Realism in the entanglement swap experiment

[kurt101]

TL;DR Summary

No need to resort to magical explanations to explain why the entanglement swapping experiment works when you measure photons 1 & 4 first.

In the thread general-argument-that-entanglement-can-only-be-created-locally @Cthugha explains why the monogamy argument used by @DrChinese in his entanglement swapping experiment explanation is bunk.

Given that the monogamy argument is bunk, if the raw measurement values of photons of 1 and 4 are truly random, then clearly one should be able to pick out pairs that show a correlation of entanglement. The real question is why does the Bell test done later reveal this entangled correlation in the raw measurement data of 1 and 4?

I don't believe in magic. I think there is a trick that the magician is hiding from us. I don't think the magician is trying to be tricky. I think the answer is that when the Bell test shows photons 2 and 3 as being the same that means the action of entanglement that caused photons 2 and 3 to be the same is why photons 1 and 4 show the entanglement correlation. Its a lot like the game jeopardy, you are asking what initial state and action gives me the answer where the photons end up being the same.

Here is another more detailed way to explain it. Effectively I will show that the entanglement swapping experiment case where 1 & 4 are first measured and later are determined to show entanglement and the EPR experiment are mirror images of each other. I will show this with just using existing knowledge of what we already know happens in experiments and no personal theories involved.

The entanglement swapping case where 1 and 4 are measured first:
1 and 4 by random chance start out as having a correlation of being entangled
Measuring polarization of photon 1 causes spooky rotation of the polarization of photon 2 to be the same as 1.
Measuring polarization of photon 4 causes spooky rotation of the polarization of photon 3 to be the same as 4.
The bell test on photons 2 and 3 indicate these photons as having the same polarization.
It took 2 rotations to go from the initial state of the photons being entangled to the final state of photons being the same.

In the EPR experiment
Photon's A and B start with the same polarization.
Measuring photon A causes spooky rotation of the polarization of photon B to be the same as A.
Measuring photon B rotates to align with the polarizer measurement device.
It took 2 rotations to go from the initial state of the photons being the same to final state of the photons being entangled.

Effectively the two cases are mirror images of each other. In the entanglement swapping experiment the photons end up in the same state, where as in the EPR experiment the photons start in the same state. In both cases there are two actions of rotation to go between the start and end states.

So no need to resort to magical explanations when the simple explanation based on knowledge of what we already know happens in these experiments is enough to explain what is happening.

 

[vanhees71]

TL;DR Summary: No need to resort to magical explanations to explain why the entanglement swapping experiment works when you measure photons 1 & 4 first.

In the thread general-argument-that-entanglement-can-only-be-created-locally @Cthugha explains why the monogamy argument used by @DrChinese in his entanglement swapping experiment explanation is bunk.

Given that the monogamy argument is bunk, if the raw measurement values of photons of 1 and 4 are truly random, then clearly one should be able to pick out pairs that show a correlation of entanglement. The real question is why does the Bell test done later reveal this entangled correlation in the raw measurement data of 1 and 4?

The monogamy of entanglement is a mathematical fact, not bunk. The use of it by @DrChinese is nevertheless unjustified. He is right in saying that in the initial preparation we have a state of the type
$$\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
where $\hat{\rho}_{jk}$ denotes a Bell state of photon pair (j,k), i.e., we have a maximally entangled photon pair (1,2) and a maximally entangled photon pair (3,4). This state clear satisfies the monogamy argument.

Now you do the following experiment: You send photon (2,3) through a Bell-state analyzer and note for each pair in which of the four possible Bell states you found it. Which one will occur is completely random (with probability 1/4 for each). Also the polarization of the photons 1 and 4 is measured at far distant places. These single photons are ideally unpolarized. In all measurement outcomes careful time-stamps are made such that in the measurement protocols it's clear that one measured the four photons prepared in the specific state above.

If you look at the full ensemble all you get is that in the Bell-state analyzer measurement at one place you get with probability 1/4 one of these Bell states and the measurements of photon 1 lead to 50:50 outcomes for the two polarization states. The same is true for photon 4.

Now you can look at the four subensembles you get by choosing only the measurement results, where photons 2 and 3 were found in 1 of the possible Bell states (this sub-ensemble consists of about 1/4 of all the prepared two photon pairs). Then you'll find the photons 1 and 4 to be in a Bell state either. The subensemble is again described by a state of the type $\hat{\rho}_{23} \otimes \hat{\rho}_{14}$. Here again the monogamy property is of course fulfilled.

This experiment has been really done by Zeilinger et al, clearly excluding the possibility of faster-than light signals due to the measurements done on the photons:

https://link.aps.org/doi/10.1103/PhysRevLett.88.017903

Entanglement swapping is just a sophisticated kind of teleportation of two-photon states.

I don't believe in magic. I think there is a trick that the magician is hiding from us. I don't think the magician is trying to be tricky. I think the answer is that when the Bell test shows photons 2 and 3 as being the same that means the action of entanglement that caused photons 2 and 3 to be the same is why photons 1 and 4 show the entanglement correlation. Its a lot like the game jeopardy, you are asking what initial state and action gives me the answer where the photons end up being the same.

There's no magic, just quantum properties of photons!

 

[kurt101]

The monogamy of entanglement is a mathematical fact, not bunk. The use of it by @DrChinese is nevertheless unjustified.

To be clear I never said monogamy of entanglement is bunk, just @DrChinese use of it. So at least on a high level we are saying the same thing.

He is right in saying that in the initial preparation we have a state of the type
$$\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
where $\hat{\rho}_{jk}$ denotes a Bell state of photon pair (j,k), i.e., we have a maximally entangled photon pair (1,2) and a maximally entangled photon pair (3,4). This state clear satisfies the monogamy argument.

I don't think the quantum mechanics math and the monogamy argument says that there can't be entangled correlation in selective pairs in the raw measurement data of 1 & 4. In other words, I think I can take two random data sets of the same length and carefully (not randomly) pull out pairs that lead to an entangled correlation. Do you agree with what I am saying?

Now you do the following experiment: You send photon (2,3) through a Bell-state analyzer and note for each pair in which of the four possible Bell states you found it. Which one will occur is completely random (with probability 1/4 for each).

Is that true? I thought it was very rare to get 2 of the 4 states in the entanglement swap experiment where 2 and 3 enter the bell-state analyzer. Only when the photons 2,3 come in with identical properties do you get two of these states (at least when your talking about Hong–Ou–Mandel) and in the entanglement swap experiment it is very rare that photons 2,3 come in identical. So 1/4 probability for all states for this experiment seems wrong to me.
Are you assuming the 2, 3 photons being identical in the assumption for the math?

 

[vanhees71]

To be clear I never said monogamy of entanglement is bunk, just @DrChinese use of it. So at least on a high level we are saying the same thing.I don't think the quantum mechanics math and the monogamy argument says that there can't be entangled correlation in selective pairs in the raw measurement data of 1 & 4. In other words, I think I can take two random data sets of the same length and carefully (not randomly) pull out pairs that lead to an entangled correlation. Do you agree with what I am saying?

It says that if you entangle more than 2 photons, there cannot be a pair within this multi-photon states which is in a Bell state, i.e., being maximally entangled. Of course there can be pair states, which are strongly correlated, but not maximally entangled. I think the Wikipedia article explains it very well:

https://en.wikipedia.org/wiki/Monogamy_of_entanglement

Is that true? I thought it was very rare to get 2 of the 4 states in the entanglement swap experiment where 2 and 3 enter the bell-state analyzer. Only when the photons 2,3 come in with identical properties do you get two of these states (at least when your talking about Hong–Ou–Mandel) and in the entanglement swap experiment it is very rare that photons 2,3 come in identical. So 1/4 probability for all states for this experiment seems wrong to me.
Are you assuming the 2, 3 photons being identical in the assumption for the math?

See, e.g.,

https://web.physics.ucsb.edu/~quopt/swap.pdf

In the decomposition of the initial state into Bell states, Eq. (3), you see that the probabilities for finding each of the four Bell states is 1/4.

For an example, where a Bell-state analyzer has been used, i.e., all four Bell states can be prepared, see

https://scholar.archive.org/work/cq...quantum.at/fileadmin/Publications/2002-06.pdf

 

[DrChinese]

A) The monogamy of entanglement is a mathematical fact, not bunk. The use of it by @DrChinese is nevertheless unjustified. He is right in saying that in the initial preparation we have a state of the type
$$\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
where $\hat{\rho}_{jk}$ denotes a Bell state of photon pair (j,k), i.e., we have a maximally entangled photon pair (1,2) and a maximally entangled photon pair (3,4). This state clear satisfies the monogamy argument.

Now you do the following experiment: You send photon (2,3) through a Bell-state analyzer and note for each pair in which of the four possible Bell states you found it. Which one will occur is completely random (with probability 1/4 for each). Also the polarization of the photons 1 and 4 is measured at far distant places. These single photons are ideally unpolarized. In all measurement outcomes careful time-stamps are made such that in the measurement protocols it's clear that one measured the four photons prepared in the specific state above.

If you look at the full ensemble all you get is that in the Bell-state analyzer measurement at one place you get with probability 1/4 one of these Bell states and the measurements of photon 1 lead to 50:50 outcomes for the two polarization states. The same is true for photon 4.

B) Now you can look at the four subensembles you get by choosing only the measurement results, where photons 2 and 3 were found in 1 of the possible Bell states (this sub-ensemble consists of about 1/4 of all the prepared two photon pairs). Then you'll find the photons 1 and 4 to be in a Bell state either. The subensemble is again described by a state of the type $\hat{\rho}_{23} \otimes \hat{\rho}_{14}$. Here again the monogamy property is of course fulfilled.

C) This experiment has been really done by Zeilinger et al, clearly excluding the possibility of faster-than light signals due to the measurements done on the photons:

https://link.aps.org/doi/10.1103/PhysRevLett.88.017903

Entanglement swapping is just a sophisticated kind of teleportation of two-photon states.

There's no magic, just quantum properties of photons!

A) I agree with all of this, except of course your characterization of how I apply MoE. You apply as I do, which is standard.

B) After the Bell state measurements (BSM), the data set can be said to be sorted into 4 subensembles as you say. All good so far!

However: the difference in our viewpoints is in whether the BSM remotely changes the state of the (1,4) pairs so they are entangled in accordance with each BSM result. Your position is the successful BSM identifies the subensemble that each (1,4) pair belongs to, but there is no remote change of state. Have I presented your position correctly? Please let me know otherwise.

I say that the only way there are any entangled (1,4) pairs is if there were an objective change of state for them. That’s true regardless of interpretation - what I call objective. And the choice of the experimenter to execute the swap - or not - is the determining factor as to whether the state change occurred.

The experimenter is free to fail the swap, in which case the related (1,4) pair does not evidence entanglement. The experimenter can fail the swap and still see all of the signs needed to sort the (1,4) pairs into the same subensemble. How is that possible, you ask?

The successful BSM requires the (2,3) pairs to be indistinguishable. If the experimenter tags these two - there are a number of ways to do this - then the swap fails. But all of the parameters are still able to be recorded. If your view were correct, this shouldn’t matter. I say it does.

 

[PeroK]

To expect QM to be realistic seems highly unrealistic to me!

 

[Morbert]

@DrChinese Do you disagree that there can be "correlation swapping" in a classical context? By this I mean the prediction, by a classical theory, of correlation between spacelike separated measurement events on systems with spacelike separated preparations?

 

[DrChinese]

To expect QM to be realistic seems highly unrealistic to me!

I certainly don’t assert QM is realistic. That would imply results of the (1,4) pairs were determined prior to measurement. I don’t believe that at all.

On the other hand: if you deny the quantum context is nonlocal, what else are you saying?

I say: the (1,4) pairs have never existed in a common light cone. I say: the (2,3) BSM occurs distant to both (1) and (4). I say the only thing that links (1) and (4) - as opposed to any other photon pairs anywhere - is the BSM and without that: there is no (1,4) entanglement.

Standard quantum applications require the entire experimental context to be considered. It is well known that such contexts can be nonlocal. What’s there to dispute here?

 

[DrChinese]

Some information about how the Bell State Measurement works, if you are not already familiar with these details. There are two basic components to a successful swap (BSM), and its identification into one of the four Bell states.

A) The (2) and (3) photons must be indistinguishable as to their source. This means that their detection must occur within a narrow coincidence time window. The must also have identical frequency (and probably another property or two that I am not thinking of right now).

B) i. they must both go through a beam splitter, and either be reflected or transmitted. ii. their polarization must be identified relative to each other as parallel or orthogonal. There are 4 distinct possible permutations corresponding to the 4 Bell states.

A little thinking about these two requirements will tell you that they operate independently. You could identify the Bell state buckets (the B option) without succeeding on the A option, for example.

So… if you don’t think the BSM is physical, and that identification of Bell state is all that is done with the BSM: you’re missing out on the critical role the A) requirement plays. All you would need to do is add a little fiber to the (2) photon path to delay it a bit(and of course adjust the time window appropriately), and you could identify the source by timestamp difference. That would prevent a successful BSM and therefore, there is no swap.

How would the distant (1,4) photon pairs know how to react differently? I.e. whether they are to appear entangled according to the identified Bell state? Or appear random? The experimenter can decide as they like, and there is in fact a difference.

 

[vanhees71]

A) I agree with all of this, except of course your characterization of how I apply MoE. You apply as I do, which is standard.

The argument is completely mute, because nowhere did I claim that MoE was violated. You just claimed the opposite of my arguments!

B) After the Bell state measurements (BSM), the data set can be said to be sorted into 4 subensembles as you say. All good so far!

However: the difference in our viewpoints is in whether the BSM remotely changes the state of the (1,4) pairs so they are entangled in accordance with each BSM result. Your position is the successful BSM identifies the subensemble that each (1,4) pair belongs to, but there is no remote change of state. Have I presented your position correctly? Please let me know otherwise.

The BSM cannot have remotely changed the state of the far distant measurements on photon 1 and on photon 4 since some realizations of entanglement swapping by construction took care to do these three local measurements space-like separated, i.e., there cannot be causal influences between these measurements since the measurement results were realized by space-like separated registration events of the corresponding outcomes. If you agree according to point A), then you cannot deny the validity of locality in the sense of obeying relativistic causality.

I say that the only way there are any entangled (1,4) pairs is if there were an objective change of state for them. That’s true regardless of interpretation - what I call objective. And the choice of the experimenter to execute the swap - or not - is the determining factor as to whether the state change occurred.

No, it's self-contradictory! The entanglement swapping is possible because of the original preparation of photons (12) and (34) in Bell states and using photon (23) in the projective measurement into a Bell state. It's of course not possible to choose beforehand which of the four Bell states will occur, because theres probaility 1/4 for each of them.

The experimenter is free to fail the swap, in which case the related (1,4) pair does not evidence entanglement. The experimenter can fail the swap and still see all of the signs needed to sort the (1,4) pairs into the same subensemble. How is that possible, you ask?

If the projection measurement fails, then of course the entire experiment fails. Such events are of course not considered. That's one of the possible loop-holes, which however have been closed by using better and better detectors (which is, btw, the most expensive part of these experiments, as I learnt recently in a colloquium!).

The successful BSM requires the (2,3) pairs to be indistinguishable. If the experimenter tags these two - there are a number of ways to do this - then the swap fails. But all of the parameters are still able to be recorded. If your view were correct, this shouldn’t matter. I say it does.

The (2,3) pairs are indeed indistinguishable, because before the projection to a Bell state it's simply an ensemble of two unpolarized and uncorrelated photons.

To understand the central issue about causality, locality (no causal connections between events space-like separted (measurement) events) and the distinction with inseparability (strong correlations between far-distant measurement outcomes due to entanglement, which is not a causal connection but a correlation, i.e., a statistical property!) you don't even need the complicated entanglement-swapping. A simpler experiement is the teleportation of single-photon states. Entanglement swapping is just a teleportation of two-photon states.

 

[DrChinese]

The BSM cannot have remotely changed the state of the far distant measurements on photon 1 and on photon 4 since some realizations of entanglement swapping by construction took care to do these three local measurements space-like separated, i.e., there cannot be causal influences between these measurements since … [usual refuge to QFT]

No, it's self-contradictory! The entanglement swapping is possible because of the original preparation of photons (12) and (34) in Bell states and using photon (23) in the projective measurement [the BSM] into a Bell state. It's of course not possible to choose beforehand which of the four Bell states will occur, because theres probaility 1/4 for each of them.

If the projection measurement fails, then of course the entire experiment fails.

The (2,3) pairs are indeed indistinguishable, because before the projection to a Bell state [the BSM] it's simply an ensemble of two unpolarized and uncorrelated photons.

You cannot see the forest for the trees!

We agree that the (1,4) pairs are NOT initially prepared in any state (Bell or otherwise) that correlates anything between them whatsoever - and we agree that MoE insures this. We agree that at a later time, the (1,4) pairs ARE entangled and are correlated in 1 of 4 randomly selected Bell states. We agree that the successful BSM event on the related (2,3) pairs is a necessary condition for the (1,4) entanglement to occur. We agree that the experimenter is free to choose to carry out the BSM - or not. We agree that the (1,4) photons may be far distant at all times from the experimenter who may decide - or not - to execute the BSM on the (2,3) pairs*. We agree that a remote entanglement swap is not evidence of a violation of signal locality, precisely because the particular Bell state that occurs is random and cannot be steered in advance. (If any of this you disagree with, please say so.)

If the experimenter's choice to execute the swap isn't the determining factor in changing the (1,4) pairs from completely unentangled (by preparation) to maximally entangled, pray tell us: What is that determining factor? What remotely changes the (1,4) pairs state into an entangled one? Please, instead of resorting to telling me how wrong I am and giving you reference-free explanations of how QFT prevents it from happening: just answer the question. How do (1,4) pairs become entangled if the distant choice of the experimenter to execute the BSM (or not) is not the determining event?*And we have even agreed that there is no requirement that the (2,3) pair ever even come near each other, as in the cases where there is a quantum repeater in between. And we have agreed that the time ordering of the BSM - before or after detection of the (1,4) pairs - is not relevant to the statistical outcome either.

 

[kurt101]

It says that if you entangle more than 2 photons, there cannot be a pair within this multi-photon states which is in a Bell state, i.e., being maximally entangled. Of course there can be pair states, which are strongly correlated, but not maximally entangled. I think the Wikipedia article explains it very well:

However anyone can take two random data sets and selectively pick pairs from the sets that have a maximally entangled correlation. I know this is true, because I have done it. So given anyone can do this and there is no principle that prevents someone from doing it, why would you think the actual experiment is special in that it can't allow these correlations to exist before the Bell state test is done?

The answer is there is absolutely nothing that prevents this maximum entangled correlation from existing in the two random data sets. So it comes back to the same question, why does the Bell test select these pairs out of the random data in a way that they have a correlation of being maximumly entangled?

This has nothing what so ever to do with the principle of monogamy of entanglement. Monogamy of entanglement does not dictate that you can't have entanglement in random data sets, because anyone can easily prove this otherwise.

So I am absolutely on the right track with my argument. It is the spooky action where the maximum entanglement is introduced and it is because of this spooky action that causes 2 and 3 to be the same when they later enter the bell test apparatus that allows one to select them out as being maximally entangled.

And maybe you don't subscribe to realism, but the realistic explanation works and does not contradict quantum mechanics in anyway that I am aware of.

 

[PeterDonis]

anyone can take two random data sets and selectively pick pairs from the sets that have a maximally entangled correlation

Yes, but only by looking at the results that are being correlated.

In the entanglement swap experiment, you pick the 1 & 4 pairs that are entangled by looking at results for 2 & 3 pairs. You don't look at the 1 & 4 results at all to pick the 1 & 4 pairs. Not at all the same thing.

To make an analogy: if I flip a pair of coins 1000 times, I can of course pick a subset of results that makes the flips look correlated. That doesn't mean the coins are actually correlated; I'm just cherry picking results.

But if I could flip 2 pairs of coins, each pair 1000 times, and then pick out a subset of the pair #1 results that were correlated by looking only at the pair #2 results, that would be analogous to what is being done to pick the subsets in the entanglement swap experiments. And it would not be explainable just by saying I'm cherry picking results.

 

[kurt101]

Yes, but only by looking at the results that are being correlated.

In the entanglement swap experiment, you pick the 1 & 4 pairs that are entangled by looking at results for 2 & 3 pairs. You don't look at the 1 & 4 results at all to pick the 1 & 4 pairs. Not at all the same thing.

Wrong, by matching up 2 & 3, you are effectively looking at 1 & 4.

To make an analogy: if I flip a pair of coins 1000 times, I can of course pick a subset of results that makes the flips look correlated. That doesn't mean the coins are actually correlated; I'm just cherry picking results.

Yes we agree. You are cherry picking the results. It is the matching up of 2 & 3, combined with the bell test, that is cherry picking the result.

But if I could flip 2 pairs of coins, each pair 1000 times, and then pick out a subset of the pair #1 results that were correlated by looking only at the pair 2 results, that would be analogous to what is being done to pick the subsets in the entanglement swap experiments. And it would not be explainable just by saying I'm cherry picking results.

No this is not analogous to the swap experiment. To make it analogous you would have to have half of the coins come together in the experiment. The analogy doesn't work.

 

[kurt101]

In the actual entanglement swap experiment what percentage of measurements in the random data of 1 & 4 are later determined to be maximumly entangled and are used in the calculation when verifying the maximum entanglement correlation?

 

[PeterDonis]

Wrong, by matching up 2 & 3, you are effectively looking at 1 & 4.

No, you are looking at 2 & 3 pairs, and using those results to pick out a subset of 1 & 4 pairs.

It is the matching up of 2 & 3, combined with the bell test, that is cherry picking the result.

No, because you are not looking at the 1 & 4 results to pick out the subset of 1 & 4 results.

We already had this discussion in a previous thread. If you continue to make these claims you will receive a misinformation warning and this thread will be closed.

The analogy doesn't work.

Analogies are always limited, but it was only intended to illustrate, not as an argument.

 

[kurt101]

No, because you are not looking at the 1 & 4 results to pick out the subset of 1 & 4 results.

We already had this discussion in a previous thread. If you continue to make these claims you will receive a misinformation warning and this thread will be closed.

I don't disagree with what you said back to me. "you are looking at 2 & 3 pairs, and using those results to pick out a subset of 1 & 4."

Let me try a different tact:

Photons 2 & 3 have to have identical properties before entering the Bell state test apparatus, for the test apparatus to indicate maximal entanglement of 1 & 4, correct?

 

[PeterDonis]

Photons 2 & 3 have to have identical properties before entering the Bell state test apparatus, for the test apparatus to indicate maximal entanglement of 1 & 4, correct?

Photons 2 & 3 have to be indistinguishable at the BSM for an entanglement swap to occur. What that means is: the BSM has two input ports and two output ports. Photons 2 & 3 are indistinguishable at the BSM if we can't tell which of them comes out each output port.

 

[DrChinese]

In the actual entanglement swap experiment what percentage of measurements in the random data of 1 & 4 are later determined to be maximumly entangled and are used in the calculation when verifying the maximum entanglement correlation?

This is a more complicated question than it might appear. Within the time window, 100% are maximally entangled, but only about 25% or 50% can be specifically identified as to the Bell state due to technical limitations. It is theoretically possible all 4 Bell states - and not just 1 or 2 - might be identifiable in the future.

This in no way affects the usefulness of the experimental results.

 

[PeroK]

I certainly don’t assert QM is realistic.

It was a reference to the thread's title.

 

[vanhees71]

However anyone can take two random data sets and selectively pick pairs from the sets that have a maximally entangled correlation. I know this is true, because I have done it. So given anyone can do this and there is no principle that prevents someone from doing it, why would you think the actual experiment is special in that it can't allow these correlations to exist before the Bell state test is done?

Sure, that's what's done in the entanglement-swapping experiment. Projecting photons 2 and 3 to a Bell state prepares an ensemble where photons 1 and 4 are also in a Bell state. But that's in accordance with the monogamy of entanglement, because now photons 1 and 2 as well as 3 and 4 are no longer entangled.

The answer is there is absolutely nothing that prevents this maximum entangled correlation from existing in the two random data sets. So it comes back to the same question, why does the Bell test select these pairs out of the random data in a way that they have a correlation of being maximumly entangled?

It's just due to the projection of the pair (2,3) given the initial state, where the pairs (1,2) and (3,4) were both in a Bell state. It's nothin else than a teleportation procedure for photon-pair states.

This has nothing what so ever to do with the principle of monogamy of entanglement. Monogamy of entanglement does not dictate that you can't have entanglement in random data sets, because anyone can easily prove this otherwise.

Nobody has claimed this. I don't know what you are arguing about. Read the Wikipedia article on monogamy of entanglement carefully again!

So I am absolutely on the right track with my argument. It is the spooky action where the maximum entanglement is introduced and it is because of this spooky action that causes 2 and 3 to be the same when they later enter the bell test apparatus that allows one to select them out as being maximally entangled.

There is no spooky action at a distance within QED, which fully describes the experiments. That's not a matter of interpretation but a mathematical feature of the theory, you can't argue by any philosophy about!

And maybe you don't subscribe to realism, but the realistic explanation works and does not contradict quantum mechanics in anyway that I am aware of.

Indeed, physics is to find out how Nature behaves. It doesn't ask for any of our philosophical prejudices. With relativistic QFT being a local but non-realistic theory describing all phenomena with great accuracy, I can only come to the conclusion that the world behaves according to this QT, and QT says that for a general state not all observable can take predetermined values, i.e., the outcome of measurements is inherently unpredictable and random. What can be predicted with high precision are the probabilities for the outcome of measurements, given the state the system is prepared in.

 

[kurt101]

Photons 2 & 3 have to be indistinguishable at the BSM for an entanglement swap to occur. What that means is: the BSM has two input ports and two output ports. Photons 2 & 3 are indistinguishable at the BSM if we can't tell which of them comes out each output port.

How the cherry picking of 1 & 4 could be done:

After the measurement of photons 1 & 4, photons 2 & 3 have a state of having been altered by 1 & 4 and altered in a way that reflects entanglement. Given that 2 & 3 have been altered in a way that reflects entanglement from 1 & 4, photons 2 & 3 have all the information needed prior to entering the Bell state test apparatus that is needed to cherry-pick a maximal entangled correlation between 1 & 4.

If you don't believe what I am saying can be done, I am happy to make a software simulation that shows in principle 2 & 3 have been given all of the information at the Bell test to cherry pick the entangled correlation in the random data sets of 1 & 4 . I would follow whatever reasonable constraints you want me to follow.

Again, my point of any of this is that there is nothing about entanglement swapping that refutes realism.
And please no comments that I am denying non-locality, because I am not. To me realism means that there is cause and effect and that we can understand what is happening in a rationale way and in principle simulate what is happening.

This is a more complicated question than it might appear. Within the time window, 100% are maximally entangled, but only about 25% or 50% can be specifically identified as to the Bell state due to technical limitations. It is theoretically possible all 4 Bell states - and not just 1 or 2 - might be identifiable in the future.

This in no way affects the usefulness of the experimental results.

What is not clear to me is the conditioning on all photons (1, 2, 3, 4) prior to 2 & 3 entering the bell test that makes it so 2 & 3 are indistinguishable. Obviously if there was not any conditioning you would have a lot of 2 & 3 pairs that are distinguishable. Is the conditioning equally applied to all photons (1, 2, 3, 4) or just to photons 2 & 3 ?

Sure, that's what's done in the entanglement-swapping experiment. Projecting photons 2 and 3 to a Bell state prepares an ensemble where photons 1 and 4 are also in a Bell state. But that's in accordance with the monogamy of entanglement, because now photons 1 and 2 as well as 3 and 4 are no longer entangled.

I can accept this description with one caveat. If I am thinking of a realistic universe I have to instead say in the case where photons 1 and 4 are measured first, that "Projecting photons 2 and 3 to a Bell state" reveals "an ensemble where photons 1 and 4 are also in a Bell state". However I don't take an issue with this description as long as your domain is QT.

I suspect that the principle of monogamy is correct when applied to the domain of QT. However when you start to discuss what is actually happening in a realistic sense, it does not apply unless you subscribe to the interpretation that the universe obeys QT in some magical sense with no underlying explanation of why it obeys it. If I am correct I wish someone would affirm this. What I find confusing is that @DrChinese seems to be applying the principle of monogamy beyond QT in to the realm of interpretation and what is actually happening.

 

[PeterDonis]

How the cherry picking of 1 & 4 could be done:

Sorry, what you are describing is not cherry picking.

After the measurement of photons 1 & 4, photons 2 & 3 have a state of having been altered by 1 & 4

Certain QM interpretations might make this claim. Mathematically, however, the only "alteration" to 2 & 3 comes from the BSM, not from the measurements on 1 & 4. The output of the BSM is sufficient to determine the post-experiment state of 2 & 3, as a matter of the math of QM, regardless of the results of the measurements on 1 & 4.

If you don't believe what I am saying can be done, I am happy to make a software simulation

This is personal speculation and is off limits here. If you really think you are contributing something new to QM research, publish a peer-reviewed paper.

my point of any of this is that there is nothing about entanglement swapping that refutes realism

It would be nice if you could find a valid reference in the literature that supports this viewpoint. Then we would have a much better basis for discussion than your personal assertions.

 

[PeterDonis]

photons 2 & 3 have all the information needed prior to entering after being measured downstream of the Bell state test apparatus that is needed to cherry-pick a tell which maximal entangled correlation between 1 & 4 was realized in that run of the experiment

See my alterations above. With the alterations, the sentence is true. Without them, i.e., as you originally posted it, the claim is false.

 

[DrChinese]

a) After the measurement of photons 1 & 4, photons 2 & 3 have a state of having been altered by 1 & 4 and altered in a way that reflects entanglement. Given that 2 & 3 have been altered in a way that reflects entanglement from 1 & 4, photons 2 & 3 have all the information needed prior to entering the Bell state test apparatus that is needed to cherry-pick a maximal entangled correlation between 1 & 4.

b) If you don't believe what I am saying can be done, I am happy to make a software simulation that shows in principle 2 & 3 have been given all of the information at the Bell test to cherry pick the entangled correlation in the random data sets of 1 & 4 . I would follow whatever reasonable constraints you want me to follow.

c) Again, my point of any of this is that there is nothing about entanglement swapping that refutes realism.
And please no comments that I am denying non-locality, because I am not. To me realism means that there is cause and effect and that we can understand what is happening in a rational way and in principle simulate what is happening.

d) What is not clear to me is the conditioning on all photons (1, 2, 3, 4) prior to 2 & 3 entering the bell test that makes it so 2 & 3 are indistinguishable. Obviously if there was not any conditioning you would have a lot of 2 & 3 pairs that are distinguishable. Is the conditioning equally applied to all photons (1, 2, 3, 4) or just to photons 2 & 3 ?

e) I can accept this description with one caveat. If I am thinking of a realistic universe I have to instead say in the case where photons 1 and 4 are measured first, that "Projecting photons 2 and 3 to a Bell state" reveals "an ensemble where photons 1 and 4 are also in a Bell state".

I suspect that the principle of monogamy is correct ...

a) This is factually incorrect. The measurement of (1) can be done at any time, as can the measurement of (4). There is absolutely nothing at this point that connects (1) with (4), or (1) with any other photon in the entire universe - it is in a monogamous relationship with (2). So no, there is no change upon (1,4) measurement that places (2,3) in any particular relationship. All you can say is that an observable of (2) can be predicted based on the outcome of that observable on (1).

b) As mentioned, after measurement of the (1,4) pairs, there is no information available that relates (2) to (3). That occurs with the swap (BSM). Typically, the following attributes are necessary for them to be indistinguishable: i) both arrive within the specified coincidence time window (of perhaps 3 ns width); ii) same wavelength; and perhaps another property. They do not need to have the same polarization, and some Bell States require that they do not.

The identification of the Bell State occurs by sorting into buckets according to the following criteria after passing through a Beam Splitter (BS) and a Polarizing Beam Splitter (PBS). We want to know if the 2 photons emerge from the BS on the same side or different sides (that splits them into 2 streams); and if their polarization is the same or orthogonal (that splits the 2 streams into 4 buckets at this point). Which of the 4 buckets occurs is completely random as far as anyone knows. So all your program can do is select randomly one of 2 possible Bell States that would be most consistent with the (1,4) results.

c) As long as you are OK with Action At A Distance of some type, there is no contradiction. But I wouldn't call your description realistic at all. That's because there are variations on the swapping setups where your explanation would not apply. For example, measuring (1,4) after (2,3) doesn't work. That's because (1,4) evidence both perfect correlations AND violation of a Bell Inequality, something that can only occur by physical swapping from the BSM.

d) The indistinguishable requirement basically comes down to the time window - arrival times of (2,3). Few (2,3) pairs will meet this criteria, but if they do, the other requirements are easy.

e) (1) can't ALSO be entangled with (2) and with (4) at the same time if monogamy is applied. It's one or the other. As mentioned many times already, this is the normal application of MoE - as both @vanhees71 and @PeterDonis have confirmed.

 

[mattt]

@kurt101

You seem to be saying in your posts that, any sufficiently large sample of measurement results of (1,2)×(3,4) (the initial state tipically prepared in the swapping entanglement experiment), can be "a posteriori" partitioned in four subsets (approximately of the same size) such that, in each of these four subsets (of measurement results, along a given axis, the same for all particles), the measured results for particle 1 and particle 4 is:

(u,u), (u,u), (u,u),.... subset1
(d,d), (d,d), (d,d), (d,d),... subset 2
(u,d), (u,d),..... subset3
(d,u), (d,u), (d,u),.... subset4

Is that all you mean?

Because that is obviously true, but it is "classically" true (it is true for black or white socks too), and has nothing to do with our (me, martinb, vanhees, cthunga and others) objection to how Dr Chinese describes/interprets this experiment results.

 

[kurt101]

Certain QM interpretations might make this claim.

Yes that is definitely where I am coming from. If QM did not exist, I think the most straight forward interpretation of Bell's work and the EPR experiment would be that measuring one of the entangled photons is affecting the other (and vice versa).

Mathematically, however, the only "alteration" to 2 & 3 comes from the BSM, not from the measurements on 1 & 4. The output of the BSM is sufficient to determine the post-experiment state of 2 & 3, as a matter of the math of QM, regardless of the results of the measurements on 1 & 4.

The problem with saying "Mathematically the only "alteration" to 2 & 3 comes from the BSM" is that the math depends on constraints. One of the constraints is making the photons 2 & 3 indistinguishable. The other constraint is an entangled pair. So the constraints are everything in this experiment, so I don't think you can just leave them out and say they don't contribute.

a) This is factually incorrect. The measurement of (1) can be done at any time, as can the measurement of (4). There is absolutely nothing at this point that connects (1) with (4), or (1) with any other photon in the entire universe - it is in a monogamous relationship with (2). So no, there is no change upon (1,4) measurement that places (2,3) in any particular relationship. All you can say is that an observable of (2) can be predicted based on the outcome of that observable on (1).

I am not disagreeing that the order does not matter. I am calling attention to the case where 1 & 4 are measured first. I understand that you can do this in any order, but the one that is most troublesome for realism is that doing something to 2 & 3 after you measured 1 & 4 affects 1 & 4. This would be crazy! (not real). I know the math does not care about the order, but in reality, the order is important to rationalize cause and effect.

b) As mentioned, after measurement of the (1,4) pairs, there is no information available that relates (2) to (3). That occurs with the swap (BSM). Typically, the following attributes are necessary for them to be indistinguishable: i) both arrive within the specified coincidence time window (of perhaps 3 ns width); ii) same wavelength; and perhaps another property. They do not need to have the same polarization, and some Bell States require that they do not.

I disagree. The constraints that go into the BSM is information. These constraints being the requirement that 2 & 3 have an entangled pair and that 2 & 3 are indistinguishable.

c) As long as you are OK with Action At A Distance of some type, there is no contradiction. But I wouldn't call your description realistic at all. That's because there are variations on the swapping setups where your explanation would not apply. For example, measuring (1,4) after (2,3) doesn't work. That's because (1,4) evidence both perfect correlations AND violation of a Bell Inequality, something that can only occur by physical swapping from the BSM.

I think the most straight forward realistic interpretation of the entanglement swap experiment works in whatever order you perform the experiment. That you can measure (1,4) after (2,3) and get the same result tells me that swapping entanglement is a very real physical thing. That you can measure (1,4) before (2,3) and get the same result tells me that it must be symmetry that makes this case work the same as the first, and that for this case it is only swapping in a logical sense and not in a physical sense. Maybe this seems like an odd take on this experiment, but I suspect it is actually very consistent and gives a lot of explanatory power as to why QM works the way it does.

e) (1) can't ALSO be entangled with (2) and with (4) at the same time if monogamy is applied. It's one or the other. As mentioned many times already, this is the normal application of MoE - as both @vanhees71 and @PeterDonis have confirmed.

What does that even mean that 1 can't be entangled with 2 and 4 at the same time? What does this mean in a practical sense? What experiment would I run to verify or refute your claim?

I don't dispute monogamy, but I think that 1 and 2 being physically entangled every time, does not prevent 1 and 4 from having different logical entanglement correlations in their data sets. It seems as if you are saying that the monogamy argument applies to both apples and oranges at the same time. If 1 and 4 were always maximally entangled in the same way as 1 and 2 then yes, that would be in conflict with monogamy, but that clearly is not the case.

You seem to be saying in your posts that, any sufficiently large sample of measurement results of (1,2)×(3,4) (the initial state tipically prepared in the swapping entanglement experiment), can be "a posteriori" partitioned in four subsets (approximately of the same size) such that, in each of these four subsets (of measurement results, along a given axis, the same for all particles), the measured results for particle 1 and particle 4 is:

(u,u), (u,u), (u,u),.... subset1
(d,d), (d,d), (d,d), (d,d),... subset 2
(u,d), (u,d),..... subset3
(d,u), (d,u), (d,u),.... subset4

Is that all you mean?

No, I don't expect the 4 subsets would have the data pattern you mentioned. I expect the data patterns in each subset to depend on how you measure 1 and 4.

If for instance we were using polarization measurements to check the entanglement between 1 and 4 in the entanglement swap experiment:
I would expect that the experiment would involve making measurements on photon 1 at some angle X and photon 4 at some angle Y for lots of photon pairs. You would use the Bell test result of 2 & 3 to differentiate the 4 subsets in this data. You would then choose to repeat this for different angles of measurement. You would make sure that all of these matched the QM prediction cosine(diff between angles of measurement)^2 for the subsets that indicate maximum entanglement.

 

[PeterDonis]

The problem with saying "Mathematically the only "alteration" to 2 & 3 comes from the BSM" is that the math depends on constraints.

I don't see why this is a problem. If the necessary conditions (which you might not have correctly captured--see below) are not met for a particular experimental run, that run is simply a "no go" run where no entanglement swapping occurs. This sort of thing is expected for any experimental protocol where the experimenter does not have complete control over the conditions (in this case, whether a particular photon 2 & 3 pair will actually meet the indistinguishability condition).

One of the constraints is making the photons 2 & 3 indistinguishable.

Yes.

The other constraint is an entangled pair.

If you mean 2 & 3, no, 2 & 3 are not entangled prior to the BSM. 1 &2 are entangled and 2 & 3 are entangled. Both of those entanglements are maximal, so no other entanglements are possible in the initially prepared state. (That is the monogamy of entanglement argument that @DrChinese has been making.)

I think that 1 and 2 being physically entangled every time, does not prevent 1 and 4 from having different logical entanglement correlations in their data sets

What does "logical entanglement correlations" even mean?

At this point you're just waving your hands and you are getting close to having this thread closed. Again.

 

[vanhees71]

If you mean 2 & 3, no, 2 & 3 are not entangled prior to the BSM. 1 &2 are entangled and 2 & 3 are entangled. Both of those entanglements are maximal, so no other entanglements are possible in the initially prepared state. (That is the monogamy of entanglement argument that @DrChinese has been making.)

In the initial state you have
$$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
where
$$\hat{\rho}_{jk}=|\Psi_{\text{Bell}} \rangle \otimes |\Psi_{\text{Bell}}' \rangle,$$
where the $|\Psi_{\text{Bell}} \rangle$ kets stand for either of the four Bell states, i.e., the Pair (12) and the pair (34) are maximally entangled, while all other pairs are uncorrelated. The Pair (23) before the projection measurement is prepared in the state
$$\hat{\rho}_{23}'=\text{Tr}_{14} \hat{\rho}=\frac{1}{4} \hat{1}.$$
So as you correctly say in the first sentence the pair (23) is not entangled (which is of course also true for the pair (14)).

 

[Morbert]

The following are some comments on realism and antirealism as it pertains to the entanglement-swapping experiment. The first two paragraphs consider a minimalist instrumentalist interpretation (which can be distinct from an unqualified "minimalist" interpretation). The last paragraph is a comment on a realist interpretation.

The initial state $|\psi^-_{1,2}\psi^-_{3,4}\rangle\langle \psi^-_{1,2}\psi^-_{3,4}|$ tells us what correlations we will see between the detectors that measure the polarisations of photons 1 and 4 in a spatial mode basis, and the detector that measures the biphoton system [2,3] in the Bell basis in a sufficiently large number of experimental runs. Using the usual notation $A+B$ = "$A$ or $B$", $AB$ = "$A$ and $B$", the outcome of the experiment will be $$(D^1_hD^4_h+D^1_vD^4_v)(D^{2,3}_{\phi^+}+D^{2,3}_{\phi^-}) + (D^1_hD^4_v+D^1_vD^4_h)(D^{2,3}_{\psi^+}+D^{2,3}_{\psi^-})$$What monogamy of entanglement tells us is operators like $|\psi^-_{1,2}\psi^-_{3,4}\psi^-_{1,4}\rangle\langle \psi^-_{1,2}\psi^-_{3,4}\psi^-_{1,4}|$ do not correspond to any valid class of preparation. It is impossible to prepare such a "state". In a sentence: Monogamy of entanglement places a limit on possible preparations, which determine the frequencies and correlations we will observe in different instrument settings.

Because we have adopted a minimalist interpretation, which is antirealist w.r.t. properties immanent in the microscopic system, we do not have to conclude any influence between spacelike separated events throughout the experiment. Just as we do not need to do so with the regular EPRB experiment. The "entanglement swapping" novelty over the EPRB experiment poses no additional obligation to conclude influence between spacelike separated events. In the same way we can move from correlation in a classical system to entanglement in a quantum system in a minimalist framework, we can move from a correlation swapping classical system to an entanglement swapping quantum system in a minimalist framework.

If we instead adopt a realist framework, then we have to move into more interpretation-dependent territory. Decoherent histories arguably lets us maintain no influence between spacelike separated events in a realist framework, at least insofar as we can discuss properties of the microscopic system independent from measurement contexts (see my post here). Note that it does so without violating MoE because at no point does it invoke a state which simultaneously entangles pairs [1,2] and [2,3] or [1,2] and [1,4] etc.

 

[kurt101]

I don't see why this is a problem. If the necessary conditions (which you might not have correctly captured--see below) are not met for a particular experimental run, that run is simply a "no go" run where no entanglement swapping occurs. This sort of thing is expected for any experimental protocol where the experimenter does not have complete control over the conditions (in this case, whether a particular photon 2 & 3 pair will actually meet the indistinguishability condition).
If you mean 2 & 3, no, 2 & 3 are not entangled prior to the BSM. 1 &2 are entangled and 2 & 3 are entangled. Both of those entanglements are maximal, so no other entanglements are possible in the initially prepared state. (That is the monogamy of entanglement argument that @DrChinese has been making.)

No I meant 1 & 2 being entangled and 3 & 4 being entangled prior to BSM measurement. That is information that is fed into 2 & 3 that goes into the BSM. In particular this is true if measuring 1 affects 2 and measuring 4 affects 3. So again, the constraints of having to be indistinguishable and having been altered from entanglement is what is necessary for the QM math on the BSM, right?

So you can't just say there was no information given to 2 & 3 about 1 & 4 in order to make a correlation between 1 & 4.

The alternative to not accepting realism is having to accept that somehow 1 & 4 see the future? I find it so strange that so many are willing to throw out realism, because they have a suspicion that realism might not work. Just a suspicion, never definitive proof. I honestly don't get it and I would love for others to continue to explain why they don't just accept realism as fact since it has not been disproven.

What does "logical entanglement correlations" even mean?

If you measure many photons from 1 & 4 and then later do the Bell state test on photons 2 & 3, if done perfectly this divides the measurements of 1 & 4 into 4 subgroups, right? Subgroup 1 of 1 & 4 is not entangled with the other 3 subgroups, right? So whatever entanglement between 1 & 4 exists is divided up and 1 & 4 as a whole is not entangled. That is what I meant.

 

[Structure seeker]

If you measure 1 & 4 and later do a bell state test on 2 & 3, the states of 2 & 3 will be classical due to collapse on the entangled pairs 1 & 2 and 4 & 3. Or do you mean a bell measurement of 1&4?

 

[kurt101]

If you measure 1 & 4 and later do a bell state test on 2 & 3, the states of 2 & 3 will be classical due to collapse on the entangled pairs 1 & 2 and 4 & 3. Or do you mean a bell measurement of 1&4?

I do mean the bell state test on 2 & 3 like in the entanglement swap experiment.

If by classical you mean the non-locality is no longer present when 2 & 3 arrive at the BSM I would agree with that. My point is that when 2 & 3 arrive at the BSM they contain enough information about 1 & 4 so the Bell test can identify data sets in 1 & 4 that have the maximal entangled correlation.

 

[Structure seeker]

By classical I mean 0 or 1. They have already been measured by measuring their entangled partner.

 

[DrChinese]

A) In a sentence: Monogamy of entanglement places a limit on possible preparations, which determine the frequencies and correlations we will observe in different instrument settings.

B) Because we have adopted a minimalist interpretation, which is antirealist w.r.t. properties immanent in the microscopic system, we do not have to conclude any influence between spacelike separated events throughout the experiment. Just as we do not need to do so with the regular EPRB experiment. The "entanglement swapping" novelty over the EPRB experiment poses no additional obligation to conclude influence between spacelike separated events. In the same way we can move from correlation in a classical system to entanglement in a quantum system in a minimalist framework, we can move from a correlation swapping classical system to an entanglement swapping quantum system in a minimalist framework.

A) Good! We agree!!

B) I say there is an remote objective change to (1,4) in the minimalist interpretation. An experimenter controlling the BSM on the (2,3) pair can flip a switch to make 2 distinguishable from 3. If he does that, there is no swap. But all of the indicators are still present, which tell us which of the four Bell states would've been initiated. i.e two of the four photon detectors kicked off regardless of whether the swap succeeds or fails.

So whether the experimenter chooses to flip the switch, one way or the other, then the(1,4) pair will be entangled or not. we have the information to determine whether the (1,4) pair is correlated, or anti-correlated for all cases. But for those cases where the photons were distinguishable, the entangled statistics will not appear.

The experimenter, who is distant, changes the relationship of the (1,4) photons at his will. How is this not an objective demonstration of non-locality?