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

[Morbert]

Polarizations of photons 2 & 3 are measured at the end of the apparatus. As I understand it, the basis in which they are measured is the same whether a swap is done or not. That means the four possible combinations of results for those measurements are the same whether a swap is done or not. So there is nothing to "distinguish" in terms of the measurement results themselves.

What you are "distinguishing" is, as I said, what the four possible combinations of results mean in terms of what states they signal. If a swap is done, they signal Bell states; if a swap is not done, they signal separable states. But that is just another way of saying that the correlations that are observed change depending on whether a swap is done. And those correlation changes also occur in the measurements of photons 1 & 4, even though photons 1 & 4 are not local to the BISA apparatus.

The BSM and SSM eigenstates as presented by Ma pertain to the spacial modes b and c, not b" and c". When Ma writes $\ket{HH}_{23}$ this corresponds to $\ket{HH}_{bc}$ but cannot imply $\ket{HH}_{b''c''}$ or $\ket{HH}_{b''b''}$ or $\ket{HH}_{c''c''}$, when the quarter-wave plate is on.

 

[Morbert]

@PeterDonis There is a distinction between adopting an interpretation, and arguing an experimental result poses a novel challenge to an interpretation. We could, for example, argue whether or not MWI's determinism sufficiently accounts for probabilistic character of QM predictions whether or not we adopt it. @DrChinese's arguments about the challenge entanglement-swapping experiments pose for pre-selection/post-selection cannot be reduced to a subjective distaste for antirealist interpretations.

 

[PeterDonis]

The BSM and SSM eigenstates as presented by Ma pertain to the spacial modes b and c, not b" and c". When Ma writes $\ket{HH}_{23}$ this corresponds to $\ket{HH}_{bc}$ but cannot imply $\ket{HH}_{b''c''}$ or $\ket{HH}_{b''b''}$ or $\ket{HH}_{c''c''}$, when the quarter-wave plate is on.

Irrelevant. The final measurement results on photons 2 & 3 are in the H-V basis whether the quarter wave plate is on or not. What they mean (at least according to Ma's analysis) changes, but the basis does not. That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

@DrChinese is interpreting the above as showing that the experimenter choosing whether or not to do a swap has a nonlocal effect on photons 1 & 4.

You are interpreting the above as something different, something about statistics and pre and post selection and so on, which you say does not show any kind of nonlocal effect.

This is a difference of opinion about interpretation that is not going to be resolved here.

There is a distinction between adopting an interpretation, and arguing an experimental result poses a novel challenge to an interpretation.

I agree. But my point stands that the disagreement you are having with @DrChinese is not going to be resolved here. Your disagreement is basically over whether these results do indeed pose a "novel challenge" to the kind of statistical, pre selection/post selection interpretation you are arguing for. That disagreement is a disagreement over choice of interpretation that is not going to be resolved here. Choice of interpretation includes choices about what an interpretation has to explain. @DrChinese is saying that an interpretation has to explain what is going on in each individual run that accounts for these results. You are saying it doesn't; that it's enough to just point out the statistics and the pre and post selection that is being done, without having to give any account of what is happening in each individual run that produces those statistics. That disagreement is not going to be resolved here, because different QM interpretations do not even agree on whether such an account is necessary or what it must contain.

 

[Morbert]

Irrelevant. The final measurement results on photons 2 & 3 are in the H-V basis whether the quarter wave plate is on or not. What they mean (at least according to Ma's analysis) changes, but the basis does not. That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

You're not following the conversation. You said I was looking at it backwards. I said I wasn't as my terminology was consistent with Ma's. You then proceed to argue against a shadow. You are implying I am papering over the detector firings and the inferred BSM or SSM, which is of course nonsense. Please make a substantive critique of my position if you have one. I will let @DrChinese speak for himself.

 

[Sambuco]

Hi @PeterDonis!

What is not the same if a swap is done vs. not done is what each of the four possible combinations of results of the final polarizations measurements on photons 2 & 3 means in terms of the states they each signal. Of course those are different if a swap is done vs. not done; that's the point. And those states are not local: they involve photons 1 & 4 as well as photons 2 & 3. That's the thing that, on any kind of realist interpretation of what the quantum state means, indicates that the experimenter choosing to do a swap vs. no swap (by turning the quarter wave plates on or off, or whatever else is done to choose swap vs. no swap in any particular experiment) is doing something real to photons 1 & 4, which are not locally present, as well as to photons 2 & 3, which are locally present.

That exactly what the paper by Mjelva analyze. I have to say that this is not my preferred interpretation of the experimental results (I'll expand in the following paragraph) but, anyway, I believe that Mjelva's analysis of the DCES (Ma's paper) is compatible with some realistic interpretations (maybe I prefer to say that it is consistent with $\Psi\text{-ontic}$ interpretations to avoid confusion about the meaning of "realistic", but no problem) and, at the same time, it does not imply a backward-in-time change of the 1&4 state, since the forward-in-time evolution of the state of the four-photon system allows him to conclude that the Bell-correlations of photons 1&4 in each subset are due to post-selection. Anyway, this does not confront the fact that these 1&4 correlations can only be revealed when Victor chooses to perform a BSM on photons 2&3. Otherwise, there is no way we can physically project the states $\ket{\Psi(t_1)}_{A,B,C,D}$ onto entangled states for photons 1&4. To avoid confusion, I'm talking about his analysis of the delayed-choice experiment, where the 2&3 BSM is in the future light-cone of the 1&4 measurements.

Let me explain why I'm not satisfied with this "realistic" interpretation. As many said, the predictions of QM are the same irrespective of how 1&4 measurements and 2&3 BSM are time-ordered. Therefore, if we want to interpret both experiments (delayed and non-delayed) in terms of cause-and-effect, we have different explanations about which is the cause and which is the effect, even when the predictions are the same. Even more, if we consider the case where 1&4 measurements and 2&3 BSM are space-like separated (as Mjelva discuss in section 5 of his paper), these interpretations say that we have to accept that which is the cause and which is the effect depends on the reference frame. Well, maybe someone could digest that, but to me, the real problem arises when we go back to the delayed/non-delayed experiments and ask simple questions. I'll give an example. If I consider the non-delayed experiment (2&3 BSM first, 1&4 measurement later) and the 2&3 BSM changes the state of 1&4, when that occurs? At the time the 2&3 BSM was performed, photons 1&4 were located at any other position, so if we want to keep some relativistic causation, then we have to argue for something like that the change of the state of 1&4 must be sitting at the edge of the future light cone of the 2&3 measurement, waiting for photons 1&4 to enter there. Not only this kind of story seems weird enough to me, what is more important is that nothing about that is within the QM formalism. Then, at least for now, my impression is that, maybe, we have to leave aside the concept of "causation" and take "correlation" as something more fundamental.

Lucas.

 

[PeterDonis]

You are implying I am papering over the detector firings and the inferred BSM or SSM, which is of course nonsense.

Is it? Do you agree with what I said in what you quoted, as far as it goes? I know it leaves out things that you have been emphasizing. But if you do agree with it as far as it goes, it would greatly help if you would say so, since from your posts so far in this thread I don't know whether you do or not.

 

[PeterDonis]

the predictions of QM are the same irrespective of how 1&4 measurements and 2&3 BSM are time-ordered. Therefore, if we want to interpret both experiments (delayed and non-delayed) in terms of cause-and-effect, we have different explanations about which is the cause and which is the effect, even when the predictions are the same. Even more, if we consider the case where 1&4 measurements and 2&3 BSM are space-like separated (as Mjelva discuss in section 5 of his paper), these interpretations say that we have to accept that which is the cause and which is the effect depends on the reference frame.

That's correct, and it's true even for the simpler case of measurements on a pair of entangled particles, with no swaps anywhere. Whatever "cause and effect" is happening in any QM experiment involving entanglement cannot work quite the same as the usual cause and effect we are used to in the classical case. But since it can produce correlations that violate the Bell inequalities, it also can't be reduced to "well, it's just revealing something that was present in the initial conditions and gets uncovered by post-selection"--at least not if you want a realist model of how the correlations get enforced in each individual case. That's a big reason why there is no single generally accepted interpretation of QM.

 

[eloheim]

In the abstract of Mjelva's paper he says:

I will argue that a careful analysis of these experiments shows that they in fact display nothing more than ‘‘ordinary’’ spacelike entanglement, and that any purported timelike entanglement is an artefact of selection bias.

To me that sounds like he's saying you still need regular spacelike entanglement (and non-locality?) to explain the experiments. Then at the projection postulate preliminary conclusions section (4.1.3) he says (my emphasis):

I have shown how, on a projection-based account, the Bell correlations displayed in the Ma et al.- and Megidish et al.-experiments can be accounted for in terms of selection bias in the post-selected subsample.
At no point in the analysis was it necessary to posit any entanglement relation obtaining between particle 1 and particle 4. In fact, it should be clear from the analysis that, as each of the states (5) and (9) following
the Bell-state measurement can be written as the tensor product of the state of particle 1, the state of particle 4 and the state of the pair (2, 3), the particles 1 and 4 are not entangled.

So he's saying entanglement is not needed to explain 1 and 4, but what about 1&2, 3&4 and 2&3? Wouldn't the non-swapped version of the runs (in Ma's version) require spacelike entanglement to explain them at a bare minimum? Or is this beyond the point?

Also one question (at risk of sounding stupid): In Ma's experiment, in the swapped-ON runs, how will the H/V polarization readings for 1 and 4 differ between the Φ+ and Φ- subsets?

 

[Morbert]

In the abstract of Mjelva's paper he says:

To me that sounds like he's saying you still need regular spacelike entanglement (and non-locality?) to explain the experiments. Then at the projection postulate preliminary conclusions section (4.1.3) he says (my emphasis):

So he's saying entanglement is not needed to explain 1 and 4, but what about 1&2, 3&4 and 2&3? Wouldn't the non-swapped version of the runs (in Ma's version) require spacelike entanglement to explain them at a bare minimum? Or is this beyond the point?

All runs start with 1&2 entangled, and 3&4 entangled.

Also one question (at risk of sounding stupid): In Ma's experiment, in the swapped-ON runs, how will the H/V polarization readings for 1 and 4 differ between the Φ+ and Φ- subsets?

They will be correlated in both the Φ+ and Φ- subsets. If Alice and Bob measure in the +/- basis instead, they will be correlated in the Φ+ subset and anticorrelated in the Φ- subset. If Alice and Bob measure in the R/L basis, they will be anticorrelated in the Φ+ subset and correlated in the Φ- subset.

 

[Morbert]

Is it? Do you agree with what I said in what you quoted, as far as it goes? I know it leaves out things that you have been emphasizing. But if you do agree with it as far as it goes, it would greatly help if you would say so, since from your posts so far in this thread I don't know whether you do or not.

That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

Victor can of course always partition runs into HH, HV, VH, VV, without regard for spatial mode resolution, and whether or not the the swap is done, but whether or not the swap is done will influence which subset a run is sorted to.

E.g. Consider photon pairs prepared in the mixture $\rho = (\ket{HH}\bra{HH} + \ket{VV}\bra{VV})/2$ incident on Victor's BiSA. If the quarter-wave plate is off, then all runs will be placed in the HH or VV subset. HV and VH will be empty. If the quarter-wave plate is on, then runs will be placed in any of the four subsets HH, VV, HV, or VH. Similarly if Victor is discarding runs that did not yield the same-polarization detection events, then when the plate is off, Victor will keep all runs, but if the plate is on, Victor will not keep all runs. Hence, Victors decision to do the swap amounts to Victor choosing one of two alternative procedures for selecting runs. This is what Mjelva means by a selection effect and what Price and Wharton mean by the Collider Loophole.

I do not know if you agree or disagree, but it is worth emphasizing that while we can label runs HH HV VH VV whether or not the swap is done, the local sorting procedure will be different, and hence the significance of the subsets will be different.

You are interpreting the above as something different, something about statistics and pre and post selection and so on, which you say does not show any kind of nonlocal effect.

This is a difference of opinion about interpretation that is not going to be resolved here.

My position is interpretation independent. My position is the Collider Loophole has explanatory power for a class of interpretations, which renders entanglement-swapping experiments no less explained than traditional EPRB experiments for these interpretations. Someone is free to adopt or reject an interpretation, but if they argue these experiments now pose an additional challenge to a class of interpretations, above standard EPRB experiments, that is an objective position that can be critiqued.

I.e. I am defending Mjelva. When he says

Though Egg’s view seems to be the most widely accepted, it has recently been criticized by Glick (2019), who argues that accepting this view renders one unable to explain the strong correlations seen in the delayed-choice experiment, leaving them as mysterious as the correlations seen in traditional Bell-type experiments appear on views that take an anti-realist stance on entanglement in general. The main objective of this paper is to answer Glick’s challenge by providing an account of the Bell correlations displayed in DCES experiments in terms of selection effects arising due to post-selection.

I am arguing he successfully met his objective.

 

[PeterDonis]

Victor can of course always partition runs into HH, HV, VH, VV, without regard for spatial mode resolution and whether or not the the swap is done

In other words, you agree that the final measurement results on photons 2 & 3 are always made in the H-V basis, and recorded as such?

whether or not the swap is done will influence which subset a run is sorted to.

You are making an implicit assumption that it makes sense to look at a run which has a swap done, and what photon 2 & 3 results it had (HH, HV, VH, or VV), and then ask what the results would have been for that run if a swap was not done. Or vice versa.

This assumption, in at least a fair portion of the literature on this topic, is called "counterfactual definiteness", and is one of the assumptions underlying Bell's Theorem. So it is one candidate for an assumption that is violated by actual quantum systems, since they can produce correlations that violate the Bell inequalities. I'm not sure whether the interpretation @DrChinese is using violates this assumption or not.

 

[PeterDonis]

My position is interpretation independent.

No, it's not. See my post #61 just now.

 

[Morbert]

In other words, you agree that the final measurement results on photons 2 & 3 are always made in the H-V basis, and recorded as such?

I agree that we can sort them into subsets based on the the H-V result of the final measurement, but the final measurement includes spatial mode information as well. The spatial modes are necessary for the partial BSM inference. E.g. When the plate is on, HVb"b" implies a Φ+ result, while HVb"c" implies a failed BSM or a separable state result.

You are making an implicit assumption that it makes sense to look at a run which has a swap done, and what photon 2 & 3 results it had (HH, HV, VH, or VV), and then ask what the results would have been for that run if a swap was not done. Or vice versa.

This assumption, in at least a fair portion of the literature on this topic, is called "counterfactual definiteness", and is one of the assumptions underlying Bell's Theorem. So it is one candidate for an assumption that is violated by actual quantum systems, since they can produce correlations that violate the Bell inequalities. I'm not sure whether the interpretation @DrChinese is using violates this assumption or not.

While counterfactual definiteness (CD) is a relevant point of discussion (see Mjelva's discussion of Price's and Wharton's "no difference test" and "counterfactual fragility test" in the paper). My narrower point avoids any CD pitfalls. It is objectively the case that turning the plate on modifies the Hamiltonian such that the selection criteria when the plate is on cannot be identified as the same criteria when the plate is off even though both use the signature "HH or VV". In Ma's experiment, when the plate is off, approximately 50% of runs will yield the signature HH or VV. When the plate is on, only 25% of runs will.

And the point is this objective effect affords a class of interpretation an explanation. The charge being defended against is that, even on their own terms, these interpretations struggle to account for entanglement-swapping results. Even if we do not like these interpretations, we can argue for their robustness against a challenge.

 

[PeterDonis]

the final measurement includes spatial mode information as well.

For the setup given in the Ma paper, yes, this is true, and for a full comparison along the lines I was describing between "swap" and "no swap" subsets, one has to pick out the spatial mode/polarization combinations that signal particular Bell states. For example, one could pick out only the subset of runs with the same polarization (HH or VV) appearing in the two different spatial modes (b'' and c''); if a swap is done this signals the $\ket{\phi^-}_{23}$ Bell state in the setup given in the Ma paper. Then the sub-subset of these runs with a swap will show the Bell state correlations between photons 1 & 4, while the sub-subset of these runs with no swap will show no correlations between photons 1 & 4.

 

[lodbrok]

In Ma's experiment, when the plate is off, approximately 50% of runs will yield the signature HH or VV. When the plate is on, only 25% of runs will.

@DrChinese and @PeterDonis, can you acknowledge this very important point from @Morbert?

 

[PeterDonis]

It is objectively the case that turning the plate on modifies the Hamiltonian

Of course.

the selection criteria when the plate is on cannot be identified as the same criteria when the plate is off even though both use the signature "HH or VV". In Ma's experiment, when the plate is off, approximately 50% of runs will yield the signature HH or VV. When the plate is on, only 25% of runs will.

Whether this makes the two cases not have "the same criteria" depends on what you think counts as "the same criteria". Which depends on what interpretation you adopt.

 

[Morbert]

Whether this makes the two cases not have "the same criteria" depends on what you think counts as "the same criteria". Which depends on what interpretation you adopt.

Even according to an interpretation involving nonlocal influence, the BiSA configured to perform a swap will modify the state as described by a unitary operator. All interpretations acknowledge this change, however they interpret the quantum state. So I don't see how the the "HH or VV, swap=off" subset can be substantively associated with the "HH or VV, swap=on" subset beyond trivially observing that they have the same coincidences in Victor's detectors. Ma says this is why he chose Φ- for comparison, but he could have alternatively chosen Φ+ for comparison (HVb"b" or HVc"c", swap=on).

Note that interpretations involving nonlocal/retrocausal influence do not need any such association between these subsets. These interpretations simply assert that Victor's successful swaps will nonlocally/retrocausally influence photons 1&4 to exhibit Bell correlations. E.g. In Egg's paper referenced by Mjelva, he defends a realistic, nonlocal account of entanglement swapping without the need to associate swap subsets with no-swap subsets.

 

[PeterDonis]

Even according to an interpretation involving nonlocal influence, the BiSA configured to perform a swap will modify the state as described by a unitary operator.

Yes, but the quantum state is not the same as the "criteria". If the "criteria" is simply "select the subset of runs that are either HH or VV", that criterion is the same no matter what percentage of the total runs that subset turns out to be.

I don't see how the the "HH or VV, swap=off" subset can be substantively associated with the "HH or VV, swap=on" subset

By the obvious fact that they are both selected as the subset of runs that are either HH or VV. To some people, including me, that's sufficient to make them selected according to "the same criteria". To you, it's not. That's a disagreement over interpretation that's not going to be resolved here.

 

[PeterDonis]

interpretations involving nonlocal/retrocausal influence do not need any such association between these subsets.

True, such interpretations require that there is an explanation of how the results of each individual run come about, at the level of the individual run. Such an explanation cannot make any use of the statistics over subsets of all the runs.

And if this is correct, then your claim that the "swap" and "no swap" subsets that are either HH or VV are not selected by "the same criteria" is simply irrelevant for the interpretation @DrChinese is using.

 

[DrChinese]

1. I agree that we can sort them into subsets based on the the H-V result of the final measurement, but the final measurement includes spatial mode information as well. The spatial modes are necessary for the partial BSM inference. E.g. When the plate is on, HVb"b" implies a Φ+ result, while HVb"c" implies a failed BSM or a separable state result.

2. ... It is objectively the case that turning the plate on modifies the Hamiltonian such that the selection criteria when the plate is on cannot be identified as the same criteria when the plate is off even though both use the signature "HH or VV".

3. In Ma's experiment, when the plate is off, approximately 50% of runs will yield the signature HH or VV. When the plate is on, only 25% of runs will.

There is a mixture of correct and incorrect information here, and this needs to be clarified to make sense of the various arguments on either side.

1. I will grant that it is at least "possible" that spatial modes are relevant as you imagine in selection criteria (besides the obvious relevance to determining if we have Φ- or Φ+). You mention a hypothetical effect you call: "... turning the plate on modifies the Hamiltonian such that the selection criteria when the plate is on cannot be identified as the same criteria when the plate is off". Let's call your concept "Materially Altered Criteria" (MAC) to make it shorter. But that is subject to experimental verification, as well comparison to theory. (And of course there is no matching theory, hopefully you already know that.)


2. If your MAC concept was valid, it would be easily detectible. Because if it weren't present at all, you are asserting the magic of "the appearance of correlation" couldn't occur - presumably the Ma experiment is "cheating" us in some manner that even they are not aware of.

But that's not true, and we know this... how? In the Ma experiment, they use the technique of the Electro Optical Modulators (EOMs) to switch quickly from one configuration of the beam splitter (50:50) to the other (0:100). The purpose of that switch is to enable/disable overlap of photons 2 & 3 in the beam splitter (via changing BS reflectivity); and to do it so rapidly that there is insufficient time for any kind of extraneous (related) influence to enter the picture. So they can close off a possible loophole (for lack of a better description).

But that technique (fast EOMs) does not lead to any change in the outcome statistics. That's because the exact same results were reported when there was no such change in the beam splitter reflectivity (from 50:50 to 0:100). In the Megidish experiment (which is very similar), they don't introduce any changing optics that might use your MAC idea. Instead, they simply delay one of the photons (say the photon 2 line) sufficiently as to cause the 2 & 3 photons not to overlap - they are now easily distinguishable due to timing. Yet you still get the same information as to Hb"Hc" and Vb"Vc" signatures. See their Fig. 3a (Φ+ swap) /3b (Φ- swap)/3c (no swap). The only physical difference here being that they are now distinguishable/indistinguishable. The observed 4-fold statistics change to match whether we have a swap or not. If MAC were correct, this shouldn't happen - because MAC depends on a change to the optical configuration of a hypothetical parameter related to "spatial mode".

Although spatial mode (reflect or transmit at a 50:50 beam splitter) is a real effect, it has absolutely no relationship whatsoever to H/V (or L/R or +/-) polarization - either theoretically or experimentally. Theoretically, there is no correlation between beam splitter T or R and any kind of polarization, that is well known. The only purpose of the beam splitter is to create indistinguishable paths, and has nothing to do with observed 4-fold polarization in and of itself. Clearly, the single independent variable in the Megidish version is whether there is overlap (or not) of photons 2 & 3. This can't be denied.

Everything you are asserting about the EOMs leading to your MAC effect is a red herring, as Megidish demonstrates. Forget the "plates" as a factor, they just don't do anything like what you imagine. Or if the authors I cite are wrong, please show me the substantial peer reviewed experimental works that support your perspective. (And Mjelva is not one of those.)


3. This is both true and false. Φ- (Hb"Hc" or Vb"Vc") is 25%, Φ+ (Hb"Vc" or Vb"Hc") is 25%, and no swap due to temporal distinguishability (Hb"Hc" or Vb"Vc" or Hb"Vc" or Vb"Hc") is 50%. Ma only reports Φ-.
So yes, 25% is half of 50%.

Note that there are also cases in which there is always distinguishability (never a swap). These are mostly skipped over in these discussions, but they exist. You can see that these are there in the Megidish Fig. 3, the Quantum State Tomography (QST). It shows all 16 permutations, and no bar is present for those cases (not sure how many there are but I think 4).

 

[DrChinese]

@DrChinese and @PeterDonis, can you acknowledge this very important point from @Morbert?

Not what I call a useful point. See my post #70, point 3. If you are unsure, look at the full quantum state tomography (QST) in the Megidish experiment, Figure 3, in which all 16 outcome permutations are presented. It's a virtually identical experiment, except in the order of measurements of photons 1-4.

 

[Morbert]

@DrChinese "My" MAC is the time-evolution described on page 14 of Ma. This evolution occurs when the plate is on, and does not occur when the plate is off. This time-evolution will alter the polarization of incident photon pairs. E.g. photon pairs prepared in the state HH, incident on the BiSA (swap=on), can yield coincidences HH or VV or HV or VH. Hence, it alters the frequencies of the different coincidences observed by Victor.

[edit] - See my post #21 for an application of this MAC to one of Mjelva's Alice + Bob projections.

 

[Morbert]

@DrChinese Maybe this is a good place to start: Do you agree with the following alternative time-evolutions applied to two HH photons? One when the plate is on, one when it is off.
$$\begin{eqnarray*}
U^\mathrm{off}|HH\rangle_{23} &=& |HH\rangle_{b''c''}\\
U^\mathrm{on}|HH\rangle_{23} &=& i(|HH\rangle_{b''c''} - |VV\rangle_{b''c''} + |HV\rangle_{b''b''} - |HV\rangle_{c''c''})/2\\
\end{eqnarray*}$$

 

[PeterDonis]

This evolution occurs when the plate is on, and does not occur when the plate is off.

The time evolution (Hamiltonian) is not the same as the "selection criteria" either. At least, if you believe it is, that's another of those things that depends on what interpretation you adopt and is not going to be resolved here.

 

[DrChinese]

... This is what Mjelva means by a selection effect and what Price and Wharton mean by the Collider Loophole. ...

My position is interpretation independent. My position is the Collider Loophole has explanatory power for a class of interpretations, which renders entanglement-swapping experiments no less explained than traditional EPRB experiments for these interpretations. Someone is free to adopt or reject an interpretation, but if they argue these experiments now pose an additional challenge to a class of interpretations, above standard EPRB experiments, that is an objective position that can be critiqued.

I.e. I am defending Mjelva. When he says I am arguing he successfully met his objective.

There is no Collider Loophole in QM. There are no applications of this far-fetched concept to entanglement swapping. Period. What Price and Wharton propose consists of a long list of loose analogies, without a single actual example of how it might apply to quantum mechanics or swapping specifically. It is what I refer to as "an idea for an idea". So to say it applies to a class of interpretations is giving it a status that it does not deserve.

A collider approach cannot be applied to perfect correlations. Now, I don't have to prove that because the Collider Loophole is not generally accepted science. And neither is much of what Mjelva says; his ideas must be made to follow accepted science - and not the speculations of others in arxiv.

---

Here is a quote from Mjelva, talking about time related projection: "Due to the relativity of simultaneity, this means that the temporal order of the three measurements will be frame-dependent: relative to some frames, Vicky’s measurement will occur before either Alice or Bob’s measurements, while relative to other frames, it will occur after." This is blatantly false. The order of measurements can be and in some cases is the same in all reference frames. It is certainly true of the Megidish experiment, where everything happens in the same place - a simple way to show that order is fixed and specific.

The point being: there is no difference between space-like entanglement and time-like entanglement, as Mjelva tries to claim. That is the entire point of experiments like Megidish (and others). And according to normal rules of entanglement: distance, time, and causal order are actually subservient to a quantum context which does not follow traditional Einsteinian notions of special relativity.

---

So what I am saying is: Mjelva has built an argument based on ideas he is comfortable with. It's a complex set of tiered logic. So is that of Price and Wharton, which is one of his building blocks. But those blocks are subject to challenge. And the burden is on those who dismiss the results of top teams with casual comments with poor support.

Again, if someone can take a specific example of how any of these ideas work and show us - without simply saying "there could be" this or that... well, that would be nice. As it is, I have repeatedly shown exactly why the Mjelva approach makes predictions that are diametrically opposed to both entanglement predictions and entanglement experiments. See my post #20 for example. And these are just disregarded as if meaningless.

 

[DrChinese]

@DrChinese Maybe this is a good place to start: Do you agree with the following alternative time-evolutions applied to two HH photons? One when the plate is on, one when it is off.
$$\begin{eqnarray*}
U^\mathrm{off}|HH\rangle_{23} &=& |HH\rangle_{b''c''}\\
U^\mathrm{on}|HH\rangle_{23} &=& i(|HH\rangle_{b''c''} - |VV\rangle_{b''c''} + |HV\rangle_{b''b''} - |HV\rangle_{c''c''})/2\\
\end{eqnarray*}$$

I really wish you wouldn't use the term "plate on" and "plate off". Plates on or off have nothing to do with swapping. It's all about distinguishability and nothing else. Plates changing are not required, and completely obscure the theory and implementation. Just say: "swap on" or "swap off" and we will all know what you are referring to. And I assume the same with your labeling of "on" and "off" above.

If you have photons 1 & 4 measured as VV, then by the normal forward in time rules: photons 2 & 3 must be HH. If they are not swapped, then they will definitely be HH when measured. They will be Hb"Hc" in the Ma experiment, but that is not generally the case. For example, that doesn't happen in the Megidish experiment.

If there is a swap: you can't really discuss what happens as you are trying to describe. They can be either Hb"Hc" or Vb"Vc", as both of those are compatible as 4-fold occurrences.

 

[Morbert]

Here is a quote from Mjelva, talking about time related projection: "Due to the relativity of simultaneity, this means that the temporal order of the three measurements will be frame-dependent: relative to some frames, Vicky’s measurement will occur before either Alice or Bob’s measurements, while relative to other frames, it will occur after." This is blatantly false. The order of measurements can be and in some cases is the same in all reference frames. It is certainly true of the Megidish experiment, where everything happens in the same place - a simple way to show that order is fixed and specific.

The point being: there is no difference between space-like entanglement and time-like entanglement, as Mjelva tries to claim. That is the entire point of experiments like Megidish (and others). And according to normal rules of entanglement: distance, time, and causal order are actually subservient to a quantum context which does not follow traditional Einsteinian notions of special relativity.

Please see the sentence right before. Mjelva is of course aware that Ma's and Megidish's experiments are constrained in ways that Hensen's isn't.

See also his analysis of the seeming frame-dependence of entanglement swapping implied by projection-based accounts.

If you have photons 1 & 4 measured as VV, then by the normal forward in time rules: photons 2 & 3 must be HH. If they are not swapped, then they will definitely be HH when measured. They will be Hb"Hc" in the Ma experiment, but that is not generally the case. For example, that doesn't happen in the Megidish experiment.

If there is a swap: you can't really discuss what happens as you are trying to describe. They can be either Hb"Hc" or Vb"Vc", as both of those are compatible as 4-fold occurrences.

If the bit in bold was true, then that would indeed be objective evidence of nonlocal influence, because Victor would keep all runs that have photons 1 & 4 measured as VV or HH, and no selection bias could occur.

Instead, even when photons 1 & 4 are VV, photons 2 & 3 can also be HVb"b" or HVc"c" (signifying Φ+), and hence discarded by Victor. If Victor always performs a swap, he will discard 50% of all runs that have 1 & 4 measured as VV. Similarly, Victor will discard 50% of runs that have 1 & 4 measured as HH. Victor only keeps all runs that have same-polarization for 1 & 4 if he never does a swap.

Hence, a swap can be consistently interpreted as a selection bias. Victor is using the information he gains from his BSM to pick out a subset of all runs that have same-polarization for 1 & 4. This is the Collider Loophole.

 

[eloheim]

If there is a swap: you can't really discuss what happens as you are trying to describe. They can be either Hb"Hc" or Vb"Vc", as both of those are compatible as 4-fold occurrences."

If the bit in bold was true, then that would indeed be objective evidence of nonlocal influence, because Victor would keep all runs that have photons 1 & 4 measured as VV or HH, and no selection bias could occur

Do you believe a local hidden-variable model can reproduce DCES (e.g. Ma et al)? Because say photons 1 and 4 have hidden values of Photon1: |R>,|+> and Photon2:|L>,|->. If Alice and Bob both measure in the R/L basis then Victor's bsm should give Φ+, and if they instead measured in +/- Victor must get Φ-. Are the wrong combinations somehow getting thrown out with discarded runs?

 

[Morbert]

Do you believe a local hidden-variable model can reproduce DCES (e.g. Ma et al)? Because say photons 1 and 4 have hidden values of Photon1: |R>,|+> and Photon2:|L>,|->. If Alice and Bob both measure in the R/L basis then Victor's bsm should give Φ+, and if they instead measured in +/- Victor must get Φ-. Are the wrong combinations somehow getting thrown out with discarded runs?

No local theory of hidden variables can reproduce the predictions of QM. The outcomes Victor can get are not limited by the choice of basis Alice and Bob make.

 

[DrChinese]

1. If the bit in bold was true, then that would indeed be objective evidence of nonlocal influence, because Victor would keep all runs that have photons 1 & 4 measured as VV or HH, and no selection bias could occur.

2. Instead, even when photons 1 & 4 are VV, photons 2 & 3 can also be HVb"b" or HVc"c" (signifying Φ+), and hence discarded by Victor.

3. If Victor always performs a swap, he will discard 50% of all runs that have 1 & 4 measured as VV. Similarly, Victor will discard 50% of runs that have 1 & 4 measured as HH. Victor only keeps all runs that have same-polarization for 1 & 4 if he never does a swap.

4. Hence, a swap can be consistently interpreted as a selection bias. Victor is using the information he gains from his BSM to pick out a subset of all runs that have same-polarization for 1 & 4.

5. This is the Collider Loophole.

A note that applies to my comments below, which I think we can all agree to. None of the referenced experiments (Ma, Megidish) provide sufficient detail to clarify the precise values N of the various outcome permutations. Consequently, there are some things we are necessarily "guessing" on in our understanding of these experiments. We might tend to imagine different N values (me vs. you), and it would be helpful if we had those numbers to work with. Instead, many of the reported values are "relative".


1. Again, this is demonstrated experimentally in the QST diagram in Megidish, Figure 3a (Φ+ swap, 4 bars) vs. 3c (no swap, 2 bars).


2. This result is incompatible with a VV for photons 1 & 4, if you assume a forward in time only analysis. But yes, it is a possible outcome. However, it is not really discarded by Victor. In the Ma experiment, they don't report it (and if you like you can say it was discarded). But in other experiments, such as Megidish, it is reported.


3. This is true, but not in the manner you are portraying it. 50% of the VV/HH swap results are discarded because they yield swap outcomes Ψ+ or Ψ-. These cannot be distinguished, and will show as 3-fold coincidences. That's because there are Vb"Vb" (and 3 other similar) permutations where both the 2 & 3 photons end up in the same detector. That registers only 1 click rather than 2 separate; and even if there were 2 clicks, it would not distinguish these 2 swap states.


4. This makes no sense. At least not to me

We are asking the simple question: What is different (the actual question posed by Price, Wharton and Mjelva) when we compare swap/no-swap results from signatures Hb"Hc"/Vb"Vc"? As @PeterDonis and I have said repeatedly, this is basic scientific method. You get the (approximately) same number of results N either way. Nothing is discarded.

And there are 2 things that ARE dramatically different:
a) There are swap outcomes HHHH and VVVV that don't appear when there is no swap; and
b) There is perfect swap case correlation for photons 1 & 4 when they are measured on the +/- or L/R basis, but not when no swap is executed.

The real mystery is the b) effect, and that is what Ma is really trying to get across. Note that in the forward in time only version of our description, which is what we are trying to accomplish in this thread: an LL (or RR) outcome for for photons 1 & 4 implies an RR (or LL) outcome for photons 2 & 3. The 2 photon, for example, when measured on the H/V basis, should have absolutely no causal connection nor correlation between the R outcome of photon 1 and a V outcome for photon 2. Agreed? Similar for photons 3 & 4.

So before a swap can occur (or not): there is no correlation between ANY of 2 of the outcomes of photons 1/2/3/4, when 1 & 4 are measured on L/R basis and 2 & 3 are measured on the H/V basis. Every one is independently random. And absolutely nothing shows up differently if we now confirm this obvious point by measuring on these bases. Agreed? No correlation whatsoever between 1 & 2 outcomes, or between 1 & 3 outcomes, or between 1 & 4 outcomes, etc.

Now we look only at the cases where there is Vb"Vc" for photons 2 & 3 (still no swap). There is still no correlation whatsoever between 1 & 2 outcomes, or between 1 & 3 outcomes, or between 1 & 4 outcomes. Of course there is correlation between the 2 & 3 outcomes, by definition. Now we execute a swap instead, same selection criteria otherwise. How can this operation* "select a subset" featuring perfect correlation between photons 1 & 4 from results we previously agreed were completely random?

Classical Example: If I start with a list of people that can be Male or Female, and can have an Odd or Even number for their Passport number - values we will take for granted as having no causal connection and appear otherwise random: How do I select a subset that features perfect correlation between Male and Odd (for example)? And how do I pick 2 persons such that every pair of Males selected both have Odd passport numbers? There cannot be such a subset without there existing some 3rd variable that we select upon. That doesn't exist in the quantum world. And if it did, we would need to re-write quite a bit of theory.


5. This literally has nothing to do with the Collider Loophole. But it would be an example of your hypothetical Selection Bias (MAC) if you could somehow tie the observed results with the predicted subsets. Unfortunately, those don't really work out, as I have mentioned.



*Answer: This operation is not a passive selection process; it is an active process that has both temporal and spatial extent. Exactly as the authors of the experiments point out.

 

[Morbert]

2. This result is incompatible with a VV for photons 1 & 4, if you assume a forward in time only analysis. But yes, it is a possible outcome. However, it is not really discarded by Victor. In the Ma experiment, they don't report it (and if you like you can say it was discarded). But in other experiments, such as Megidish, it is reported.

$$\begin{eqnarray*}
U^\mathrm{on}|HH\rangle_{23} &=& i(|HH\rangle_{b''c''} - |VV\rangle_{b''c''} + |HV\rangle_{b''b''} - |HV\rangle_{c''c''})/2\\
\end{eqnarray*}$$

The possibility of a Φ+ result follows directly from a forward in time only analysis.

3. This is true, but not in the manner you are portraying it. 50% of the VV/HH swap results are discarded because they yield swap outcomes Ψ+ or Ψ-. These cannot be distinguished, and will show as 3-fold coincidences. That's because there are Vb"Vb" (and 3 other similar) permutations where both the 2 & 3 photons end up in the same detector. That registers only 1 click rather than 2 separate; and even if there were 2 clicks, it would not distinguish these 2 swap states.

Even if they could be measured, Ψ+ or Ψ- are not possible in runs where 1 & 4 are VV or HH, as $\bra{VV}\psi^\pm\rangle = \bra{HH}\psi^\pm\rangle = 0$. Instead, 50% of runs where 1 & 4 are VV or HH are discarded because Victor obtained a Φ+ result. This follows from the time-evolution I presented above.

 

[DrChinese]

The possibility of a Φ+ result follows directly from a forward in time only analysis.

OK, of course the Φ+ result occurs - that would be something like VHVV₁₂₃₄ (or if you prefer, VΦ+V₁₂₃₄). But it doesn't follow from a forward in time analysis UNLESS the swap physically changes the possible 4 fold outcomes. That's exactly what you appear to be showing here with the swap=on option. Because after 1&4 are measured as VV, the 2&3 photons are definitely HH and cannot be HV - again, as you show. We need HH₂₃ to evolve to HV₂₃ to get a Φ+ signature.

So please, answer this: How can the Φ+ result occur a) if Φ+ (like Φ-) is merely a "subset" of HH or VV outcomes for 1 & 4; and/or b) unless the Φ+ swap changes the polarization of 2 & 3 from HH to HV or VH (the signature polarizations for Φ+ as you presented) ?

Because a) and b) conflict. One says there is no polarization change to 2 & 3 upon swap, the other says there is. So are you agreeing to b) - and therefore denying a)?

I think one of the issues for me in reading Mjelva's paper is determining what he is saying on this precise question. Because if there is a physical "forward in time" swap - the b) option - then clearly that involves nonlocal influences. But on the other hand, he repeatedly says variations of:

Mjelva: "I will argue that a careful analysis of these experiments shows that they in fact display nothing more than “ordinary” spacelike entanglement, and that any purported timelike entanglement is an artefact of selection bias."

Is his "spacelike entanglement" meaning "nonlocal entanglement"? And if it does, where is the selection bias? Because as you describe it, there is no selection bias when swapping is considered a physical action (assuming I understand your position, which is questionable ).

 

[Morbert]

OK, of course the Φ+ result occurs - that would be something like VHVV₁₂₃₄ (or if you prefer, VΦ+V₁₂₃₄). But it doesn't follow from a forward in time analysis UNLESS the swap physically changes the possible 4 fold outcomes. That's exactly what you appear to be showing here with the swap=on option. Because after 1&4 are measured as VV, the 2&3 photons are definitely HH and cannot be HV - again, as you show. We need HH₂₃ to evolve to HV₂₃ to get a Φ+ signature.

So please, answer this: How can the Φ+ result occur a) if Φ+ (like Φ-) is merely a "subset" of HH or VV outcomes for 1 & 4; and/or b) unless the Φ+ swap changes the polarization of 2 & 3 from HH to HV or VH (the signature polarizations for Φ+ as you presented) ?

Because a) and b) conflict. One says there is no polarization change to 2 & 3 upon swap, the other says there is. So are you agreeing to b) - and therefore denying a)?

I don't see the contradiction. How does a) forbid a polarization change to 2 & 3?

I think one of the issues for me in reading Mjelva's paper is determining what he is saying on this precise question. Because if there is a physical "forward in time" swap - the b) option - then clearly that involves nonlocal influences. But on the other hand, he repeatedly says variations of:

Is his "spacelike entanglement" meaning "nonlocal entanglement"? And if it does, where is the selection bias? Because as you describe it, there is no selection bias when swapping is considered a physical action (assuming I understand your position, which is questionable ).

Yes, Mjelva focuses on explaining "timelike entanglement" with selection bias, not all entanglement in general. He remarks on some papers that attempt to account for conventional, spacelike entanglement as a selection effect, but it is not his concern in the paper.

So in Ma's experiment, Mjelve's projection based account would involve spatial nonlocal influence: Alice immediately collapses photon 2's state when she measures 1, and Bob immediately collapses photon 3's state when he measures 4. But no temporal nonlocal influence (i.e. No retroactive entanglement swap imparted on 1 & 4 by Victor's measurement on 2 & 3). We have been using the categories swap vs no-swap to describe Victor's decision, but strictly speaking no swap ever occurs (according to Mjelva's account). Only post-selection of perfect correlations.

 

[DrChinese]

1. I don't see the contradiction. How does a) forbid a polarization change to 2 & 3?

2. So in Ma's experiment, Mjelve's projection based account would involve spatial nonlocal influence: Alice immediately collapses photon 2's state when she measures 1, and Bob immediately collapses photon 3's state when he measures 4. But no temporal nonlocal influence (i.e. No retroactive entanglement swap imparted on 1 & 4 by Victor's measurement on 2 & 3). We have been using the categories swap vs no-swap to describe Victor's decision, but strictly speaking no swap ever occurs (according to Mjelva's account). Only post-selection of perfect correlations.

1. If there is a subset of all initial 1&2 and 3&4 pairs that can evidence perfect correlations between 1&4 merely by identifying some criteria defining that subset: then a swap is not a physical action changing a quantum state. That a) conflicts with b), which says it is a nonlocal/nontemporal physical change.

And you are claiming both a) and b) are true. Those contradict.


2. The remote collapse idea is nonlocal, I agree with that. But that alone is far insufficient to describe what is happening to lead to perfect correlations. Let's get specific.

---

A. We know that after a Ma's observation of |LL> for photons 1 & 4, by that Mjelva's (and your) same logic regarding collapse: we must have |RR> for photons 2 & 3. Agreed? That quantum state, |RR>₂₃, cannot - by normal rules of QM, lead to any *certain* outcome prediction on the H/V measurement basis for those photons. After all, that would require wholesale rewrite of the Uncertainty relations. Agreed?

Similarly: We know that after a Ma's observation of |LR> for photons 1 & 4, by that Mjelva's (and your) same logic regarding collapse: we must have |RL> for photons 2 & 3.

B. What needs to happen - in order for your and Mjelva's concept to work - is as follows. (We will consider the ideal case, and compare to the quantum mechanical prediction, and Ma's explicit experimental results):

i. The 2 & 3 photons do NOT physically overlap, there is NO swap; and the specific signature outcomes of Hb"Hc" or Vb"Vc" are recorded (SSM):
-There is NO difference in correlation between the Hb"Hc"/Vb"Vc" outcomes for photons 2 & 3, and either the |LL>₁₄ or |RL>₁₄ states recorded in the earlier measurement of photons 1 & 4. These occur equally often.

-AND ALSO-

ii. The 2 & 3 photons DO physically overlap, there is a swap: and the specific signature outcomes of Hb"Hc" or Vb"Vc" (Φ- Bell state) are recorded (BSM):
- ii.a) There is HIGH correlation (ideal case) between the Hb"Hc"/Vb"Vc" outcomes for photons 2 & 3, and the |LL>₁₄ states; and
- ii.b) There is NO correlation between the Hb"Hc"/Vb"Vc" for photons 2 & 3, and the |RL>₁₄ states recorded in the earlier measurement of photons 1 & 4.

C. These are apples to apples comparisons*. Each of the signatures is exactly the same, and 100% of the cases I specify are considered. What's different? I see one difference, and it is a physical difference - overlapping in the beam splitter. In cases for both i. and ii. we have the same information: which of 4 detectors clicked for the 2 & 3 photons. That is: both being HH or VV; and each appearing on opposite sides of the beam splitter. So how is a different subset being "selected" if the information is the same either way (swap vs. no swap)?

In fact: when no swap is performed, we have an additional piece of information that we don't when a swap is performed. That being: we can now distinguish which is the 2 photon and which is the 3 photon. That extra piece of information not helping explain things in any way though, exactly the opposite of what you might expect.


*And note that in the Megidish experiment, concurring results are reported - but without any modification of wave plates to control the swap=on/swap=off settings. (I mention that because you think this distinction seems to matter in the Ma experiment, but it doesn't.)

 

[Morbert]

Unless explicitly stated otherwise, all my descriptions below are in accordance with Mjelva's projection-based account.

1. If there is a subset of all initial 1&2 and 3&4 pairs that can evidence perfect correlations between 1&4 merely by identifying some criteria defining that subset: then a swap is not a physical action changing a quantum state. That a) conflicts with b), which says it is a nonlocal/nontemporal physical change.

And you are claiming both a) and b) are true. Those contradict.

The evolution only acts on 2 & 3. In the case we are considering, where Alice and Bob recorded VV, It is
$$\begin{eqnarray*}I_{14}\otimes U_{23}\ket{VV}_{14}\ket{HH}_{23}&=&\ket{VV}_{14}\otimes(U_{23}\ket{HH}_{23})\end{eqnarray*}$$Similarly, whatever outcome Victor records, he projects onto a state of the form $\ket{VV}_{14}\otimes\cdots$ so no matter what Victor does the run belongs to the set where 1 & 4 are VV. This cannot be undone even though 2 & 3 are subject to change. So a BSM result by Victor both i) subjects 2&3 to change and ii) belongs to the set of runs where Alice & Bob recorded HH or VV (assuming they measured in the H/V basis).

2. The remote collapse idea is nonlocal, I agree with that. But that alone is far insufficient to describe what is happening to lead to perfect correlations. Let's get specific.

---

A. We know that after a Ma's observation of |LL> for photons 1 & 4, by that Mjelva's (and your) same logic regarding collapse: we must have |RR> for photons 2 & 3. Agreed? That quantum state, |RR>₂₃, cannot - by normal rules of QM, lead to any *certain* outcome prediction on the H/V measurement basis for those photons. After all, that would require wholesale rewrite of the Uncertainty relations. Agreed?

Similarly: We know that after a Ma's observation of |LR> for photons 1 & 4, by that Mjelva's (and your) same logic regarding collapse: we must have |RL> for photons 2 & 3.

B. What needs to happen - in order for your and Mjelva's concept to work - is as follows. (We will consider the ideal case, and compare to the quantum mechanical prediction, and Ma's explicit experimental results):

i. The 2 & 3 photons do NOT physically overlap, there is NO swap; and the specific signature outcomes of Hb"Hc" or Vb"Vc" are recorded (SSM):
-There is NO difference in correlation between the Hb"Hc"/Vb"Vc" outcomes for photons 2 & 3, and either the |LL>₁₄ or |RL>₁₄ states recorded in the earlier measurement of photons 1 & 4. These occur equally often.

-AND ALSO-

ii. The 2 & 3 photons DO physically overlap, there is a swap: and the specific signature outcomes of Hb"Hc" or Vb"Vc" (Φ- Bell state) are recorded (BSM):
- ii.a) There is HIGH correlation (ideal case) between the Hb"Hc"/Vb"Vc" outcomes for photons 2 & 3, and the |LL>₁₄ states; and
- ii.b) There is NO correlation between the Hb"Hc"/Vb"Vc" for photons 2 & 3, and the |RL>₁₄ states recorded in the earlier measurement of photons 1 & 4.

C. These are apples to apples comparisons*. Each of the signatures is exactly the same, and 100% of the cases I specify are considered. What's different? I see one difference, and it is a physical difference - overlapping in the beam splitter. In cases for both i. and ii. we have the same information: which of 4 detectors clicked for the 2 & 3 photons. That is: both being HH or VV; and each appearing on opposite sides of the beam splitter. So how is a different subset being "selected" if the information is the same either way (swap vs. no swap)?

In fact: when no swap is performed, we have an additional piece of information that we don't when a swap is performed. That being: we can now distinguish which is the 2 photon and which is the 3 photon. That extra piece of information not helping explain things in any way though, exactly the opposite of what you might expect.


*And note that in the Megidish experiment, concurring results are reported - but without any modification of wave plates to control the swap=on/swap=off settings. (I mention that because you think this distinction seems to matter in the Ma experiment, but it doesn't.)

Here is what happens if Alice and Bob record LL: The state collapses to $$\begin{eqnarray*}\ket{LL}_{14}\ket{RR}_{23} &=& \ket{LL}_{14}\otimes(\ket{H}_2 + i\ket{V}_2)\otimes(\ket{H}_3 + i\ket{V}_3)/2\\
&=&\ket{LL}_{14}\otimes(\ket{HH}_{23}-\ket{VV}_{23} +i\ket{HV}_{23}+i\ket{VH}_{23})/2\\
&=&\ket{LL}_{14}\otimes(\ket{\phi^-}_{23} +i\ket{\psi^+}_{23})/\sqrt{2}\end{eqnarray*}$$If Victor performs an SSM on this state, he can get any of the four possible results for 2 & 3. If Victor attempts a BSM, he can only get either Φ- or fail. No matter what Victor does, this run is one where Alice and Bob measured LL. 1 & 4 don't change.

If Alice and Bob record LR respectively, then we have the projection onto
$$\begin{eqnarray*}\ket{LR}_{14}\ket{RL}_{23} &=& \ket{LR}_{14}\otimes(\ket{H}_2 + i\ket{V}_2)\otimes(\ket{H}_3 - i\ket{V}_3)/2\\
&=&\ket{LR}_{14}\otimes(\ket{HH}_{23}+\ket{VV}_{23} -i\ket{HV}_{23}+i\ket{VH}_{23})/2\\
&=&\ket{LR}_{14}\otimes(\ket{\phi^+}_{23} -i\ket{\psi^-}_{23})/\sqrt{2}\end{eqnarray*}$$If Victor performs an SSM on this sate then like before he can get any of the four possible results for 2 & 3. If Victor attempts a BSM he can only get either Φ+ or fail. No matter what Victor does, this run is one where Alice and Bob measured LR. 1 & 4 don't change.

You can see that, for all cases above, no true swap occurs. When Alice and Bob complete their measurements, 1 & 4 are projected onto a separable state that does not change no matter what Victor does. All Victor can do is keep or discard each run based on a measurement he might or might not do: A measurement that has no effect on 1 & 4.

 

[DrChinese]

1. Unless explicitly stated otherwise, all my descriptions below are in accordance with Mjelva's projection-based account.

2. The evolution only acts on 2 & 3. In the case we are considering, where Alice and Bob recorded VV...
so no matter what Victor does the run belongs to the set where 1 & 4 are VV. This cannot be undone even though 2 & 3 are subject to change. So a BSM result by Victor both i) subjects 2&3 to change and ii) belongs to the set of runs where Alice & Bob recorded HH or VV (assuming they measured in the H/V basis).

3. Here is what happens if Alice and Bob record LL: The state collapses to $$ \begin{eqnarray*}\ket{LL}_{14}\ket{RR}_{23} & =& \ket{LL}_{14}\otimes(\ket{H}_2 + i\ket{V}_2)\otimes(\ket{H}_3 + i\ket{V}_3)/2\\
&=&\ket{LL}_{14}\otimes(\ket{HH}_{23}-\ket{VV}_{23} +i\ket{HV}_{23}+i\ket{VH}_{23})/2\\
&=&\ket{LL}_{14}\otimes(\ket{\phi^-}_{23} +i\ket{\psi^+}_{23})/\sqrt{2}\end{eqnarray*}$$If Victor performs an SSM on this state, he can get any of the four possible results for 2 & 3. If Victor attempts a BSM, he can only get either Φ- or fail. No matter what Victor does, this run is one where Alice and Bob measured LL. 1 & 4 don't change.

4. If Alice and Bob record LR respectively, then we have the projection onto ...

5. You can see that, for all cases above, no true swap occurs.

6. When Alice and Bob complete their measurements, 1 & 4 are projected onto a separable state that does not change no matter what Victor does. All Victor can do is keep or discard each run based on a measurement he might or might not do: A measurement that has no effect on 1 & 4.

1. Great. Also @Morbert (and everyone else!): Thanks for the time and effort put in to follow these interesting related papers, and the detail of the theory and experiment. I know it gets difficult to follow at times. I can't speak for anyone else, but I am gaining a lot of understanding just working through the various permutations.

2. That's the Morbert/Mjelva hypothesis. Agreed otherwise.

3. Fully agreed as to your first equation line, I consider this canonical. The second and third lines are incorrect, unless they are supposed to be post-swap. After all, before the swap, they have no connection whatsoever and there is nothing to connect these particular photons. So I'll assume post-swap is what you intend, and continue on that line.

So... I agree that if we go SSM (no swap), any of the 4 outcomes are possible. And I agree that we evolve after a BSM (swap) to what you have for equation lines 2 & 3 post swap, where we are agreeing that there is a physical change. So if Alice and Bob see LL: Victor can see |Φ->₂₃ outcomes but not |Φ+>₂₃ outcomes. I'm not agreeing that this evolution actually occurs as you present it; but I will take this idea forward and see where it leads. We will see shortly that it is contradicted by basic entanglement theory.

4. Agreed conditionally as per 3.

5. This is inconsistent with your statement that there is evolution to entangled Bell states when a swap occurs. Obviously, this is a physical change. The first line of your 3./4. scenarios NEVER evolves to the second line unless a physical action occurs: namely, there is physical overlap in the Beam Splitter.

6. It would seem you have presented an argument supporting your hypothesis in point 2, although you must acknowledge what I said in point 5. But... don't celebrate quite yet!

There is a major theoretical problem with your premise that once 1 & 4 are measured as LL, they can evolve to a Φ- (or from LR to Φ+). This is physically impossible, and only can occur when full 4-fold analysis is done.

---

Specifically: A peculiarity of Type II parametric down conversion (PDC) sources, as used in the Ma experiment, is that they require tight restrictions on output cones. They must overlap to create polarization entangled pairs. You could alternately select from conic sections that are labeled Vertical and Horizontal, as marked in the diagram below. In that case, the output pairs will have known polarizations |VH>. They will NOT be polarization entangled. Such unentangled pairs can be manipulated (with suitable wave plates) as desired to be any of |HV>₁₂, |LR>₁₂ or |+->₁₂. Let's call this variation "Ma-X" if it were to be hypothetically executed in the same Ma setup we have been discussing.

Ma-X: If the sources of the pairs are intentionally made to be |LR>₁₂ and |RL>₃₄ (i.e. not in the Ψ- Bell state per the actual experiment), then Alice and Bob will observe |LL>₁₄ - exactly per your 3. Also, as you state, the middle pair is |RR>₂₃. And that means that if a BSM occurs, that evolves exactly as you say so that the middle pair is now in the entangled state (|Φ->₂₃ + |Ψ+>)₂₃/√2. You are saying "no true swap occurs".

In the Ma-X scenario: there is no correlation between the |LL>₁₄ outcomes and the |Φ->₂₃ outcomes versus the |Φ+>₂₃ outcomes. That is basic entanglement swapping theory, you must have the source pairs entangled for the BSM to lead to a physical swap across 4 photons. And yet, if your concept of the evolution of the state of the 2 & 3 photons were correct, there should be the same results as Ma observed in the Figure 3a (L/R basis). In other words: for all Ma-X results, there will be an approximately equal number of |Φ-> BSMs and |Φ+> BSMs. But you say that |Φ+> BSMs only belong with |LR>₁₄ or |RL>₁₄ results by Alice and Bob.

In the quantum world: Entanglement Swapping is manifested by a 4-fold context that spans both space and time. Given the usual predictions of QM, it is not possible to provide a meaningful forward in time only description, as either you or Mjelva sought to do here. Of course, there are Interpretations that might get around this issue with other assumptions. IMHO: They would still need to consider a 4-fold context.


Edited to add:
-For polarization, Ma tests 3 mutually unbiased bases: H/V, +/- (usually +45 degrees/-45 degrees), and L/R. The general rules apply identically regardless of which of these are being discussed, and generally the basis can be changed from one to the other by appropriate use of wave plates.
-How do we know I'm right about the Ma-X outcomes being different than the original Ma experimental setup? Well, obviously they wouldn't need to overlap Vertical/Horizontal cone regions if that wasn't a requirement (see diagram) to obtain successful entanglement swapping.
-I would characterize the relationship between photons 2 & 3 - after a BSM - as entangled, regardless of whether a swap occurs with photons 1 & 4. In the Ma-X scenario, that is what occurs. That entanglement is essentially useless though.

 

[DrChinese]

This (A) is the Cliffs Notes version of my post #86. I also tie it back (B) directly to Mjelva's paper. I could not have done this without the work @Morbert put in to translate for me.

A. Morbert has supplied in his post #85 a precise blueprint for the evolution of entanglement swapping states as envisioned by Mjelva to describe the Ma et al experiment. Their common assumption is: Swapping cannot change the state of photons 1 & 4, already recorded by Alice and Bob, due to a later Bell State Measurement (BSM) by Victor. A forward in time only description follows that seems reasonable. However: That assumption is contradicted by an alternative treatment (my "Ma-X" scenario) which should evolve following Morbert's blueprint, but yields different experimental results than he would predict. Only a 4-fold description of overall context, disregarding any variation on order of measurement, can properly describe the quantum mechanical expectation.

B. Referring to Mjelva's 4.1.2. A projection-based account of the Megidish et al. -experiment: There is agreement between the ideas of Morbert's and Mjelva's through Mjelva's (9). I agree that IF their assumption were correct (that there is no actual swapping occurring, it is a selection artifact of a BSM projection): THEN (9) would be a fair description. Paraphrased from (9):

i. If we have photon 1 as up, then a BSM recorded as |Φ-> cannot be associated with photon 4 being down.
ii. If we have photon 1 as up, then a BSM recorded as |Φ+> cannot be associated with photon 4 being up.

"The story is thus entirely temporally local: Alice’s measurement “steers” the state of particle 2, which is sent to Vicky, in turn influencing the state of particle 3 (and hence also particle 4) through Vicky’s Bell-state measurement. This does involve spatial nonlocality (which was not at issue), but no temporal nonlocality."

But I provide a counterexample (Ma-X) that demonstrates both i. and ii. are false. We have PDC pairs with photon 1 up* and BSM of |Φ-> producing photon 4 outcomes of down; and PDC pairs with photon 1 up* and BSM of |Φ+> producing photon 4 outcomes of up. The counterexample relies on a peculiarity of Type II PDC sources that can provide states as described in Mjelva's (8) and (9), but does not evolve as he predicts. Therefore Mjelva's statement is false: "At no point in the analysis was it necessary to posit any entanglement relation obtaining between particle 1 and particle 4."

Conclusion: Entanglement swapping is a real, physical effect changing entanglement from initially entangled photons 1 & 2 (and also 3 & 4) to later and final entangled photons 1 & 4 (and also 2 & 3). Time, space, order are not constraints on this effect, as is amply demonstrated in experiments.


*Note that choice of basis as up/down, or L/R, or H/V, or +/- is not really important. If photons 1 & 4 are measured on a basis that is unbiased relative to the measurements performed on photons 2 & 3, the results and conclusions are the same.

 

[Morbert]

3. Fully agreed as to your first equation line, I consider this canonical. The second and third lines are incorrect, unless they are supposed to be post-swap. After all, before the swap, they have no connection whatsoever and there is nothing to connect these particular photons. So I'll assume post-swap is what you intend, and continue on that line.
[...]
5. This is inconsistent with your statement that there is evolution to entangled Bell states when a swap occurs. Obviously, this is a physical change. The first line of your 3./4. scenarios NEVER evolves to the second line unless a physical action occurs: namely, there is physical overlap in the Beam Splitter.

The state isn't post swap. The state is post Alice and Bob measurements. All three lines are equivalent. The difference between the first and second line for example is just the expanding out the brackets. If Victor has the BiSA configured to carry out a BSM, then the state is subject to the evolution$$\begin{eqnarray*}I_{14}\otimes U_{23}\ket{LL}_{14}\ket{RR}_{23} &=& \ket{LL}_{14}\otimes(U_{23}\ket{RR}_{23})\\
&=&\ket{LL}_{14}\otimes(U_{23}\ket{\phi^-}_{23} +iU_{23}\ket{\psi^+}_{23})/\sqrt{2}\end{eqnarray*}$$This evolution lets Victor infer $\ket{\phi^-}_{23}$ from, the detectors registering the state $\ket{HH}_{b''c''}$ or $\ket{VV}_{b''c''}$. Hence, Mjelva's forward-in-time projection-based account is wholly consistent with the predictions of QM.

There is a major theoretical problem with your premise that once 1 & 4 are measured as LL, they can evolve to a Φ- (or from LR to Φ+). This is physically impossible, and only can occur when full 4-fold analysis is done.

I'm saying the opposite. Once 1 & 4 are measured as LL, they stay as LL regardless of what Victor does. Victor can only influence 2 & 3. So whatever Victor does, the state will be of the form $\ket{LL}_{14}\otimes\cdots_{23}$. E.g. A successful BSM could project the state onto $\ket{LL}_{14}\otimes\ket{HH}_{b''c''}$. This is in contrast with experiments alternative to Ma, where a successful BSM by Victor can project onto a state, say, of the form $\ket{\phi^-}_{14}\otimes\ket{HH}_{b''c''}$ or $\ket{\phi^+}_{14}\otimes\ket{HV}_{b''b''}$.

[edit] - Updated example states to be consistent.

Ma-X: If the sources of the pairs are intentionally made to be |LR>₁₂ and |RL>₃₄ (i.e. not in the Ψ- Bell state per the actual experiment), then Alice and Bob will observe |LL>₁₄ - exactly per your 3. Also, as you state, the middle pair is |RR>₂₃. And that means that if a BSM occurs, that evolves exactly as you say so that the middle pair is now in the entangled state (|Φ->₂₃ + |Ψ+>)₂₃/√2. You are saying "no true swap occurs".

In the Ma-X scenario: there is no correlation between the |LL>₁₄ outcomes and the |Φ->₂₃ outcomes versus the |Φ+>₂₃ outcomes. That is basic entanglement swapping theory, you must have the source pairs entangled for the BSM to lead to a physical swap across 4 photons. And yet, if your concept of the evolution of the state of the 2 & 3 photons were correct, there should be the same results as Ma observed in the Figure 3a (L/R basis). In other words: for all Ma-X results, there will be an approximately equal number of |Φ-> BSMs and |Φ+> BSMs. But you say that |Φ+> BSMs only belong with |LR>₁₄ or |RL>₁₄ results by Alice and Bob.

In the Ma-X scenario, Alice and Bob measurements must yield LL (if they measure in the L/R basis), while Victor's attempted BSM measurement must yield either Φ-, or must fail (and hence yield an SSM result).

 

[DrChinese]

In the Ma-X scenario, Alice and Bob measurements must yield LL (if they measure in the L/R basis), while Victor's attempted BSM measurement must yield either Φ-, or must fail (and hence yield an SSM result).

This is physically incorrect. That’s my point. Type II PDC works exactly as I describe. If you like, read about it:

Kwiat et al (1995)

If 1 & 2 are LR and not initially polarization entangled, then the evolution you (and Mjelva) present predicts a completely wrong result. You predict correlation, but there won’t be any.

A swap is a swap is a swap. It’s definitely not something your forward in time only evolution can support. Again, it’s ruled out by theory and experiment due to the analysis I presented above.

There is literally nothing controversial in what I am saying. If you think Type II works differently, let’s see a good reference. It should be obvious that a) the Ma-X setup should evolve like the Ma original does according to your assumption; but b) cannot reproduce Ma’s swapping results.

Please, let me know how you disagree with either a) or b).

(No point in even addressing the other issues in your post until you concur with my assessment.)

 

[Morbert]

This is physically incorrect. That’s my point. Type II PDC works exactly as I describe. If you like, read about it:

Kwiat et al (1995)

If 1 & 2 are LR and not initially polarization entangled, then the evolution you (and Mjelva) present predicts a completely wrong result. You predict correlation, but there won’t be any.

The correlation not present in the Ma-X experiment is correlation between Victor's Φ- result, and Alice's and Bob's measurement in the other two unbiased bases, H/V and +/-.

In the original Ma, experiment, if Victor observes Φ-, then he can expect correlation if Alice and Bob measured in the H/V or R/L basis, and anticorrelation in the +/- basis.

In the Ma-X experiment, if* Victor observes Φ- (and he cannot ever observe Φ+) then he knows if Alice and Bob measured in the R/L basis, they will be correlated (trivially so, they must be LL). But if Alice and Bob measure in the H/V or +- basis. They will be uncorrelated.

A la Fig 3 from Ma, we could make this comparison

*Here I say "if" to keep focus on runs with Φ-, but in reality, in the Ma-X experiment, whatever Victor measures doesn't matter (whether he gets Φ- or an SSM result). The correlations will be as they are on the right hand side of the above chart regardless.

Please, let me know how you disagree with either a) or b).

So I agree with a) and b)

[edit] - improved wording

 

[DrChinese]

The correlation not present in the Ma-X experiment is correlation between Victor's Φ- result, and Alice's and Bob's measurement in the other two unbiased bases, H/V and +/-.

...

In the Ma-X experiment, if* Victor observes Φ- (and he cannot ever observe Φ+) then he knows if Alice and Bob measured in the R/L basis, they will be correlated (trivially so, they must be LL).
...

OK, first where we agree: We are specifying measurement of 1 & 4 on one basis, and measurement of 2 & 3 on some other unbiased basis.

Now, it was you who turned me on to understanding Mjelva's logic. He says in that situation: Once you know the 1 & 4 outcomes (say up-up, per his 9A for example), then the 2 & 3 BSM (swap) is via selection where Φ- can result. That matches experiment and would, in fact have the effect of delivering the proper results for both BSMs and for SSMs. So that is not the point of disagreement.

And how that happens, according to the forward in time only view: If we know 1 & 4 are LL - or up-up in Mjelva's (9A) - then a Φ- BSM is compatible, but not a Φ+ BSM. But again: when we have the Ma-X version, we know 1 & 4 are LL (or up-up) just as before. Your problem is: A Φ- BSM is an actual compatible outcome, but equally frequent is a Φ+ BSM experimental outcome. This is diametrically opposed to what you assert, and is also opposed to what Mjelva claims in his (9A).

I am flat out saying that's what happens, and you are exactly incorrect as to what experiment shows. Because if it didn't, Type II polarization entangled PDC sources would not need to overlap the V and H cones as shown in the diagram. If they didn't overlap, it would be my Ma-X version. But we also know that doesn't lead to entanglement swapping. Surely you can agree with this point - there is nothing controversial about it. You need 1 & 2 to be initially polarization entangled (anti-correlated) to get entanglement swapping in this regime. That entangled state is qualitatively different than an initial state of up-down (or whatever). That accounts for the results being different; so the evolution cannot work as you describe.

So... that's our point of departure - and we should focus on this and nothing else for now. The state evolution cannot be as you describe below, because my Ma-X example follows that but yields the wrong prediction (using your logic). What I am applying to get that wrong prediction, verbatim:

$$\begin{eqnarray*}I_{14}\otimes U_{23}\ket{LL}_{14}\ket{RR}_{23} &=& \ket{LL}_{14}\otimes(U_{23}\ket{RR}_{23})\\
&=&\ket{LL}_{14}\otimes(U_{23}\ket{\phi^-}_{23} +iU_{23}\ket{\psi^+}_{23})/\sqrt{2}\end{eqnarray*}$$
Nope. Actual results include both Φ+ and Ψ- terms.

 

[eloheim]

So... that's our point of departure - and we should focus on this and nothing else for now. The state evolution cannot be as you describe below, because my Ma-X example follows that but yields the wrong prediction (using your logic). What I am applying to get that wrong prediction, verbatim:

$$\begin{eqnarray*}I_{14}\otimes U_{23}\ket{LL}_{14}\ket{RR}_{23} &=& \ket{LL}_{14}\otimes(U_{23}\ket{RR}_{23})\\
&=&\ket{LL}_{14}\otimes(U_{23}\ket{\phi^-}_{23} +iU_{23}\ket{\psi^+}_{23})/\sqrt{2}\end{eqnarray*}$$
Nope. Actual results include both Φ+ and Ψ- terms.

So in the Ma-X version, even if Alice and Bob "measure" in the prepared basis (if we already know their photons are L and L there's no point in measuring, right?) the result of Victor putting 2 and 3 into a bell state by making them indistinguishable will produce different results than the original Ma setup?

Just going through the math for the other combinations has Φ- only being produced from LL, RR, +-, and Φ+ only from ++, --, LR.

 

[Morbert]

And how that happens, according to the forward in time only view: If we know 1 & 4 are LL - or up-up in Mjelva's (9A) - then a Φ- BSM is compatible, but not a Φ+ BSM. But again: when we have the Ma-X version, we know 1 & 4 are LL (or up-up) just as before. Your problem is: A Φ- BSM is an actual compatible outcome, but equally frequent is a Φ+ BSM experimental outcome. This is diametrically opposed to what you assert, and is also opposed to what Mjelva claims in his (9A).

As described by Ma, $\ket{L} = (\ket{H} - i\ket{V})/\sqrt{2}$, and so $$\bra{\phi^+}LL\rangle = 0$$That holds however $\ket{LL}$ was prepared, so a BSM carried out on a system prepared as $\ket{LL}$ cannot yield $\phi^+$. This is a constraint imposed directly by the theory/the orthogonality of the states, and is not dependent on the specifics of the preparation or the measurement apparatus. Any BSM on $\ket{LL}$ that yields both $\phi^+$ and $\phi^-$ is either i) Not a BSM or ii) contradicts quantum mechanics. Show me such a scenario in literature. It is not the case in the original Ma experiment, and it is not the case in the Type II PDC described by Kwiat et al.

 

[DrChinese]

So in the Ma-X version, even if Alice and Bob "measure" in the prepared basis (if we already know their photons are L and L there's no point in measuring, right?) the result of Victor putting 2 and 3 into a bell state by making them indistinguishable will produce different results than the original Ma setup?

Just going through the math for the other combinations has Φ- only being produced from LL, RR, +-, and Φ+ only from ++, --, LR.

Yes, it produces distinctly different results. There is a qualitative difference between an entangled state before all measurements are completed, and a state with specific outcomes. But according to the evolution as presented by Mjelva (see his 9A especially, showing specific outcomes before all measurements completed): it should produce the same results. You might ask: Why does this experimental difference matter?

The entire premise of the forward in time only hypothesis - which by the way is completely reasonable - is: Once a measurement is performed, and a possible quantum outcome is selected (by random chance of course), then there can be no additional connection with the quantum components so measured. In Ma, those are photons 1 & 4; while in Megidish, it's only photon 1.

Mjelva: "So we see that on projection-based accounts, the projection ensures that there can be no entanglement between particle 1 and particle 4, and thus rules out timelike entanglement as an explanation of the observed correlations."

But that is not how the actual predictions are generated in the quantum world. A full 4-fold quantum context is required to properly model and predict entanglement swapping outcomes and outcome statistics. And such context is not limited to regions of spacetime constrained by Einsteinian locality or causality, as .

Ma: They start with (1) which is agreed by everyone. But their post-swap state (2) is a 4 photon state which does not resemble the presentation of Mjelva's (9). They say photons 1 & 4 become entangled after the fact. "Consequently photons 1 (Alice) and 4 (Bob) also become entangled [after the fact] and entanglement swapping is achieved. ... Note that after the entanglement swapping, photons 1&2(and 3&4) are not entangled with each other anymore, which manifests the monogamy of entanglement."

Megidish: They also start with (1), and their post-swap state (3) is the same as Ma's. Their characterization is likewise distinctly in opposition: "When the two photons of time τ (photons 2 and 3) are projected onto any Bell state, the first and last photons (1 and 4) collapse also into the same state and entanglement is swapped. The first and last photons, that did not share between them any correlations, become entangled."

When the Ma, Megidish, Hensen experimental teams design their experiments, they cannot use the Mjelva forward only projection logic. Why? It's simply wrong (as I demonstrated based on the cited papers). They are setting out to experimentally disprove that "semi-classical" thinking anyway. Unfortunately, their experiments are specifically designed to highlight only a single particular variation of the quantum time ordering/nonlocality issues. Accordingly, you must look from paper to paper to get a full understanding of the quantum rules.


Note: The Megidish experiment (Ma too) has always seemed to me to be one of the most radical examples of the strange role of ordering in the quantum world. I started a thread here on it the day it appeared in 2012 . Since then, it seems to have mostly been of interest to other experimenters and researchers, and I consider it generally accepted science at this point. But I have seen very little about it online. So I was very happy to see Mjelva's detailed attempt to tear into it, even though his analysis is ultimately flawed (IMHO of course - each person must decide for themself).

 

[DrChinese]

1. As described by Ma, $\ket{L} = (\ket{H} - i\ket{V})/\sqrt{2}$, and so $$\bra{\phi^+}LL\rangle = 0$$That holds however $\ket{LL}$ was prepared, so a BSM carried out on a system prepared as $\ket{LL}$ cannot yield $\phi^+$.

This is a constraint imposed directly by the theory/the orthogonality of the states, and is not dependent on the specifics of the preparation or the measurement apparatus.

2. Any BSM on $\ket{LL}$ that yields both $\phi^+$ and $\phi^-$ is either i) Not a BSM or ii) contradicts quantum mechanics.

3. Show me such a scenario in literature. It is not the case in the original Ma experiment, and it is not the case in the Type II PDC described by Kwiat et al.

1. All of your statements are completely wrong, as you hold onto a physical point that cannot be supported. You have yet to present any kind of support for your thinking, other than Mjelva's words (obviously not a suitable reference). Here's what he says (swap is not real) versus what top teams say (swaps are real):

Mjelva: "So we see that on projection-based accounts, the projection ensures that there can be no entanglement between particle 1 and particle 4, and thus rules out timelike entanglement as an explanation of the observed correlations."

Ma: "Consequently photons 1 (Alice) and 4 (Bob) also become entangled [after the fact] and entanglement swapping is achieved. ... Note that after the entanglement swapping, photons 1&2(and 3&4) are not entangled with each other anymore, which manifests the monogamy of entanglement."

Megidish: "When the two photons of time τ (photons 2 and 3) are projected onto any Bell state, the first and last photons (1 and 4) collapse also into the same state and entanglement is swapped. The first and last photons, that did not share between them any correlations [or coexistence], become entangled."


2. How can it not be a BSM? It exactly fits your definition of a BSM. Anyway, it does project photons 2 & 3 into an entangled state, either Φ+ or Φ- equally.


3. As already stated: Every single experiment ever performed using Type II PDC sources to create polarization entangled photons for entanglement swapping is a demonstration of what I say. I already cited something from 1995 by a Zeilinger team showing the details of Type II. The Ma and Megidish experiments use that technique to create Ψ- pairs. If source pairs useful for swapping could be created without the requirement of overlapping the Vertical and Horizontal cones (and taking the small indistinguishable cross-section), then why do they bother to do all this extra work?

Obviously, they get different results when they pull pairs outside the Vertical and Horizontal overlapping regions. And you already agree that the evolution should be the same, and therefore not produce different results.

 

[Morbert]

@DrChinese You are denying basic textbook relations in QM. Relations that are necessary if we are to show that a forward-in-time analysis, consisting of textbook unitary evolutions and textbook state reductions, can reproduce the frequencies and correlations observed in any of these experiments, from Ma's to Megidish's to Hensen's.

For example, it is not "completely wrong" that $\bra{\phi^+}LL\rangle = 0$, and hence a BSM carried out on a system prepared as $\ket{LL}$ cannot yield the outcome $\phi^+$. It can be plainly shown.

 

[PeterDonis]

$\ket{LL}$ was prepared

What is your basis for this statement?

 

[Morbert]

What is your basis for this statement?

It is the premise supposed in the Ma-X experiment.

 

[PeterDonis]

It is the premise supposed in the Ma-X experiment.

Where, specifically, in the Ma paper does it state this premise?

 

[Morbert]

Where, specifically, in the Ma paper does it state this premise?

Ma-X, not Ma. See @DrChinese's earlier posts. It is his modification.