A Forward-in-time analysis of delayed-choice entanglement swapping

[Sambuco]

Hi,

I was following some discussions here about delayed-choice entanglement swapping (DCES) and its implications regarding causality. I'm recently came across the following paper where the authors provides a forward-in-time analysis that seems to avoid any backwards influence due to the BSM and I want to share it here to find out what other members think about it.

Lucas.

 

[DrChinese]

Hi,

I was following some discussions here about delayed-choice entanglement swapping (DCES) and its implications regarding causality. I'm recently came across the following paper where the authors provides a forward-in-time analysis that seems to avoid any backwards influence due to the BSM and I want to share it here to find out what other members think about it.

Lucas.

Sure Lucas, I'd like to make a few comments. That's probably not a shocker if you've seen my posts. First off, thanks for posting this. It is exactly down the alley of those recent threads. I was not familiar with this particular author (Mjevla). I was very happy to see that he is well up-to-date on both experiment and theory. I assume that by posting a paper that is not so well known, you are looking for some detail comments.

Second, he actually centers his analysis around 2 of my frequently cited papers. Yay! Not only that, he provides a fair discussion describing those papers:

i) Experimental delayed-choice entanglement swapping, Ma et al
ii) Entanglement Between Photons that have Never Coexisted, Megadish et al

Third, he also cites papers by Huw Price and Ken Wharton. The specific ones he cites are papers around the concept of "Collider Bias" as a statistical artifact. They argue that Collider Bias is a potential loophole in entanglement swapping related experiments which allows the appearance of nonlocality. As fate would have it, I am fairly familiar with a number of papers by Price and Wharton. I would say I am somewhat of a fan of their work, which is often as a pair. They often write on Retrocausal topics in QM, for example. I am definitely familiar with their arguments on Collider Bias, coincidentally having reviewed these papers over this past weekend:

iii) W as the Edge of a Wedge: Bell Correlations via Constrained Colliders, Price
iv) A Mechanism for Entanglement?, Price and Wharton

For those that are not familiar with the terminology: They use the term "W" shaped Bell experiments to describe Entanglement Swapping types, and the term "V" shaped Bell experiments to describe more traditional Entanglement types. Therefore: A W type starts out life as V ⊗ V before a swap. If you look at Figure 1 of the Mjevla paper, you can see how it maps to a "W".

Fourth, and before I get into any critique of these works: There are a number of points we need to spell out that I would call relevant to these arguments. And I don't think these points are controversial, but they should be stated. Some are experimental, some are theoretical, some are historical and some are pure canon to Quantum Mechanics as understood today.

a) We should accept the stated results of the Ma and Megadish experiments in the sense that if they say there are strong correlations that are in line with the predictions of QM, then we will consider those specific results as confirming QM. I will then proceed to discuss those results from the perspective of the QM prediction in the ideal case, understanding that those results are not the actual values obtained experimentally. Also, let's agree that W entanglement swapping is a special form of traditional entanglement (V type) with both similarities and differences.

b) The EPR correlations seen in V shape entanglement tests (traditional PDC polarization entanglement) are those in which perfect correlations are obtained. I refer to these as "perfect" correlations, because the outcome of a measurement (on any entangled basis) on Alice allows a perfect prediction of the result to be obtained by a later measurement (same basis) on Bob.

c) The Bell correlations (violation of Bell Inequalities) are the most common statistical results presented to demonstrate entanglement. Generally, such violations are considered concrete evidence of entanglement - but certainly that is subject to debate.

d) But for our purposes, I wish to propose as follows: Most of my presentation is centered around the EPR perfect correlations. Those are on full display in the Ma paper, they don't rely on Bell statistics. Accordingly, EPR entanglement must be explained by any proposed description of entanglement that does NOT include any "nonlocal" feature. Since Mjevla's paper is based around (post) selection as an explanation, let's call it "Local Subset".

e) And by "nonlocal", I would throw in any physical effect that does not obey strict Einsteinian locality and/or causality. Let's call interpretations/theories in that line of thinking: "Nonlocal Influence".

f) On the other hand, I would also hold that either concept - Local Subset or Nonlocal Influence - should be able to explain equally well both EPR and Bell correlations. And a critical point: In swapping experiments, we are not only explaining outcomes of Alice and Bob (photons 1 & 4). We are explaining 4 fold outcomes (photons 1 & 2 & 3 & 4), including Vicky/Victor.

So if what I am saying sounds of interest (to anyone!), please let me know and I will continue...

It's Local Subset versus Nonlocal Influence!

 

[Sambuco]

Sure Lucas, I'd like to make a few comments. That's probably not a shocker if you've seen my posts. First off, thanks for posting this. It is exactly down the alley of those recent threads. I was not familiar with this particular author (Mjevla). I was very happy to see that he is well up-to-date on both experiment and theory. I assume that by posting a paper that is not so well known, you are looking for some detail comments.

Yeah! What caught my attention from the Mjevla's paper is the claim (especially in section 4.1.1 of the paper) that it is possible, solely from the math of QM, to predict Bell correlations in the 1&4 pairs that correspond to 2&3 pairs entering the BSM and becoming entangled, without assuming that the BSM itself is the cause of these correlations (I'm talking about the Ma's DCES experiment).

Since, in other threads, you favored the interpretation that the BSM is, in fact, the cause of the correlation between photons 1&4, even if they were measured long before Victor chooses to perform a BSM on photons 2&3, I thought that Mjevla's paper may be of interest.

Third, he also cites papers by Huw Price and Ken Wharton. The specific ones he cites are papers around the concept of "Collider Bias" as a statistical artifact.

Yes, I'm aware of the papers by Price & Wharton, and I must say that I find it hard to digest their "explanation" of Bell correlations, even in the usual EPR case (V-shape entanglement).

c) The Bell correlations (violation of Bell Inequalities) are the most common statistical results presented to demonstrate entanglement. Generally, such violations are considered concrete evidence of entanglement - but certainly that is subject to debate.

This is a critical point for the evaluation of Mjelva's result, because, if correct, it showed that certain subsets of 1&4 pairs that show Bell correlations never have an entangled (non-separable) state at any time.

d) But for our purposes, I wish to propose as follows: Most of my presentation is centered around the EPR perfect correlations. Those are on full display in the Ma paper, they don't rely on Bell statistics. Accordingly, EPR entanglement must be explained by any proposed description of entanglement that does NOT include any "nonlocal" feature. Since Mjevla's paper is based around (post) selection as an explanation, let's call it "Local Subset".

e) And by "nonlocal", I would throw in any physical effect that does not obey strict Einsteinian locality and/or causality. Let's call interpretations/theories in that line of thinking: "Nonlocal Influence".

d) and e) are fine to me.

So if what I am saying sounds of interest (to anyone!), please let me know and I will continue...

It's Local Subset versus Nonlocal Influence!

Let's go!

Lucas.

 

[eloheim]

Hello! I've been following along with the previous thread and would also enjoy any discussion of Mjelva's work.

Reading through it, I would point out that Mjelva is proposing to explain all these entanglement swapping phenomena via regular non-local space-like entanglement (as opposed to retrocausal influence/time-like entanglement), so the vast majority of the paper doesn't address the fundamental disagreement over locality which is often at the heart of these debates (right?). The only thing about strictly local physical models (at least when it comes to the projection postulate portion?) I found was possibly footnote 8:

8 These entanglement relations are often considered as global properties of the joint system, which cannot be reduced to the local properties of the subsystems (see Wallace, 2012b). However, Deutsch and Hayden (2000) have developed a formalism where a description of the local properties of the subsystems also includes entanglement. This formalism has since been applied to give an account of DCES experiments (see Hewitt-Horsman & Vedral, 2007).

Also, it has some concrete concepts/vocabulary that could aid in these discussions (collider bias, sufficient conditions for asserting causality, etc.) but I'm not too familiar with any of it specifically.

A lot of the paper seems to boil down to the symmetry entanglement swapping experiments and the problems that causes for projection postulate interpretations. If they can be viewed equally as Victor's measurements 'causing' Alice and Bob's results in the NON-delayed version (where Victor measures first), and Alice and Bob's 'causing' Victor's in the delayed version, then perhaps a symmetric (unitarity-respecting) interpretation like Bohmian mechanics or MWI is the most parsimonious explanation.

 

[DrChinese]

Hello! I've been following along with the previous thread and would also enjoy any discussion of Mjelva's work.

Reading through it, I would point out that Mjelva is proposing to explain all these entanglement swapping phenomena via regular non-local space-like entanglement (as opposed to retrocausal influence/time-like entanglement), so the vast majority of the paper doesn't address the fundamental disagreement over locality which is often at the heart of these debates (right?). The only thing about strictly local physical models (at least when it comes to the projection postulate portion?) I found was possibly footnote 8:

Thanks for this. I realized that Mjelva was talking about the time-like side of swapping experiments. I.e. he rejects retrocausal explanations. But I think I missed that he was NOT arguing in favor of locality. I am going to have to read it a little closer before I address his own reasoning.

 

[DrChinese]

Regarding the Price/Wharton "collider bias" explanation: I reject this explanation as it applies to QM and entanglement swapping.

The Price Wharton papers in no way demonstrate any possible example/mechanism to say how it might apply to Entanglement Swapping. If I say that a card trick is based on sleight of hand, that is not an explanation for Entanglement Swapping. But it is an explanation of how some card tricks work. See my point? We need an actual example, and it must do the following: i) explain EPR correlations, and ii) explain Bell correlations.

Generally speaking, it is not possible to stretch an explanation that handles ii) above into one that handles i). That's because i) features the perfect correlations that leave no "wiggle" room.

 

[DrChinese]

A lot of the paper seems to boil down to the symmetry entanglement swapping experiments and the problems that causes for projection postulate interpretations. If they can be viewed equally as Victor's measurements 'causing' Alice and Bob's results in the NON-delayed version (where Victor measures first), and Alice and Bob's 'causing' Victor's in the delayed version, then perhaps a symmetric (unitarity-respecting) interpretation like Bohmian mechanics or MWI is the most parsimonious explanation.

That's a fair point. I think we will quickly see that what you call "a symmetric (unitarity-respecting) interpretation" falls apart too. An indicator of that is that nothing changes in the quantum mechanical expectation regardless of ordering. It is ONLY the overall context that matters.

I do have some further points to make about this, will save for later.

 

[Sambuco]

Reading through it, I would point out that Mjelva is proposing to explain all these entanglement swapping phenomena via regular non-local space-like entanglement (as opposed to retrocausal influence/time-like entanglement), so the vast majority of the paper doesn't address the fundamental disagreement over locality which is often at the heart of these debates (right?). The only thing about strictly local physical models (at least when it comes to the projection postulate portion?) I found was possibly footnote 8:

Yes, I think that we have two separate "weird" things here:

1. How to explain Bell inequalities violation in a common EPR experiment (just two photons, not four).

2. How to explain that 1&4 photons were Bell-correlated, long before Victor chooses to entangle photons 2&3 by the BSM (Ma's DCES experiment).

For me, Mjelva is trying to discuss whether (2) implies some kind of backward causation, i.e. that the "cause" of the correlations between photons 1&4 in a given subset is the BSM/swap of 2&3.

Lucas.

 

[eloheim]

For me, Mjelva is trying to discuss whether (2) implies some kind of backward causation, i.e. that the "cause" of the correlations between photons 1&4 in a given subset is the BSM/swap of 2&3

Yes I do believe this is the heart of the matter. Some of us want a more intuitive explanation as to why the DCES experiments (and their variations) behave the way they do.

In a traditional EPR scenario (your #1, with just 1 photon pair) you can count the number of ways their measurement results could match up using only local information, and when that bound is exceeded by your experimental results you can intuitively understand that non-local action is at play (if you chose to interpret it that way, at least). I think we all would like something analogous (as in that simple) for the DCES case (your #2) but it gets complicated dealing with "mediating" photons and subsets and technical limitations.

I really feel like @DrChinese was getting there in the previous thread (about Ma et al), but then people still said "you're not taking into account the runs you throw away" or "it's because the spatial modes are being interpreted contextually", etc. and keeping all these objections in mind simultaneously is extremely tough (for me at least).

I believe Mjelva is trying to address the same thing in his paper (your #2) but ironically enough it seems like he comes to the conclusion that delayed-choice entanglement swapping CAN be seen as an artifact of post selection, but by the same criteria so can ALL entanglement experiments (your #1) so we're sort of back where we started.

 

[Morbert]

I believe Mjelva is trying to address the same thing in his paper (your #2) but ironically enough it seems like he comes to the conclusion that delayed-choice entanglement swapping CAN be seen as an artifact of post selection, but by the same criteria so can ALL entanglement experiments (your #1) so we're sort of back where we started.

The author's argument is fairly narrow, yes. He looks at a broad category of W shaped Bell experiments and accounts for them with post-selection of Bell-inequality-violating correlations between outcomes or pre-selection to ensure entanglement.

The argument presented in this paper does not [...] conclusively show that there is no such thing as timelike entanglement or temporal nonlocality. It might well be the case that the most mature theory will contain something like timelike entanglement, or that we – as Adlam (2018) suggests – might see better progress if we abandon our commitment to temporal locality. However, the delayed-choice experiments by Ma et al. and Megidish et al. fail to demonstrate anything of that sort.

As an aside: His distinction between entangled particles (pre-selection) and particles that exhibited Bell-inequality-violating correlations (post-selection) is interesting though I suspect anti-realist interpretations would dissolve any physical significance of that distinction, and he shows that for spacelike separated configurations of W experiments, they become relative.

 

[eloheim]

As an aside: His distinction between entangled particles (pre-selection) and particles that exhibited Bell-inequality-violating correlations (post-selection) is interesting though I suspect anti-realist interpretations would dissolve any physical significance of that distinction, and he shows that for spacelike separated configurations of W experiments, they become relative.

Yes you are right. Treating bell-type experiments as a special case of selection effect is brought up mostly as an aside but it seemed like something others might make use of.

As a sidenote, the latter proposal also offers an intriguing perspective on Bell correlations more generally: as the traditional Bell experiment may be seen as a special case of the non-delayed entanglement swapping experiment where one disregards all but one subsample, it would suggest that Bell correlations in general can be explained as a selection effect. This conjecture has recently been explored by Price and Wharton (2023a, 2023b, 2023c). In short, their proposal is to treat the source of the EPR-pair in the Bell experiment as a ‘‘constrained collider’’, i.e., a collider where the value of the collider variable is fixed. This, they argue, would turn normally non-counterfactual-supporting selection effects into counterfactual-supporting Bell correlations.10

 

[Morbert]

Regarding the Price/Wharton "collider bias" explanation: I reject this explanation as it applies to QM and entanglement swapping.

The Price Wharton papers in no way demonstrate any possible example/mechanism to say how it might apply to Entanglement Swapping. If I say that a card trick is based on sleight of hand, that is not an explanation for Entanglement Swapping. But it is an explanation of how some card tricks work. See my point? We need an actual example, and it must do the following: i) explain EPR correlations, and ii) explain Bell correlations.

Generally speaking, it is not possible to stretch an explanation that handles ii) above into one that handles i). That's because i) features the perfect correlations that leave no "wiggle" room.

This paper discusses the Delft experiment (and a delayed choice modification of it).

Do you not consider the Delft experiment to be an entanglement swapping experiment? It seems to me that it is. The primary difference being that the initial entanglement is not two pairs of photons each in a Bell state, and is instead two qubit-"photon mode" pairs, where each qubit is entangled with a photon number for a respective mode. A successful swap entangles the photon number of the two modes, and hence the spin of the two qubits.

See here for a more detailed description of the apparatus.

 

[Sambuco]

Thanks for the references!

Do you not consider the Delft experiment to be an entanglement swapping experiment? It seems to me that it is.

In fact, Mjelva also considers Delft experiment as "a variant of the delayed-choice experiments where all of the measurements occur at spacelike separation".

 

[DrChinese]

Yes, I think that we have two separate "weird" things here: ...

2. How to explain that 1&4 photons were Bell-correlated, long before Victor chooses to entangle photons 2&3 by the BSM (Ma's DCES experiment).

For me, Mjelva is trying to discuss whether (2) implies some kind of backward causation, i.e. that the "cause" of the correlations between photons 1&4 in a given subset is the BSM/swap of 2&3.

Lucas.

I'm sure you've seen my arguments discussing this exact point. I thought I'd recap a few:

a) "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."-Kaltenbach et al (2008)

Edited to add:
"It is also evidence that the first and last photons did not somehow share any entanglement before the projection of the middle photons." -Megidish et al (2012)
"The result shows that the photons didn’t reveal any entanglement whatsoever before the swapping operation." -Goebel et al (2008)

b) Prior to Victor entangling photons 2&3: What connection (and therefore what correlation) is there between photons 1&4? 1 & 4 conceivable could be any photons in the entire universe, right? Now, we know that photons 1&2 are entangled in the state Ψ-. Ditto for photons 3&4.

What possible prediction does QM give about correlations between 1&4? Certainly, you must agree that without conditioning on measurements of 2 & 3: There is absolutely zero correlation, no more than there is any correlation between successive coin flips. And in fact Monogamy of Entanglement prevents 1 from being entangled with both 2 & 3 at the same time.


c) But... what if we condition our 1 & 4 predictions on measurement outcomes for the 2 & 3 photons? This being the case where 2 & 3 are NOT brought to a beam splitter at all - they are simply measured on the H/V basis. So now we have the situation in your 2. above. According to QM: what is the 1 & 4 correlation if we have the specific outcome: |HH> for photons 2 & 3?

If 1 & 4 are measured on the H/V basis: The certain outcomes for 1 & 4 are obviously |VV>. An H result for photon 2 means a V result for photon 1, and similar for photon 4. So that is perfect correlation from a subset of our original universe. This was confirmed experimentally in the Ma experiment. And in such case, the 1 & 4 photons were measured BEFORE the 2 & 3 photons. We could then have predicted, with certainty, the result of the measurement of the 2 & 3 photons by reference to the |VV> result on photons 1 & 4. Right? And this is for the full universe of results with 1 & 4 being |VV>.

If 1 & 4 are measured on the L/R (or +/-) basis: An H result for photon 2 does not correlate to any particular L or R outcome for photon 1. And similar for photon 4 relative to photon 3. There is no subset conditioned on the 2 & 3 outcomes on their H/V basis with 1 & 4 outcomes on the L/R basis. This was confirmed experimentally in the Ma experiment. (Again, the no swap case.)


So we see a) that scientists conducting these experiments think there is no initial correlation between photons 1 & 4. That should tell us something significant. We see b) that there can definitely be no physical connection or correlation whatsoever between 1 & 4 *prior* to their partners 2 & 3 entering a beamsplitter. And QM predicts: c) before entering a beam splitter, they can have no initial correlation on the L/R (or +/-) basis. Conclusion: There is no initial correlation between photons 1 & 4.

 

[javisot20]

b) Prior to Victor entangling photons 2&3: What connection (and therefore what correlation) is there between photons 1&4? 1 & 4 conceivable could be any photons in the entire universe, right? Now, we know that photons 1&2 are entangled in the state Ψ-. Ditto for photons 3&4.

What possible prediction does QM give about correlations between 1&4? Certainly, you must agree that without conditioning on measurements of 2 & 3: There is absolutely zero correlation, no more than there is any correlation between successive coin flips. And in fact Monogamy of Entanglement prevents 1 from being entangled with both 2 & 3 at the same time.

That is something that worries me, what prevents it? Choose a quantum object (1), the one you want, now compare it with all the quantum objects that have never interacted with (1), neither locally (EPR) nor non-locally through swapping (Bell).

What law implies that the correlation with these other objects must be 0, with any of them? Monogamy itself?

Two quantum objects not entangled with other objects, which are also not entangled with each other, it does not violate monogamy to show quantum correlations, we simply assume that it is highly improbable, or impossible?

 

[DrChinese]

This paper discusses the Delft experiment (and a delayed choice modification of it).

Do you not consider the Delft experiment to be an entanglement swapping experiment? It seems to me that it is. The primary difference being that the initial entanglement is not two pairs of photons each in a Bell state, and is instead two qubit-"photon mode" pairs, where each qubit is entangled with a photon number for a respective mode. A successful swap entangles the photon number of the two modes, and hence the spin of the two qubits.

See here for a more detailed description of the apparatus.

Yes, agreed, Delft (Hensen et al) is entanglement swapping.

However, Price/Wharton are far off in a number of statements in your cited paper. For example, they state (quotes are in italics):

a) "In DD, it is uncontroversial that the measurement choices at A and B may exert a causal influence on the result of the measurement C. This is certainly so in orthodox QM, in which the measurements at A and B affect the state of the particles converging on C from the left and right, respectively. (The fact that the measurements at A and B take place before that at C is crucial in this account, of course.)"

This is diametrically the opposite of what occurs. The C location can be sufficiently far enough from A and B that the selection of measurement settings for A & B occurs too late to affect a result at C unless it is via "action at a distance" (their term, AAD). That is the case even in what the call the Delayed Delft (DD), as the C location can be anywhere. So no, definitely cannot agree with their first sentence. On the other hand, it is certainly possible that there is AAD, as that would be compatible with experiment.

b) No Difference Test: "The first test starts with this question. Would An or Bn have been different, if the measurement C had not (later) taken place? The intuitive answer to this question is ‘No’. Because C lies in the future with respect to the measurements A and B, allowing it to influence the measurement results at A and B would amount to retrocausality, which we are assuming is impossible (NoRA)."

Agreed that the intuitive answer is No. But of course either retrocausality or AAD could in fact be a mechanism to explain experimental results. Ruling out one by assumption (NoRA here) merely makes the other one a suitable candidate.

Let's go on to the "No Difference Test" definition. The wrong question is being asked. Instead of asking if the A and B results would be different*, you must ask if the 4 fold results would be different. After all: you can conduct the sequence of events at A (1 measurement), B (1 measurement), and C (2 measurements) in any order. Further, the C measurements can be performed in any order as well (they do not need to be contemporaneous).

What is the answer to that question? Certainly it is yes. A swap inherently is a physical operation that changes the state of A and B remotely, along with the state of C. That's because the state of the 4 entangled particles changes as a result of a swap.

Before a swap: 1 & 2 are entangled, and 3 & 4 are entangled. But 1 & 4 are not entangled, and 2 & 3 are not entangled. Nor are they correlated. (See my post #14 for discussion of this particular point.)
After a swap: 1 & 4 are entangled, and 2 & 3 are entangled. But 1 & 2 are not entangled, and 3 & 4 are not entangled.

So of course these different entangled states cannot produce a pattern that consistent between the Before and After. Hopefully, this is obvious since different states produce different statistics. But if you aren't sure: I will provide a proof of that in my next post. The proof simply shows that there are outcomes of the "After" case that don't exist in any "Before" case. Note also that for my proof, I will use the Ma example (which like the DD of Price/Wharton, is a delayed version).

So it will be an absolute proof that there IS a difference in the 4 fold version of the question - which is all that matters. That in turn covers any variation on the ordering of measurements. The QM predictions for swapping do not depend on order. So you might reasonably assume that there is no significant difference between the underlying physics for the delayed case versus the non-delayed case.


*The answer to this can never be answered in the affirmative.

 

[DrChinese]

1. What law implies that the correlation with these other objects must be 0, with any of them? Monogamy itself?

Two quantum objects not entangled with other objects, which are also not entangled with each other, it does not violate monogamy to show quantum correlations, we simply assume that it is highly improbable, or impossible?

1. Yes, Monogamy forbids this.

2. Why would there be correlations between quantum objects that are not entangled, other than spurious correlations?

For example: If I take 2 beams of photons (say A and B) polarized at 0 degrees, they will show a variety of correlations at a variety of (same) angles. But they are spurious. Averaged at all angles, the correlation will be zero.

On the other hand: 2 polarization entangled beams will exhibit constant correlation at any (same) angle.

 

[Morbert]

a) "In DD, it is uncontroversial that the measurement choices at A and B may exert a causal influence on the result of the measurement C. This is certainly so in orthodox QM, in which the measurements at A and B affect the state of the particles converging on C from the left and right, respectively. (The fact that the measurements at A and B take place before that at C is crucial in this account, of course.)"

This is diametrically the opposite of what occurs. The C location can be sufficiently far enough from A and B that the selection of measurement settings for A & B occurs too late to affect a result at C unless it is via "action at a distance" (their term, AAD). That is the case even in what the call the Delayed Delft (DD), as the C location can be anywhere. So no, definitely cannot agree with their first sentence. On the other hand, it is certainly possible that there is AAD, as that would be compatible with experiment.

DD specifically refers to versions of the Delft experiment where C is in the future light cones of A and B. You are describing the Delft experiment itself, which the authors fully accept as an intermediate case where A and B can be spacelike separated from C. They discuss it in section 6.

b) No Difference Test: "The first test starts with this question. Would An or Bn have been different, if the measurement C had not (later) taken place? The intuitive answer to this question is ‘No’. Because C lies in the future with respect to the measurements A and B, allowing it to influence the measurement results at A and B would amount to retrocausality, which we are assuming is impossible (NoRA)."

Agreed that the intuitive answer is No. But of course either retrocausality or AAD could in fact be a mechanism to explain experimental results. Ruling out one by assumption (NoRA here) merely makes the other one a suitable candidate.

Let's go on to the "No Difference Test" definition. The wrong question is being asked. Instead of asking if the A and B results would be different*, you must ask if the 4 fold results would be different. After all: you can conduct the sequence of events at A (1 measurement), B (1 measurement), and C (2 measurements) in any order. Further, the C measurements can be performed in any order as well (they do not need to be contemporaneous).

Asking if the 4 fold results would be different if C had not taken place will always trivially result in the answer yes because two of those results will not exist if C does not take place. Their formulation of the No Difference test avoids this problem.

And as mentioned above, the authors look at three scenarios and discuss each in detail:

Delayed Delft (DD): C lies in the future light cone of A and B
Early Delft (ED): C lies in the past light cones of A and B
Real Delft: C is spacelike separated from A and B

Ironically, they find the ED the least vulnerable to the Collider Loophole.

What is the answer to that question? Certainly it is yes. A swap inherently is a physical operation that changes the state of A and B remotely, along with the state of C. That's because the state of the 4 entangled particles changes as a result of a swap.

Before a swap: 1 & 2 are entangled, and 3 & 4 are entangled. But 1 & 4 are not entangled, and 2 & 3 are not entangled. Nor are they correlated. (See my post #14 for discussion of this particular point.)
After a swap: 1 & 4 are entangled, and 2 & 3 are entangled. But 1 & 2 are not entangled, and 3 & 4 are not entangled.

So of course these different entangled states cannot produce a pattern that consistent between the Before and After. Hopefully, this is obvious since different states produce different statistics. But if you aren't sure: I will provide a proof of that in my next post. The proof simply shows that there are outcomes of the "After" case that don't exist in any "Before" case. Note also that for my proof, I will use the Ma example (which like the DD of Price/Wharton, is a delayed version).

So it will be an absolute proof that there IS a difference in the 4 fold version of the question - which is all that matters. That in turn covers any variation on the ordering of measurements. The QM predictions for swapping do not depend on order. So you might reasonably assume that there is no significant difference between the underlying physics for the delayed case versus the non-delayed case.

In fear of relitigating the recently closed thread, I will not go too far down this path, other than to say that everyone involved agrees that measurements can change states remotely and instantly. The question the authors are interested is the physical significance of this, in the face of the Collider Loophole in particular.

As Asher Peres points out, the analogous case in classical physics is when a measurement instantly and remotely changes the Liouville function in phase space. We can account for this classical context instantaneous change without action at a distance. The question everyone is interested in is if the Collider Loophole allows us to account for the instantaneous change of the state in entanglement swapping experiments without action at a distance.

 

[DrChinese]

1. DD specifically refers to versions of the Delft experiment where C is in the future light cones of A and B.

2. Asking if the 4 fold results would be different if C had not taken place will always trivially result in the answer yes because two of those results will not exist if C does not take place.

3. In fear of relitigating the recently closed thread, I will not go too far down this path, other than to say that everyone involved agrees that measurements can change states remotely and instantly. The question the authors are interested is the physical significance of this, in the face of the Collider Loophole in particular.

1. You are correct, and I misread. Probably because I don't understand why they chose that constraint.

2. I both agree and disagree with your assessment that 2 of the results don't appear if C had not taken place. It is true as written. However: in every version of swapping we have discussed, the point we have been talking about swap versus no swap. Certainly there are 4 fold results in both of those cases. It is that difference that matters. Looking at the A & B results by themselves is meaningless. And that is my point entirely. Only the 4 fold results matter.

3. Agreed about not repeating the content of the prior threads. However, there is no "Collider Loophole", which is a topic for this thread. First, Price/Wharton merely assert such a "loophole" exists by general analogy. But where is any actual example as it relates to entanglement phenomena? You may as well assert that a loophole in tax regulations proves entanglement swapping is this or that.

Second: It should be pretty clear that when there are perfect correlations, a Collider Loophole could never apply. That's because in entanglement swapping, there is exactly one and only one cause: the physical overlapping of photons in a beam splitter.

 

[DrChinese]

Before a swap: 1 & 2 are entangled, and 3 & 4 are entangled. But 1 & 4 are not entangled, and 2 & 3 are not entangled. Nor are they correlated. (See my post #14 for discussion of this particular point.)
After a swap: 1 & 4 are entangled, and 2 & 3 are entangled. But 1 & 2 are not entangled, and 3 & 4 are not entangled.

So of course these different entangled states cannot produce a pattern that consistent between the Before and After. Hopefully, this is obvious since different states produce different statistics. But if you aren't sure: I will provide a proof of that in my next post. The proof simply shows that there are outcomes of the "After" case that don't exist in any "Before" case. Note also that for my proof, I will use the Ma example (which like the DD of Price/Wharton, is a delayed version).

So it will be an absolute proof that there IS a difference in the 4 fold version of the question - which is all that matters. That in turn covers any variation on the ordering of measurements. The QM predictions for swapping do not depend on order. So you might reasonably assume that there is no significant difference between the underlying physics for the delayed case versus the non-delayed case.

(1) We start with Ma's (1), which is: |Ψ〉₁₂₃₄ = |Ψ−〉₁₂ ⨂ |Ψ−〉₃₄

Since |Ψ−〉₁₂= (|𝐻〉₁|𝑉〉₂− |𝑉〉₁|𝐻〉₂)/√2 and likewise for |Ψ−〉₃₄, we should agree on the following without debate:

(2) |Ψ〉₁₂₃₄ = (|𝐻〉₁|𝑉〉₂− |𝑉〉₁|𝐻〉₂)/√2) ⨂ (|𝐻〉₃|𝑉〉₄− |𝑉〉₃|𝐻〉₄)/√2)

So when measured on the H/V basis, this can produce only 4 possible 4-fold outcomes: HVVH, HVHV, VHVH and VHHV. That is for the entire universe of our initial state. If we end up with any 4-fold outcomes OTHER than those 4, we would know for certain that the ending state was unquestionably different than the initial state. Or said another way: there is no subensemble or subset of from the universe that produces outcomes different from the above unless the state objectively changes.

Now, because of the fact that the middle two photons 2 & 3 become indistinguishable after an entanglement swap (BSM), we must allow for several additional permutations. An HVHV outcome might appear as HHVV (photons 2 & 3 reversed); a VHVH outcome might appear as VVHH (photons 2 & 3 reversed). So any of the following 6 permutations must be considered as being possible outcomes of a swap event (these might result from the 4 possible Bell states) and are therefore compatible with Ma's initial state:

• Bell State Measurement outcomes Compatible with Input States: HVVH, HVHV*, VHVH*, VHHV, HHVV*, VVHH* (2 H's and 2 V's, same as the 4 initial states)
• Bell State Measurement outcomes Incompatible with Input States: HHHH, VVVV (4 H's or 4 V's)

What is not compatible with the initial state are the following outcomes: HHHH or VVVV, and also outcomes with 3xH and 1xV or vice versa. But as we can see in our Megidish swapping experiment, outcomes HHHH and VVVV do occur. See figure 3a and 3b (swap occurs) versus 3c (no swap occurs). You can see that there are fewer outcomes when no swap occurs as compared to when a swap occurs. Note: it is difficult to see on the graphs, but 3a and 3b show 4 correlated/anticorrelated outcomes while 3c only shows 2. So 2 of the outcomes on the [3a/|φ+> swap] and [3b/|φ-> swap] graphs don't occur at all if there was no swap (which is 3c).

If you start with 2 screws and 2 nails, then measure them and select: You won't ever find 4 nails.

Something physically changed as a result of the swap. So it couldn't have been merely a selection issue. No experimentalist has ever performed a swapping experiment and concluded they were choosing subsets that show Entanglement that are an artifact of their selection criteria. They all say the same thing: The initial state did not have any correlation between photons 1 and 4 on any basis. And therefore (after a swap) there could be no subset in which 1 and 4 have correlation resembling Entangled State statistics UNLESS the final state was different - as is predicted by QM. That final swapped state being (a la Ma):

(3) |Ψ〉₁₂₃₄ = |Φ−〉₁₄ ⨂ |Φ−〉₂₃

Which is in fact different than (1), as proven experimentally and as is as predicted.

And please note: My argument here applies to the full universe, not a subset. All swaps are considered, even Bell states that could not be identified distinctly. One of the things many don't understand is that if there is a either a 3-fold result or a 4-fold result of a Bell State Measurement, a swap occurred. Only 2 of the 4 possible Bell states can be uniquely identified when there is a 4-fold result, leaving the other 2 Bell states as ambiguous as to which is which in a 3-fold result. But none of that matters if you are seeing any HHHH or VVVV outcomes. Since those results do not correspond to any permutation we started with initially, we must reject our premise. Which also means the "Collider Loophole" concept is disproven - since it also postulates that there was no physical change. And we also reject the "No Difference Test", which likewise presupposes nothing changed.


*Note that these 4 outcomes are compatible with the input states; but because they have the VH or HV as the 2 & 3 photons, they are distinguishable as to which is the 2 photon and which is the 3 photon. Therefore there is no entanglement swap (BSM) when these appear, that only happens with indistinguishable permutations.

 

[Morbert]

So when measured on the H/V basis, this can produce only 4 possible 4-fold outcomes: HVVH, HVHV, VHVH and VHHV. That is for the entire universe of our initial state. If we end up with any 4-fold outcomes OTHER than those 4, we would know for certain that the ending state was unquestionably different than the initial state. Or said another way: there is no subensemble or subset of from the universe that produces outcomes different from the above unless the state objectively changes.
[...]
What is not compatible with the initial state are the following outcomes: HHHH or VVVV

In the Ma experiment, when the quarter-wave plate is on, the state indeed objectively and unitarily changes via the operator $I_{14}\otimes U_{23}$ before any detection events at Victor, and hence we can observe HHHH or VVVV in the Ma experiment. In an attempt to stay on topic, I will consider a projection-based account in the style of Mjelva, with a slight modification to align with @DrChinese's account: Both alice and Bob measure in the H/V basis.

After Alice and Bob carry out their measurements, the state is projected onto one of four product states with equal probability:
\begin{eqnarray*}\ket{H}_1\ket{H}_4\ket{V}_2\ket{V}_3\\\ket{H}_1\ket{V}_4\ket{V}_2\ket{H}_3\\\ket{V}_1\ket{H}_4\ket{H}_2\ket{V}_3\\\ket{V}_1\ket{V}_4\ket{H}_2\ket{H}_3\end{eqnarray*}Let's say Alice and Bob both get the outcome V. The projected state is therefore$$\ket{V}_1\ket{V}_4\ket{H}_2\ket{H}_3$$If victor has the quarter-wave plate on, then before any 2&3 detection event, the state evolves to$$I_{14}\otimes U_{23}\ket{V}_1\ket{V}_4\ket{H}_2\ket{H}_3 = \ket{V}_1\ket{V}_4\otimes \frac{i}{2}(\ket{HV}_{b''b''} - \ket{HV}_{c''c''} + \ket{HH}_{b''c''} - \ket{VV}_{b''c''})$$Victor might, for example, register two V detector clicks (and hence infer $\Phi^-$). In which case Alice would have registered V, Bob would have registered V, and Victor would have registered VV. I.e. VVVV

[edit] - Replaced symbols with LaTex in response to @iste's comment

 

[Morbert]

PS Note that this evolution $I_{14}\otimes U_{23}$ is entirely localised to the 2&3 photons, and is not, by itself, responsible for any swap. Instead, the "nonlocal" swap is Victor projecting onto a state upon registering outcomes. The unitary evolution through the quarter-wave plate=on configuration enables a swap, but is not a swap. It is the projection, not the unitary evolution, that is accounted for by Mjelva with post-selection (in Ma's delayed choice experiment).

 

[iste]

|𝑉〉1|𝑉〉4|𝐻〉2|𝐻〉3

Is it just me that cannot see any of your symbols??

 

[Morbert]

Is it just me that cannot see any of your symbols??

Can you see the symbols in @DrChinese's posts?

 

[iste]

Can you see the symbols in @DrChinese's posts?

No I cannot.

 

[DrChinese]

No I cannot.

Oops, sorry. Not sure of the issue. I can see the symbols on both my phone and computer.

 

[DrChinese]

In the Ma experiment, when the quarter-wave plate is on, the state indeed objectively and unitarily changes via the operator $I_{14}\otimes U_{23}$ before any detection events at Victor, and hence we can observe HHHH or VVVV in the Ma experiment.

I do not follow what you are saying here. Forget the quarter wave plate and operators. To swap, overlap at the beam splitter. To not swap, simply delay the 2 photon. That way the other things you mention are not a factor.

If the swap hasn’t occurred yet, the state is as my (1) and (2). Agreed?

 

[Morbert]

I do not follow what you are saying here.

On page 14 Ma describes the unitary evolution of incident photons moving through Victor's BiSA that allow him to infer Bell states from his polarization-resolution detections. I have applied this evolution to a projected state in line with Mjelva's projection-based account.

Forget the quarter wave plate and operators. To swap, overlap at the beam splitter. To not swap, simply delay the 2 photon. That way the other things you mention are not a factor.

I would rather not gloss over the details because that's where the devil is. What enables the "selection" interpretation of entanglement swapping is the understanding that the four possible outcomes of Victor's partial BSM measurement $\{\ket{\Phi^+}, \ket{\Phi^-}, \ket{HV}, \ket{VH}\}$ do not map directly to the four subensembles previously identified by Alice's and Bob's measurement. Ma makes this explicit in his careful description of the time-evolution of photons through the BiSA.

If the swap hasn’t occurred yet, the state is as my (1) and (2). Agreed?

Assuming that by "the swap hasn't occurred yet" we mean photons 2&3 have not yet reached Victor's BiSA:

If we adopt Ma's conventions, then we describe the state as your (1) and (2), but we must be aware that Ma's convention will hide the distinction between entangled photons 1&4, and perfectly correlated outcomes of already-performed measurements on photons 1&4. As this is a delayed-choice experiment, photons 1&4 no longer exist leading up to the swap.

If we adopt Mjelva's projection-based account, we preserve this distinction by projecting onto one of four states after Alice's and Bob's measurements.

Assuming the projection postulate, Alice and Bob’s measurements have the effect of projecting the state into one of the following four product states

In which case, the state is not your (1) and (2) but a projection onto one of the for terms in the relevant expansion.

[edit] - Clarified parts of Ma's convention.

[edit 2] - PS I am somewhat reluctant to continue with Ma's convention because it might bring us too close to the closed thread. I am happier to proceed with Mjelva's conventions, as it is the focus of this thread.

 

[iste]

[edit] - Replaced symbols with LaTex in response to @iste's comment

Thanks, much appreciated!

 

[Sambuco]

a) "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."-Kaltenbach et al (2008)

I'm not sure why you mentioned this paper. It's not a delayed-choiced version of entanglement swapping. Am I right? In the non-delayed case, I agree that standard QM (by standard I mean textbook QM) predicts that after the BSM measurement on 2&3, photons 1&4 will be in an entangled (non-separable) state.

b) Prior to Victor entangling photons 2&3: What connection (and therefore what correlation) is there between photons 1&4? 1 & 4 conceivable could be any photons in the entire universe, right? Now, we know that photons 1&2 are entangled in the state Ψ-. Ditto for photons 3&4.

What possible prediction does QM give about correlations between 1&4? Certainly, you must agree that without conditioning on measurements of 2 & 3: There is absolutely zero correlation, no more than there is any correlation between successive coin flips. And in fact Monogamy of Entanglement prevents 1 from being entangled with both 2 & 3 at the same time.

If you are still referring to the non-delayed case, I completely agree with you.

So we see a) that scientists conducting these experiments think there is no initial correlation between photons 1 & 4. That should tell us something significant. We see b) that there can definitely be no physical connection or correlation whatsoever between 1 & 4 *prior* to their partners 2 & 3 entering a beamsplitter. And QM predicts: c) before entering a beam splitter, they can have no initial correlation on the L/R (or +/-) basis. Conclusion: There is no initial correlation between photons 1 & 4.

I also agree with what you say here. In any case (delayed or non-delayed), the initial state of the four-photon system has no correlation between photons 1 and 4, since they are entangled with photons 2 and 3, respectively.