence short of FTL signaling.

But again, interpretations vary on this point. What I am saying above is that there seems to be a contradiction between at least one of four points for which there is some or a lot of experimental support.
 
  • #4
DrChinese said:
I haven’t really seen any standard “usual” explanations of delayed choice experiments. Unless you refer to the act of bringing all of the information together in one place as some kind of action intimately tied to the swap. Is that what you mean?
No, I just meant the explanation about how the total of all results measured on P14 are the same whether or not you do the BSM on P23; you only see "Bell correlations" when you pick subsets of the P14 measurements associated with a specific P23 BSM result. This partially demystifies the delayed choice stuff to my intuition, since I can seemingly assume P14 are in a mixed state of all 4 Bell states regardless of the delayed choice on P23. Right?

DrChinese said:
I haven’t really seen any standard “usual” explanations of delayed choice experiments. Unless you refer to the act of bringing all of the information together in one place as some kind of action intimately tied to the swap. Is that what you mean?

Personally, I call any explanation up that alley as being completely circular. After all, any attempt to demonstrate action at a distance, necessarily requires bringing the information from distant points together at a later time. If that is your explanation, then obviously you will never believe in an FTL influence short of FTL signaling.
Agree.

DrChinese said:
What I am saying above is that there seems to be a contradiction between at least one of four points for which there is some or a lot of experimental support.
I don't see the contradiction at first, given the explanation above in this post. Still thinking...
 
  • #5
msumm21 said:
I can seemingly assume P14 are in a mixed state of all 4 Bell states regardless of the delayed choice on P23. Right?
Not if you want to correctly predict the statistics of the subsets corresponding to each P23 Bell state result. QM, when properly used, can make those predictions correctly as well. If you just ignore them, you are ignoring a valid case of the application of QM. And that case is not just an arbitrary selection of subsets: the presence or absence of those subsets corresponds to an explicit manipulation by the experimenter, of whether to let the swap happen at the BSM or not. To just ignore the difference that explicit manipulation makes in whether there are subsets to pick out that have particular statistics predicted by QM, would fly in the face of how scientific theories are tested: we test theories by making particular experimental manipulations that the theory predicts will have particular results, and seeing whether those results actually happen or not.
 
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  • #6
PeterDonis said:
Not if you want to correctly predict the statistics of the subsets corresponding to each P23 Bell state result. QM, when properly used, can make those predictions correctly as well. If you just ignore them, you are ignoring a valid case of the application of QM. And that case is not just an arbitrary selection of subsets: the presence or absence of those subsets corresponds to an explicit manipulation by the experimenter, of whether to let the swap happen at the BSM or not. To just ignore the difference that explicit manipulation makes in whether there are subsets to pick out that have particular statistics predicted by QM, would fly in the face of how scientific theories are tested: we test theories by making particular experimental manipulations that the theory predicts will have particular results, and seeing whether those results actually happen or not.
I may not be following you. You agree that the total of all results (not looking at P23) are the same regardless of a BSM on P23, right? (I understand that if a BSM is done on P23 and you look at the subset of P14 results with a specific P23 result you get correlations of the associated Bell state within that subset, but for all I know that subset existed without the BSM I just couldn't pick it out....)

Is your point about the "existence" of the subsets changes with the BSM? It seems possible that, even if there is no BSM, 25% of the P14s could have been in each of the 4 Bell states (subsets). OR is there an experimental result counter to this (interference?).
 
  • #7
msumm21 said:
You agree that the total of all results (not looking at P23) are the same regardless of a BSM on P23, right?
No. I agree that, if you just look at the statistics of all the results taken together, as one set of runs, you can't tell whether a BSM swap operation was done on P23 or not.

But you can tell whether a BSM swap operation was done on P23 by looking at the subsets of the runs where the P23 measurement results, which are done after the BSM swap operation (if such an operation takes place), correspond to each of the four possible Bell states. If a BSM swap is done, the measurement results for P14 in each subset will show the appropriate Bell state correlations, corresponding to the Bell state that is signaled by the P23 measurement results for that subset. If a BSM swap is not done, they won't. And that means that "the total of all results", i.e., taking all the results together without looking at individual subsets, cannot actually be the same for those two cases. It just looks the same, statistically, when you limit yourself to only doing statistics on the total set of results. But there are correlations between the subsets when the BSM swap is done that don't appear when you just look at the total set of results.
 
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  • #8
msumm21 said:
I may not be following you. You agree that the total of all results (not looking at P23) are the same regardless of a BSM on P23, right? (I understand that if a BSM is done on P23 and you look at the subset of P14 results with a specific P23 result you get correlations of the associated Bell state within that subset, but for all I know that subset existed without the BSM I just couldn't pick it out....)

Is your point about the "existence" of the subsets changes with the BSM? It seems possible that, even if there is no BSM, 25% of the P14s could have been in each of the 4 Bell states (subsets). OR is there an experimental result counter to this (interference?).
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.

Clearly, you must be able to see the experimental distinction in the results. Regardless of whether you think there is some "hidden" coincidence in unentangled streams, they are showing something that occurs when the "swap" setting is on and something that does not occur when that setting is off. There is nothing to dispute here, unless you are saying the reported experimental results are bogus.

In your thinking, there can be no distinction between "swap" and "no-swap" cases because you don't think a FTL/after-the-fact swap can occur in the first place. And yet, it did.

And just to be clear, there is no such thing as you speculate: "even if there is no BSM, 25% of the P14s could have been in each of the 4 Bell states (subsets)." That would violate Monogamy of Entanglement. 1 & 4 cannot be entangled if 1&2 are entangled and 3&4 are entangled.
 
  • #9
msumm21 said:
I can seemingly assume P14 are in a mixed state of all 4 Bell states regardless of the delayed choice on P23. Right?
Were that true (which it isn't): I hope you could see that means ALL pairs of entangled photons produced anywhere and anytime are also in 1 of 4 Bell states with each other.

Pair 1&2 produced in London, and pair 3&4 produced in Lisbon, have had no BSM - just as you speculate. Oh, and there's also pair 5&6 from Texas and pair 7&8 from Toronto, no BSMs for them either - and produced at about the same time. Why would 1&4 be in a common Bell state, there's been no interaction between them*? Why not 1&6 or 4&8? Or are you saying all PDC produced pairs are in a common state (which they are, according to PDC type) and must therefore share entangled correlations with all photons from all other pairs? Because they don't share any correlation (on mutually unbiased bases) at all unless a swap is executed.



I really think it would benefit us to discuss the examples in my post #1. If we did, you might see the issues better. Of maybe I would. :smile:


* Because if there had been an interaction, it would be nonlocal, thus demonstrating the precise nonlocality you want to deny.
 
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  • #10
DrChinese said:
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.
Yes, but the 1 & 4 statistics for that subset of runs is different for the two cases. In the entangled case (i.e., a swap occurs), the 1 & 4 statistics show the appropriate Bell state correlations. In the separable case (i.e., no swap occurs), they don't. In other words, we can tell whether or not the swap was done by looking at whether the Bell state that is indicated by the 2 & 3 signature does in fact show up in the 1 & 4 correlations.

That is the crucial experimental fact that must be included in order to explain why the swap operation, which can be controlled by the experimenter, must be some kind of actual effect and cannot be merely an artifact of how the statistics are done. Or, to put it another way, it is the crucial experimental indicator that tells us that the experimenter, in choosing whether or not a swap operation occurs at the BSM on photons 2 & 3, is having some real effect on photons 1 & 4, even though those photons can be light years away and can even have already been measured.

In any other branch of science, a specific result being present or absent depending on how the experimenter chooses to manipulate some input is considered the standard test for whether a real effect is present.
 
  • #11
PeterDonis said:
No. I agree that, if you just look at the statistics of all the results taken together, as one set of runs, you can't tell whether a BSM swap operation was done on P23 or not.
I'm hearing "no agreement" but then looks like agreement in the following sentence. So we agree the BSM has no effect on the statistics of the entire set of measurement results?

PeterDonis said:
But you can tell whether a BSM swap operation was done on P23 by looking at the subsets of the runs where the P23 measurement results, which are done after the BSM swap operation (if such an operation takes place), correspond to each of the four possible Bell states.
Yes, agree. I think everything here is in agreement with what I was trying to say.

The main point I was trying to make was the lack of retro causality--doing the BSM or not doesn't change the aggregate P14 results. The BSM gives additional information with which you can use to make condition probabilities more precise, but I personally wouldn't view that itself as spooky, retro causal, or contradictory.

DrChinese said:
Were that true (which it isn't): I hope you could see that means ALL pairs of entangled photons produced anywhere and anytime are also in 1 of 4 Bell states with each other.
So in your experiments II and III are the aggregate P14 measurement results not what you'd get from the mixed state of 1/4 of each of the 4 Bell states?
 
  • #12
PeterDonis said:
Yes, but the 1 & 4 statistics for that subset of runs is different for the two cases. In the entangled case (i.e., a swap occurs), the 1 & 4 statistics show the appropriate Bell state correlations. In the separable case (i.e., no swap occurs), they don't. In other words, we can tell whether or not the swap was done by looking at whether the Bell state that is indicated by the 2 & 3 signature does in fact show up in the 1 & 4 correlations.

That is the crucial experimental fact that must be included in order to explain why the swap operation, which can be controlled by the experimenter, must be some kind of actual effect and cannot be merely an artifact of how the statistics are done. Or, to put it another way, it is the crucial experimental indicator that tells us that the experimenter, in choosing whether or not a swap operation occurs at the BSM on photons 2 & 3, is having some real effect on photons 1 & 4, even though those photons can be light years away and can even have already been measured.

In any other branch of science, a specific result being present or absent depending on how the experimenter chooses to manipulate some input is considered the standard test for whether a real effect is present. [Emphasis added]
So well said that I am not going to say anything... :smile: 😁 :oldbiggrin:
 
  • #13
msumm21 said:
we agree the BSM has no effect on the statistics of the entire set of measurement results?
On the statistics of the entire set, taken as a single set, yes, we agree that the BSM has no effect on that. But the BSM--more precisely, whether or not a swap operation takes place there, which is under the experimenter's control--does affect the statistics of subsets. And those are part of the data. So whether or not a BSM swap is done does affect the data. It just does not affect it in one particular way that you are focusing on, while ignoring other ways it does effect the data that are important to the discussion.

msumm21 said:
the lack of retro causality--doing the BSM or not doesn't change the aggregate P14 results.
Your second clause is not sufficient to establish your first clause. Doing the BSM swap vs. not doing it does affect the data--just not the one particular view of the data that you insist on singling out. Establishing "no retrocausality" would require establishing that doing the BSM swap vs. not doing it does not affect the data in any way whatsoever. And you have certainly not established that; you can't since it's manifestly false.

msumm21 said:
in your experiments II and III are the aggregate P14 measurement results not what you'd get from the mixed state of 1/4 of each of the 4 Bell states?
If you insist on aggregating all the P14 measurement results and ignoring subsets, yes. So what? That doesn't prove what you are trying to make it prove. See above.
 
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  • #14
msumm21 said:
1. So we agree the BSM has no effect on the statistics of the entire set of measurement results? ... The main point I was trying to make was the lack of retro causality--doing the BSM or not doesn't change the aggregate P14 results.

2. So in your experiments II and III are the aggregate P14 measurement results not what you'd get from the mixed state of 1/4 of each of the 4 Bell states?
1. The results do not support your statements in any manner. so there can be no such agreement. The results, as indicted in the 3a versus 3b graphs, show such a large difference that the most reasonable explanation is: The distant BSM actually changes the 1&4 results. That means the results ARE consistent with retrocausality. But they are also consistent with a variety of nonlocal interpretations, and they may be consistent with a few other interpretations too. So one's conclusion as to how the entanglement mechanism operates may vary from person/interpretation to person/interpretation.

I would expect that any proponent of any interpretation would want to know and factor in these results. After 15+ years, each interpretation should have long ago addressed this experiment directly (or any of many similar experiments) without resorting to comments like "Bell doesn't apply" or "there is no FTL signaling". In this experiment: Bell's Inequality is not referenced at all. There is no claim of FTL signaling. But... there is a verifiable change in statistics based on a long distance (in terms of c) or delayed choice action, presumably an influence under the experimenter's control. There has been no assertion in the literature that the reported results were not accurate.


2. My example III only includes an identifiable Bell state and matches the appropriate data to that. There is no aggregate results on 1&4, what you describe is meaningless. In science, you categorize results according to a stated set of parameters. They clearly state that the only state being considered is |Φ-> for Entangled (indicated by VV or HH at the beam splitter), and also by VV or HH at the beam splitter for a Separable state.

If you were performing a statistical analysis of whether children are born to females or males, you would not combine the female/male results to conclude that there is no correlation between being a mother and being female. Similarly, we don't combine results of |Φ-> states with results of |Φ+> states to conclude there is no correlation with results and states. The |Φ-> states produce diametrically opposite results to |Φ+>, and that has been demonstrated in dozens (hundreds?) of experiments. The entire point of the experiment is to identify and quantify an independent variable, which is the usual method in any scientific experiment. That was successfully accomplished.
 
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  • #15
PeterDonis said:
On the statistics of the entire set, taken as a single set, yes, we agree that the BSM has no effect on that. But the BSM--more precisely, whether or not a swap operation takes place there, which is under the experimenter's control--does affect the statistics of subsets. And those are part of the data. So whether or not a BSM swap is done does affect the data. It just does not affect it in one particular way that you are focusing on, while ignoring other ways it does effect the data that are important to the discussion.
I may be differing from your opinion due to a different definition of "effect the data." Here's an analogy trying to highlight my view.

We receive 1000 temperature readings at location X on Earth, spread throughout the year 2023. I can do statistics on these and see e.g. the average temperature is 60degF. Now let's say I subsequently have the option to "push a button" which will tag each temperature reading with the season (spring, summer, fall, winter) of the measurement. Now I can get conditional statistics to see the e.g. winter reading had a lower average. To me, this button did not change the weather, it just gave my brain more information about the data I was looking at.

DrChinese said:
My example III only includes an identifiable Bell state and matches the appropriate data to that.
Apologies, when I referred to III I didn't realize you'd already post selected P23=|VV>, I was mistakenly referring to "no post selection."

DrChinese said:
The results, as indicted in the 3a versus 3b graphs, show such a large difference
I agree & understand that once you've post selected a particular BSM result you will have the results that differ from the entire set and can even get Bell violations. I was not attempting to argue that (my mistake about III and poor wording may have appeared that way).

DrChinese said:
Were that true (which it isn't): I hope you could see that means ALL pairs of entangled photons produced anywhere and anytime are also in 1 of 4 Bell states with each other
Trying to clarify this, maybe due to my not clarifying what I was referring to. In the case we look at P14 with 0 knowledge of P23's fate, what does QM say the state of P14 is? I think it is a mixed state of all Bell states (which is equal to a mixed state of 00, 01, 10, 11), right? Is this wrong?
 
  • #16
msumm21 said:
I may be differing from your opinion due to a different definition of "effect the data." Here's an analogy trying to highlight my view.

We receive 1000 temperature readings at location X on Earth, spread throughout the year 2023. I can do statistics on these and see e.g. the average temperature is 60degF. Now let's say I subsequently have the option to "push a button" which will tag each temperature reading with the season (spring, summer, fall, winter) of the measurement. Now I can get conditional statistics to see the e.g. winter reading had a lower average. To me, this button did not change the weather, it just gave my brain more information about the data I was looking at.
That is not at all an analogous description of the Ma experiment. The button we push does NOT identify the season, the season is always* identified as graphed in figure 3. We are looking ONLY at winter readings (the analogy is to the |Φ-> entangled state and the |VV+HH> separable state). The button changes from entangled state to separable state. In the analogy, that changes the winter weather from one average temperature to another, completely in line with theoretical predictions. If you can see that the average winter temperature readings are different when the button is pushed (say 10 degrees above 0) versus (say) 0 degrees when the button is not pushed.

I know you think that's impossible, and that is precisely why you need to know about this experiment and factor it in. They actually do what you say cannot be done: The "weather" changes remotely and after the fact.


*You may be confused because the experimenters did perform a run without that "season" identification just to demonstrate there was no correlation in the sample. That was simply to rule out a possible background issue. That had nothing whatsoever to do with the reported results, and should not be confused with the experimental objective (demonstrating delayed choice entanglement swapping).
 
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  • #17
msumm21 said:
Trying to clarify this, maybe due to my not clarifying what I was referring to. In the case we look at P14 with 0 knowledge of P23's fate, what does QM say the state of P14 is? I think it is a mixed state of all Bell states (which is equal to a mixed state of 00, 01, 10, 11), right? Is this wrong?
It is a mixed state, yes, but not of Bell states. 1&4 outcomes of {00, 01, 10, 11} do not indicate whether a swap occurred.

1&4 Bell states *only* result from a swap. If you don't have information about the BSM setup and the 2&3 outcomes, you don't know if there was a swap or not. Without a swap, the 2&3 state is (|V2>+|H2>) x (|V3>+|H3>) which is Product (Separable) state, not an Entangled state. Either way (swap/no swap), the 1&4 state matches the 2&3 state.
 
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  • #18
msumm21 said:
I may be differing from your opinion due to a different definition of "effect the data."
It seems pretty straightforward. Here's the experimental procedure:

Make a bunch of runs. For each run, record the measurement results for all four photons.

Separate the runs into four buckets, corresponding to the four possible combinations of measurement results on photons 2 & 3: HH, HV, VH, VV.

Evaluate the correlations between the photon 1 & 4 measurement results in each bucket. Consult a pre-determined table that maps each combination of photon 2 & 3 results to one of the four possible Bell states. If the photon 1 & 4 measurement results for a given bucket match the expected correlations for the Bell state that is indicated by the photon 2 & 3 results for that bucket, a BSM swap operation was done. If the photon 1 & 4 measurement results for a given bucket show no correlations, a BSM swap operation was not done.

If the above does not match your definition of "the BSM swap affects the data", then I don't understand what definition you are using or why you think it matters. As I have already pointed out, in any other area of science, what I described above--having a clear test you can make on the data to determine whether or not the experimenter made a particular manipulation--is the standard way of testing whether the experimenter is producing a real effect.
 
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  • #19
DrChinese said:
I know you think that's impossible, and that is precisely why you need to know about this experiment and factor it in. They actually do what you say cannot be done: The "weather" changes remotely and after the fact.
Copy, let me read it. Is this paper y'all are referring to: https://arxiv.org/pdf/1203.4834 ?

DrChinese said:
It is a mixed state, yes, but not of Bell states. 1&4 outcomes of {00, 01, 10, 11} do not indicate whether a swap occurred.

1&4 Bell states *only* result from a swap. If you don't have information about the BSM setup and the 2&3 outcomes, you don't know if there was a swap or not. Without a swap, the 2&3 state is (|V2>+|H2>) x (|V3>+|H3>) which is Product (Separable) state, not an Entangled state. Either way (swap/no swap), the 1&4 state matches the 2&3 state.
The uniform mixture of the 4 Bell states is separable (not entangled).

Looks like you are saying P23 is (|V2>+|H2>) x (|V3>+|H3>) which is a pure state. I'm rusty on this stuff, but given that P23 is a subsystem of P1234 and the entanglements of P1&P2 and P3&P4 I thought P23 must be in a mixed state, right?

Agree the state of 1&4 is the same as 2&3, equation 2 in that paper. But if you consider the state of 1&4 alone (or 2&3 alone), I think you must treat those subsystems as mixed.
 
  • #20
msumm21 said:
The uniform mixture of the 4 Bell states
Is not the state of the system consisting of photons 1 & 4, considering all runs (i.e., not picking out any subsets), if a BSM swap operation is not done by the experimenter.

I suggest that you think carefully about that.
 
  • #21
msumm21 said:
Copy, let me read it. Is this paper y'all are referring to: https://arxiv.org/pdf/1203.4834 ?


The uniform mixture of the 4 Bell states is separable (not entangled).

Looks like you are saying P23 is (|V2>+|H2>) x (|V3>+|H3>) which is a pure state. I'm rusty on this stuff, but given that P23 is a subsystem of P1234 and the entanglements of P1&P2 and P3&P4 I thought P23 must be in a mixed state, right?

Agree the state of 1&4 is the same as 2&3, equation 2 in that paper. But if you consider the state of 1&4 alone (or 2&3 alone), I think you must treat those subsystems as mixed.
Correct paper, yes. The weather changes to the past, in your analogy.

Bell states are entangled. Using the word “mixed” doesn’t really help, and neither does using “pure” states. Talking about 1&4 alone (or 2&3 alone) is avoiding the issue. The 4 fold stats are what is reported in the graph, figure 3. Swaps on left, no swaps on right.

The difference between swap-on and swap-off is obvious. Let’s start there. Clearly, the results follow the future switch setting.
 
  • #22
DrChinese said:
Bell states are entangled. Using the word “mixed” doesn’t really help
I understand a Bell state is entangled, but the uniform mixture of all 4 of them is not. The density matrix of this mixture is just a multiple of the identity matrix.

Regarding the state of P14 being above
PeterDonis said:
Is not the state of the system consisting of photons 1 & 4, considering all runs (i.e., not picking out any subsets), if a BSM swap operation is not done by the experimenter.
What is the state of P14, given the state of P1234 is as provided in the Ma paper (equation 2)?
 
  • #23
msumm21 said:
What is the state of P14, given the state of P1234 is as provided in the Ma paper (equation 2)?
When 2&3 register as phi- which is also VV or HH(swap enabled), 1&4 are also phi- and will be correlated on the R/L basis. When the swap is disabled and 2&3 register as VV or HH, 1&4 will be completely uncorrelated on the R/L basis.
 
  • #24
DrChinese said:
When 2&3 register as phi- which is also VV or HH(swap enabled), 1&4 are also phi- and will be correlated on the R/L basis. When the swap is disabled and 2&3 register as VV or HH, 1&4 will be completely uncorrelated on the R/L basis.
Agree but my question was while P1234 is in the state described in equation 2. Upon measuring P23 the state changes as you've described.
 
  • #25
DrChinese said:
1. The results do not support your statements in any manner. so there can be no such agreement. The results, as indicted in the 3a versus 3b graphs, show such a large difference that the most reasonable explanation is: The distant BSM actually changes the 1&4 results.
Check out the explanation for figure 3--that difference again is after picking out a subset of the tests (the subset in which P23 was measured to be phi-, presumably about a quarter of the BSM-enabled tests).

My claim: if you give me Ma's test results with SSM-enabled (no P14 entanglement), I can pick out a subset of about 1/4 of those points that has the same statistics. (This has to be the case because the overall statistics are the same complete randomness with or without BSM, the more specific statistics you see are only within the e.g. phi- subset.) My point is, all these things we can find in the BSM data, we can also find in the SSM data. The only difference is that, with the BSM data, we can pick out the subsets using the P23 result.

When I think about it, this kinda demystifies these delayed-choice experiments to me. Doesn't seem nearly as surprising/fascinating as e.g. Bell violations.
 
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  • #26
Consider four photons () whose polarizations live in a four-fold tensor product of two-dimensional Hilbert spaces. The initial state is

where

is a Bell state produced by two independent sources, (emitting and ) and (emitting and ).

An interaction, represented by a unitary operator (which can be approximated as a SWAP operation between and , along with a CNOT and Hadamard, up to local unitaries and a phase), acts on and . A Bell-state measurement (BSM) on and is described by the projector

where are the four Bell states.

The probability of obtaining outcome is

If the BSM yields , the state of and collapses to a Bell state. This is can be seen using the identity:


For each outcome , there exists a unitary (acting on or ) such that the post-measurement state (unnormalized) is:


Indistinguishability of and ensures each Bell state outcome has probability . Distinguishability, however, destroys these perfect correlations and leads to a mixed state for and .

So the key point is that BSM doesn't create the perfect correlations between and , it reveals them. The potential for these correlations is encoded in the initial entangled state . The choice to perform the BSM (represented by ) and the distinguishability of and determine which subset of the ensemble of and measurements will exhibit these perfect correlations.

We can formalize this using a linear functional that gives the total probability of a successful BSM. Decomposing into spacelike slices representing detections and the later choice of measurement on , we find

where controls the conditional state of and :


No causality violation occurs. The delayed choice doesn't retroactively alter correlations. It selects which part of the pre-existing, entangled reality becomes accessible. The reduced state of and alone (without knowledge of the BSM outcome) is maximally mixed (i.e., completely random and showing no correlations), indicating no faster-than-light signaling. Only after classical communication of the BSM result does the corresponding subensemble of and show perfect correlations.The correlations were always present, it just required the proper measurement to make the correlations between and apparent.
 
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  • #27
msumm21 said:
My claim: if you give me Ma's test results with SSM-enabled (no P14 entanglement), I can pick out a subset of about 1/4 of those points that has the same statistics.
That's not the point. The point is that the subsets that correspond to each of the four possible 2&3 combinations do not have the same statistics.

Picking out a subset arbitrarily after you have the data is pointless. The subsets that are relevant are the ones that correspond to the four possible combinations of 2&3 results. And that method of picking out subsets is predetermined before the experiment is done; you don't even have to see the data to know how to pick out subsets that way.
 
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  • #28
msumm21 said:
What is the state of P14, given the state of P1234 is as provided in the Ma paper (equation 2)?
Tracing over P23 from that equation 2 state gives you the state of P14 when an entanglement swap occurs, over the entire set of runs (no subsets picked out). That state is a uniform mixture of the 4 Bell states.

But the point at issue is what the state is of P14 when an entanglement swap does not occur.
 
  • #29
PeterDonis said:
The point is that the subsets that correspond to each of the four possible 2&3 combinations do not have the same statistics.
I understand this, but I don't agree it's plays a role in an argument towards retro causality. This is just like the temperature example I gave in post #15. Temperatures were very likely different in the 4 different seasons (different statistics), but that doesn't mean that revealing the season to me changed the weather.
 
  • #30
PeterDonis said:
Tracing over P23 from that equation 2 state gives you the state of P14 when an entanglement swap occurs, over the entire set of runs (no subsets picked out). That state is a uniform mixture of the 4 Bell states.

But the point at issue is what the state is of P14 when an entanglement swap does not occur.
Equation 2 was the state of the system before measurement/swap of P23.
 
  • #31
msumm21 said:
I understand this, but I don't agree it's plays a role in an argument towards retro causality.
Sorry, but you're wrong.

msumm21 said:
This is just like the temperature example I gave in post #15.
No, it isn't. In your temperature example, the correlations will never violate the Bell inequalities. In the QM example, they will.
 
  • #32
msumm21 said:
Equation 2 was the state of the system before measurement/swap of P23.
Ah, sorry, I misread your post. You are correct that that is the state before the swap.

Then the question is, what is the state after the swap, if the swap takes place? It's not Equation (2).
 
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  • #33
msumm21 said:
My point is, all these things we can find in the BSM data, we can also find in the SSM data. The only difference is that, with the BSM data, we can pick out the subsets using the P23 result.
No, you can't when it's apples to apples. The data is selected from 2&3 results being VV or HH. You get completely different results when the swap switch is on.
 
  • #34
msumm21 said:
1. I understand this, but I don't agree it's plays a role in an argument towards retro causality.

2. This is just like the temperature example I gave in post #15. Temperatures were very likely different in the 4 different seasons (different statistics), but that doesn't mean that revealing the season to me changed the weather.
1.The argument is not about retrocausality. It is simply a possibility.

2. And yet again, you have the analogy wrong. We're only discussing "winter" statistics when the switch is on versus the switch is off. It has nothing to do with "revealing the season".
 
  • #35
thomsj4 said:
1. So the key point is that BSM doesn't create the perfect correlations between and , it reveals them.

2. The potential for these correlations is encoded in the initial entangled state .

3. The choice to perform the BSM (represented by ) and the distinguishability of and determine which subset of the ensemble of and measurements will exhibit these perfect correlations.

4. Only after classical communication of the BSM result does the corresponding subensemble of and show perfect correlations.

5. The correlations were always present, it just required the proper measurement to make the correlations between and apparent.
Welcome to the discussion! :smile:

1. This concept is directly contradicted by co-author Zeilinger in an earlier paper. "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."

And it is also directly contradicted by standard theoretical grounds. When no swap is performed (and from the Ma paper):

"When Victor performed the separable-state measurement on photons 2 and 3, we find that entanglement between photons 1&2 and between photons 3&4 remained. These entanglements vanished when Victor performed the Bell-state measurement on photons 2 and 3. This is consistent with the entanglement monogamy relation."

In other words: Entanglement between 1&2 and 3&4 remains after a separable measure (no swap), and because of Monogamy of Entanglement 1&4 cannot be entangled if 1&2 are entangled - and vice versa.

2. It should be obvious that when there is no swap, there is no relationship whatsoever between the pairs 1&2 and 3&4 other than they start in the same |Φ> state. Your presentation of the |Ψ1234> is misleading: because for anything you say to be true, there would also need to be correlations with every entangled pair ever created in the same |Φ> state. There is no such relationship between different pairs in the same |Φ> state unless a swap is executed, in which case the 1&2 / 3&4 entanglement ceases. It's one or the other.

3. Not sure if you meant to say "indistinguishability" rather than "distinguishability". Regardless, we are selecting 4 fold coincidences for swap and no-swap using the same consistent criteria for the 2&3 results: VV or HH outcomes. That is the only "subset" under consideration, and it's not a subset so much as a fair selection criteria. We are selecting those data points only, and recording whether there is also 1&4 correlation or not. Perfectly normal for any scientific experiment.

4. This is a meaningless point. All scientific studies of correlations require the data to be brought together using classical communication. Or are you saying something changes when the data is brought together at a central point?

5. There is correlation when swap execution is chosen, no correlation when it is not. If there was always correlation waiting to become "apparent", then there should be no difference in the results for swap versus no-swap. But there is.
 
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