Realism in the entanglement swap experiment

[martinbn]

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?

This is misleading. If you only measure the (1,4) photons with no further information i.e. if you look at all pairs and make whatever measurements you like you cannot see any difference whether someone has done something to (2,3) or not.

 

[vanhees71]

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.

That's the key misunderstanding: When the Bell-analyzing measurment event on the pair (2,3) as well as the measurement events on photons 1 and 4 are all space-like separated (e.g., being simultaneous in some arbitrary frame of reference), there cannot be any influence of the measurement on the pair (2,3) on the measurements on photons 1 and 4 due to the microcausality property of relativistic QFT.

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?

The experimenter cannot change the relationship of the (1,4) photons at his will. All he can do is to select subensembles according to what random (!) result the Bell-analyzing experiment on the (2,3) photons delivers. He cannot choose a specific Bell state at his will, he can do only the Bell-analyzing experiment. That means, he cannot with certainty prepare a given (1,4) photon pair in a given Bell state. All he knows is that, if he finds photons (2,3) (with probability 1/4) in one of the four Bell states, then he knows that photons (1,4) must be in the corresponding Bell state.

The key for resolving the paradoxes of EPR is to keep in mind that all there is are the statistical properties of measurement outcomes!

 

[Structure seeker]

The key for resolving the paradoxes of EPR is to keep in mind that all there is are the statistical properties of measurement outcomes!

No, it's accepting nonlocal behaviour between correlated wavefunctions. In order for a model to describe reality, we should argue that realism supersedes locality. If wavefunctions are only mathematical wisps, there is no reason for why they would explain any real thing to behave some way. Entanglement is a property that is real, a property of wavefunctions. If those aren't real, you've lost me if entanglement suddenly IS real.

 

[DrChinese]

The experimenter cannot change the relationship of the (1,4) photons at his will. All he can do is to select subensembles according to what random (!) result the Bell-analyzing experiment on the (2,3) photons delivers. He cannot choose a specific Bell state at his will, he can do only the Bell-analyzing experiment. That means, he cannot with certainty prepare a given (1,4) photon pair in a given Bell state. All he knows is that, if he finds photons (2,3) (with probability 1/4) in one of the four Bell states, then he knows that photons (1,4) must be in the corresponding Bell state.

And I say this is objectively incorrect. The distant experimenter at the BSM has the following information:

a) Which 2 (of 4 total) detectors kicked off, which indicates which of the random Bell states occurred. The detectors indicate the following 2 bits of information:
i) Whether the 2,3 photons exited the same or different ports of the Beam Splitter.
ii) Whether the 2,3 photons have the same or different polarization.
These two bits are used to determine 2 of 4 possible Bell States. Pairs not in these 2 Bell States are ignored.
We have no difference of opinion on this as far as I know.

b) Whether the experimenter chooses to tag the (2) photons so that it is distinguishable from the (3) photon. He could do this, for example, by adding a bit of fiber to the path length (2) photons - but not the (3) photons. Fast switching can select whether the (2) and the (3) photons arrive at detector simultaneously (within a narrow time window), or instead that the (2) photon arrives sufficiently later so as to be identified. If it is identified, the (2,3) pair is not indistinguishable, and therefore there can be no swap. (As far as I know, this particular setup has not been executed - but it might have.)

The important thing here is that the a) information is available and tells us the same information about the Bell State regardless of what occurs with the b) information. The b) information, of course, is the decision of the experimenter to execute a successful swap - or not. For all those that characterize entanglement swapping as being selection of Bell state without any physical remote change in (1,4) state: There should be no effect from the experimenter's choice! But there will be no swap if the experimenter decides to make the (2) photon distinguishable from the (3) photon.

QED.

 

[PeterDonis]

No I meant 1 & 2 being entangled and 3 & 4 being entangled prior to BSM measurement.

Ok.

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.

"Measuring 1 affects 2" and "measuring 4 affects 3" are only true on certain interpretations of QM.

Also, even if we adopt an interpretation for which those are true, it only matters if the 1 & 4 measurements are done before the 2 & 3 BSM. If the 2 & 3 BSM is done first, 1 & 4 haven't been measured so nothing can have affected 2 & 3.

However, the actual results are independent of the order in which the measurements are done. So an explanation that depends on the order in which the measurements are done doesn't seem like it could be right.

We have had this discussion before as well. If your only purpose in this thread is to rehash that question, there is no point; it has already been more than adequately discussed in prior threads.

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?

I don't know what you mean by "having been altered from entanglement".

The alternative to not accepting realism is having to accept that somehow 1 & 4 see the future?

I don't see why this is the case.

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?

It divides the experimental runs into 4 subgroups (that is if you are doing an ideal BSM on 2 & 3 that can distinguish all four possible outcomes. In the actual experiments that have been done, only one of the four possible BSM outcomes is distinguishable, so only those runs are picked out.)

Subgroup 1 of 1 & 4 is not entangled with the other 3 subgroups, right?

This doesn't even make sense. One experimental run can't be entangled with a different experimental run.

So whatever entanglement between 1 & 4 exists is divided up and 1 & 4 as a whole is not entangled. That is what I meant.

This is word salad. It makes no sense.

 

[PeterDonis]

The experimenter, who is distant, changes the relationship of the (1,4) photons at his will.

You seem to be saying that the experimenter at the BSM could send signals faster than light to experimenters at the (1, 4) photon measurement locations. I don't think that's what you intend, since this would violate the no signaling theorem. But it illustrates how difficult it is to describe what is going on in these experiments in ordinary language. And that means one needs to be very careful about claims that other people's ordinary language descriptions, different from yours, are wrong.

For example:

The experimenter cannot change the relationship of the (1,4) photons at his will. All he can do is to select subensembles according to what random (!) result the Bell-analyzing experiment on the (2,3) photons delivers. He cannot choose a specific Bell state at his will, he can do only the Bell-analyzing experiment. That means, he cannot with certainty prepare a given (1,4) photon pair in a given Bell state. All he knows is that, if he finds photons (2,3) (with probability 1/4) in one of the four Bell states, then he knows that photons (1,4) must be in the corresponding Bell state.

And I say this is objectively incorrect.

No, it isn't. It's just focusing on a different aspect of the situation: the fact that the experimenter cannot control which Bell state is produced in 2 & 3 (and hence 1 & 4) if he chooses to execute the swap. All he can control is whether or not the swap is executed; which of the four Bell states results from the swap is random. That is why the experimenter cannot use this method to violate the no signaling theorem.

In other words, both of you are making correct statements, and reconciling them is possible, but it requires being very, very careful about exactly what is and is not being said. That is very difficult to do with ordinary language.

 

[DrChinese]

You seem to be saying that the experimenter at the BSM could send signals faster than light to experimenters at the (1, 4) photon measurement locations. I don't think that's what you intend, since this would violate the no signaling theorem. But it illustrates how difficult it is to describe what is going on in these experiments in ordinary language. And that means one needs to be very careful about claims that other people's ordinary language descriptions, different from yours, are wrong.

For example:
No, it isn't. It's just focusing on a different aspect of the situation: the fact that the experimenter cannot control which Bell state is produced in 2 & 3 (and hence 1 & 4) if he chooses to execute the swap. All he can control is whether or not the swap is executed; which of the four Bell states results from the swap is random. That is why the experimenter cannot use this method to violate the no signaling theorem.

In other words, both of you are making correct statements, and reconciling them is possible, but it requires being very, very careful about exactly what is and is not being said. That is very difficult to do with ordinary language.

I have repeatedly said there is no possibility of FTL signaling using the experimenter’s choice to execute a swap or not. As you say, the Bell state result is random. I think we all agree to this point.

The Bell state is indicated by the particular combination of detectors that are triggered. The 2 psi states require the 2 and 3 photons to be orthogonal. The psi- state has 2 and 3 emerging from different ports on the beam splitter, while psi+ has them emerging from the same port.

You get this same information (identifying psi- or psi+) whether the experimenter flips the photon 2 delay switch (which fails the swap) or not.

Objectively, there is now a subensemble of psi- results. The subensemble splits into 2 subensembles: 1 in which the swap succeeded and there is the expected correlation. In the other, the swap failed and the results are random.

 

[vanhees71]

But here the the two statements obviously contradict each other, as you point rightfully out yorself. It's clear that you can't in any way choose which Bell state occurs at will and thus you can't send a message in this way. That's interpretation independent.

 

[kurt101]

"Measuring 1 affects 2" and "measuring 4 affects 3" are only true on certain interpretations of QM.

Also, even if we adopt an interpretation for which those are true, it only matters if the 1 & 4 measurements are done before the 2 & 3 BSM. If the 2 & 3 BSM is done first, 1 & 4 haven't been measured so nothing can have affected 2 & 3.

However, the actual results are independent of the order in which the measurements are done. So an explanation that depends on the order in which the measurements are done doesn't seem like it could be right.

Yes, I think you understand my position.

I agree with you that "an explanation that depends on the order in which the measurements are done doesn't seem like it could be right", but I think that is what the magician wants you to think. When you realize how simple the trick is, the illusion loses its power. No matter what order the experiment is done, the experiment is still just doing two spooky rotations on random polarization states. Of course all of this requires you to accept an interpretation where "measuring 1 affects 2" but once you accept such an interpretation I think the trick is apparent.

I don't know what you mean by "having been altered from entanglement".

2 having been altered by measurement of 1 for example.

I don't see why this is the case.

Ok, I trust you are probably correct that other interpretations don't need to look into the future, but can you name one or two of the most obvious examples for me?

This doesn't even make sense. One experimental run can't be entangled with a different experimental run.

Yes you are right, not sure what I was thinking there.

This is word salad. It makes no sense.

Yes, let me try again. The raw data between 1 & 4 does not have a correlation of being entangled. Only when you look at the data within one of the four subsets in 1 & 4 raw data do you see the correlation of being entangled. So I don't see why the monogamy argument applies here given that 1 & 4 are not really entangled when the entire data set is considered. The only things in the experiment that are consistently entangled are 1 & 2 and 3 & 4.

 

[PeterDonis]

I agree with you that "an explanation that depends on the order in which the measurements are done doesn't seem like it could be right", but I think that is what the magician wants you to think.

What "magician" are you talking about?

 

[kurt101]

What "magician" are you talking about?

No one in particular, just an analogy between an audience trying to understand what is happing in a magic show and us trying to understand what is happening in the entanglement swapping experiment.

 

[PeterDonis]

1 & 4 are not really entangled when the entire data set is considered.

Again, this is interpretation dependent. You are basically adopting an ensemble interpretation, and making it more strict than it usually is, by refusing to consider any subensemble smaller than the full set of raw data. Normally considering the subensemble of 1 & 4 runs that is picked out by the given conditions on the 2 & 3 BSM is perfectly acceptable according to an ensemble interpretation. (What is not acceptable is to pick out a subensemble of 1 & 4 runs based on the results of 1 & 4 measurements. But that is not what is being done here. We've been over this.)

But @DrChinese is using a different interpretation, in which the quantum state describes each individual run, not an ensemble of runs. What you call "subensembles" to him are just particular sets of runs described by particular conditions. The fact that the full set of runs does not show the same correlations as the particular set he is interested in is irrelevant on the interpretation he is using.

The only things in the experiment that are consistently entangled are 1 & 2 and 3 & 4.

By your own claimed method, this is wrong. If you look at the full set of raw data, refusing to pick out any "subensembles" whatever, then there is no entanglement anywhere. 1 & 2 and 3 & 4 aren't entangled any more than 1 & 4 and 2 & 3 are.

In order to actually see the entanglements between 1 & 2 and 3 & 4 in data, you would have to either (1) pick out subensembles in which the BSM conditions were not met and therefore no entanglement swap was made, or (2) eliminate the BSM entirely and just make measurements on the initially prepared state.

 

[PeterDonis]

No one in particular, just an analogy between an audience trying to understand what is happing in a magic show and us trying to understand what is happening in the entanglement swapping experiment.

This analogy does not work because in a magic show, there is at least one person--the magician--who knows the trick and can give the true explanation of how it works.

In QM, however, nobody is in that position. All we know is the basic math and predictions, which everyone agrees on, and the different, incompatible intepretations, about which there has never been general agreement among all physicists about which one is the "true explanation".

 

[vanhees71]

Again, this is interpretation dependent. You are basically adopting an ensemble interpretation, and making it more strict than it usually is, by refusing to consider any subensemble smaller than the full set of raw data. Normally considering the subensemble of 1 & 4 runs that is picked out by the given conditions on the 2 & 3 BSM is perfectly acceptable according to an ensemble interpretation. (What is not acceptable is to pick out a subensemble of 1 & 4 runs based on the results of 1 & 4 measurements. But that is not what is being done here. We've been over this.)

In the initial state, the photons 1 and 4 are not entangled, and that's an interpretation independent mathematical fact. As is easily calculated, the reduced stat. op. is
$$\hat{\rho}_{14}=1/4 \hat{1}\otimes \hat{1}.$$

But @DrChinese is using a different interpretation, in which the quantum state describes each individual run, not an ensemble of runs. What you call "subensembles" to him are just particular sets of runs described by particular conditions. The fact that the full set of runs does not show the same correlations as the particular set he is interested in is irrelevant on the interpretation he is using.

Correlations can only be tested on ensembles, not with a single measurement.

By your own claimed method, this is wrong. If you look at the full set of raw data, refusing to pick out any "subensembles" whatever, then there is no entanglement anywhere. 1 & 2 and 3 & 4 aren't entangled any more than 1 & 4 and 2 & 3 are.

But the initial state is such that photons 1&2 as well as 3&4 are both in a Bell state, i.e., maximally entangled.

In order to actually see the entanglements between 1 & 2 and 3 & 4 in data, you would have to either (1) pick out subensembles in which the BSM conditions were not met and therefore no entanglement swap was made, or (2) eliminate the BSM entirely and just make measurements on the initially prepared state.

To see that either of the pairs are entangled, you've to measure the single-photon polarizations, but this precludes any Bell-state measurement and thus entanglement swapping.

QT is only about measurements that are done, not about unperformed measurements.

 

[PeterDonis]

In the initial state, the photons 1 and 4 are not entangled, and that's an interpretation independent mathematical fact.

Correlations can only be tested on ensembles, not with a single measurement.

the initial state is such that photons 1&2 as well as 3&4 are both in a Bell state, i.e., maximally entangled.

None of these things contradict anything I said. I am not disputing any of the math or the experimental facts. I am simply pointing out that different interpretations say different, and often incompatible, things in addition to the math and the experimental facts.

 

[vanhees71]

But the math is unanimously telling the statistical properties for the outcome of measurements, independent of any metaphysical believes.

 

[PeterDonis]

the math is unanimously telling the statistical properties for the outcome of measurements

Yes, that's correct. It also doesn't contradict anything I said.

 

[kurt101]

But @DrChinese is using a different interpretation, in which the quantum state describes each individual run, not an ensemble of runs. What you call "subensembles" to him are just particular sets of runs described by particular conditions. The fact that the full set of runs does not show the same correlations as the particular set he is interested in is irrelevant on the interpretation he is using.

What do you mean by an individual run? Is that 1 photon from each source being considered in the experiment as a run? Or does that mean many photons from each source with a fixed measurement considered in the experiment as a run?

 

[PeterDonis]

What do you mean by an individual run?

Each individual set of photons 1 through 4, prepared and going through the experiment as described in the experimental protocol.

 

[vanhees71]

Yes, that's correct. It also doesn't contradict anything I said.

I only wanted to argue against your statement that all this depends on "interpretation", as if there'd be no objective scientific meaning of QT. That's the greatest harm done by the early overemphasis of philosophy by part of the "founding fathers" of QT.

There are clear unanimous objective probabilistic predictions about empirically testable facts, and probabilistic predictions need statistics on ensembles, no matter which other philosophical argumentz are envoked on the meaning of probabilities.

 

[PeterDonis]

I only wanted to argue against your statement that all this depends on "interpretation"

I said no such thing. I was quite specific about what is interpretation and what isn't.

 

[mattt]

@DrChinese

If the swap fail for some of the runs (deliberate or not) then you can partition the whole ensemble in five subensembles (the four ones like in the ideal case, plus another subset that corresponds to the failed swap runs).

And still the whole ensemble (the union of the five subsets) of the (1,4) pairs is characterized by the same statistics (state) as in the beginning.

You may think that "something changed" for each individual (1,4) pair (depending on the deliberate action of the experimenter at (2,3) site to fail or not fail the swap) only if you think that the state is a physical property of each (1,4) pair.

It adds nothing essentially new in this respect to the EPR type experiments.

 

[DrChinese]

It's clear that you can't in any way choose which Bell state occurs at will and thus you can't send a message in this way. That's interpretation independent.

Correct. We have never had a disagreement on these points.

Let’s focus on a single Bell state, psi-. This state occurs 25% of the time, and is of course random. The identifying characteristics are the 2,3 photons emerging from separate Beam Splitter ports, and polarizations orthogonal.

Our experimenter at the BSM sees those random cases that identify as psi-. That means 2,3 are triggering 2 detectors that identify them per above. When those specific combinations are registered, the related 1,4 pairs will be perfectly anti-correlated at all angles… but only if the 2,3 photons are indistinguishable! So when the 1,4 pairs that have been identified as psi- are reviewed, there will be no statistical relationship when the experimenter flips the switch one way, and will be a perfect match to the quantum expectation when the switch is flipped the other way.

The experimenter makes a choice, flipping a switch, causing the distant 1,4 to become anti correlated - or be completely uncorrelated. Depending on whether there is indistinguishability…

This is an objective result, not subject to interpretation. I say it rules out an entire class of interpretations. There is no FTL signaling, but strict Einsteinian causality is not preserved. The order of measurements is not a factor, and light cones are not a limiting factor.

 

[PeterDonis]

This is an objective result, not subject to interpretation.

Careful. Statements like this...

causing the distant 1,4 to become anti correlated - or be completely uncorrelated

strict Einsteinian causality is not preserved

...are interpretation dependent. They are not "objective results". We can observe statistics, but we can't directly observe causation. And "strict EInsteinian causality", in QFT terms, becomes what @vanhees71 calls "microcausality"--spacelike separated measurements must commute. Which is not violated in these experiments (indeed, the results commute regardless of the spacetime relationship between the measurement events).

 

[DrChinese]

@DrChinese

If the swap fail for some of the runs (deliberate or not) then you can partition the whole ensemble in five subensembles (the four ones like in the ideal case, plus another subset that corresponds to the failed swap runs).

And still the whole ensemble (the union of the five subsets) of the (1,4) pairs is characterized by the same statistics (state) as in the beginning.

You may think that "something changed" for each individual (1,4) pair (depending on the deliberate action of the experimenter at (2,3) site to fail or not fail the swap) only if you think that the state is a physical property of each (1,4) pair.

It adds nothing essentially new in this respect to the EPR type experiments.

Please see my post #58, where I analyze the psi- case specifically.

When the experimenter fails the swap, he still gets the same information about the Bell state that would have been been obtained had the swap succeeded. There’s no difference in which detectors are triggered. The only change is distinguishability, which fails the swap but still allows the Bell state to be identified (if the swap had succeeded).

 

[DrChinese]

Careful. Statements like this...

...are interpretation dependent. They are not "objective results". We can observe statistics, but we can't directly observe causation.

The measured statistics change, according to the experimenter’s choice. I’d call that objective. Correlated/anti correlated vs no correlation at all.

Of course, there is no FTL signaling. You must bring the Bell State data (ie which events are identified as psi- or whatever) plus the experimenter’s choices (whether delay switch flipped or not) together with the outcome of the 1,4 pair measurements. Only then does the nonlocal action become visible. And that requires classical communication. So nonlocal action, no nonlocal signal.

 

[PeterDonis]

The measured statistics change, according to the experimenter’s choice. I’d call that objective.

That's not the claim I quoted as being interpretation dependent.

 

[Morbert]

You get this same information (identifying psi- or psi+) whether the experimenter flips the photon 2 delay switch (which fails the swap) or not.

I am suspicious of this claim. It sounds like you are carrying out an intermediate measurement which would affect the [2,3] pair, such that if you register a psi- or psi+ you can no longer be sure you would have registered that same result even if you hadn't added the delay. Can you provide the explicit time-evolution of the two scenarios (delay vs no delay)? Or some expression a la equation 3 in this paper that distinguishes the the two cases?

 

[DrChinese]

I am suspicious of this claim. It sounds like you are carrying out an intermediate measurement which would affect the [2,3] pair, such that if you register a psi- or psi+ you can no longer be sure you would have registered that same result even if you hadn't added the delay. Can you provide the explicit time-evolution of the two scenarios (delay vs no delay)? Or some expression a la equation 3 in this paper that distinguishes the the two cases?

Fair question.

Sure, I am familiar with your reference. Equation 3 presents all four Bell states. We will focus on a single of those four, the phi- Bell state, which they seek. The BSM uses a projecting PBS instead of a beam splitter for the first test, but the principle is the same as other setups. The second test consists of a polarizing beam splitter at each of the output ports of the projecting PBS. There are then photon detectors at each of those output ports, four in total.

The desired phi- state requires the 2,3 photons to exit different output ports of the projecting PBS. They must end up as hv or vh in the final polarization test. In this case, the 1,4 photons become cast into a perfectly anti-correlated state. Analogously, when the phi+ State occurs, the 1,4 photons become cast into a perfectly correlated state.

Interestingly, this experiment actually demonstrates exactly what I am saying. Not sure why I missed this on previous reading, but here it is in black and white. See figure 3c and related text (the paragraph beginning with “One can also choose…”). They used Temporal delay to create the distinguishability. The results are exactly as I predicted. Which is, of course, in keeping with usual quantum mechanics.

Once again: the experimenter may choose to have a successful swap, or not, while retaining all the information needed to discriminate between Bell states which occur randomly. When the experimenter adds delay to cause the swap to fail due to distinguishability, the remote 1,4 photons objectively change their state (as demonstrated from the density matrices of figure 3) from entangled to unentangled.

 

[Morbert]

Interestingly, this experiment actually demonstrates exactly what I am saying.

Indeed, this is why I thought it would be the best example to better understand your claim.

Fair question.

Sure, I am familiar with your reference. Equation 3 presents all four Bell states. We will focus on a single of those four, the phi- Bell state, which they seek. The BSM uses a projecting PBS instead of a beam splitter for the first test, but the principle is the same as other setups. The second test consists of a polarizing beam splitter at each of the output ports of the projecting PBS. There are then photon detectors at each of those output ports, four in total.

The desired phi- state requires the 2,3 photons to exit different output ports of the projecting PBS. They must end up as hv or vh in the final polarization test. In this case, the 1,4 photons become cast into a perfectly anti-correlated state. Analogously, when the phi+ State occurs, the 1,4 photons become cast into a perfectly correlated state.

Interestingly, this experiment actually demonstrates exactly what I am saying. Not sure why I missed this on previous reading, but here it is in black and white. See figure 3c and related text (the paragraph beginning with “One can also choose…”). They used Temporal delay to create the distinguishability. The results are exactly as I predicted. Which is, of course, in keeping with usual quantum mechanics.

Once again: the experimenter may choose to have a successful swap, or not, while retaining all the information needed to discriminate between Bell states which occur randomly. When the experimenter adds delay to cause the swap to fail due to distinguishability, the remote 1,4 photons objectively change their state (as demonstrated from the density matrices of figure 3) from entangled to unentangled.

From the paper

In this case [distinguishability], the phase between the two terms of the |φ〉 projected state is undefined, resulting in a mixture of |φ+〉 and |φ−〉 in the projected state, and the first and last photons do not become quantum entangled but classically correlated.

I read this to mean, when distinguishability is established, the apparatus can no longer project onto |φ+〉 or |φ−〉 and instead projects onto some state $a|\phi^+\rangle\langle\phi^+| + b|\phi^-\rangle\langle\phi^-|$. How do you square this with your claim

You get this same information (identifying psi- or psi+) whether the experimenter flips the photon 2 delay switch (which fails the swap) or not.

because it sounds like you lose the ability to identify phi+ or phi- and must settle for a mixture. The caption under figure 3c calls this case a failure to project.

 

[vanhees71]

Correct. We have never had a disagreement on these points.

Fine, so where's finally the disagreement? Let's see...

Let’s focus on a single Bell state, psi-. This state occurs 25% of the time, and is of course random. The identifying characteristics are the 2,3 photons emerging from separate Beam Splitter ports, and polarizations orthogonal.

Yes, that's the most simple case, because here you can deal with a simple beam splitter. The disadvantage is that you can only filter out one of the four interesting projections, i.e., only to the "singlet Bell state". So a complete Bell-state analysis is favorible, because then you can a posteriori (delayed choice!) look at the four interesting sub-ensembles. But anyway, for the discussion of the locality/causality issue it's enough.

Our experimenter at the BSM sees those random cases that identify as psi-. That means 2,3 are triggering 2 detectors that identify them per above. When those specific combinations are registered, the related 1,4 pairs will be perfectly anti-correlated at all angles… but only if the 2,3 photons are indistinguishable! So when the 1,4 pairs that have been identified as psi- are reviewed, there will be no statistical relationship when the experimenter flips the switch one way, and will be a perfect match to the quantum expectation when the switch is flipped the other way.

If the 2,3 photons are projected to $\psi^-$, they are indeed indistinguishable. That's the whole point of this state being a maximally entangled state, i.e., a "Bell state". Of course, for this perpose the experimenter doing the projection must project to this Bell state. This experiment then doesn't tell you anything about what would have been found when doing another experiment, i.e., QT does not tell anything about experiments that haven't been performed or measurements that cannot be performed given the measurement really done. E.g., in an SG experiment you can measure the spin component in one direction but not at the same time in another direction, because the direction is uniquely chosen only with a correspondingly directed and taylored magnetic field. The same holds here for polarization measurements. You have to choose which observations you want to make, i.e., measuring the polarization of single photons in a specific direction, which then of course never leads to the projection to an entangled state or you can decide to project to a Bell state.

The experimenter makes a choice, flipping a switch, causing the distant 1,4 to become anti correlated - or be completely uncorrelated. Depending on whether there is indistinguishability…

I think, we agree up to this point.

This is an objective result, not subject to interpretation. I say it rules out an entire class of interpretations. There is no FTL signaling, but strict Einsteinian causality is not preserved. The order of measurements is not a factor, and light cones are not a limiting factor.

Now, you are contradicting yourself again. If there is no FTL signalling possible, then relativistic causality is preserved, i.e., in other words, there are no causal connections between space-like separated events possible, then relativistic causality is fulfilled. Maybe you have another definition for what you call "Einsteinian causality". Maybe what you in fact mean is not causality but determinism or, in the sense of the original paper of Bell's (obviously he changed his terminology over time, as I learnt recently from some paper, mentioned in one of the threads her on PF, which I can look for again if needed) "realism", i.e., the believe that all observables of a system must always take determined values, independent of the state of the system. This contradicts standard QT and that's why "hidden variables" are invoked, that are unknown and unobservable, so that the probabilities come in only due to "ignorance" (which may not be avoidable from first principle, if for some reason the hidden variables are not even in principle determinable in any way), i.e., as in classical statistical physics.

However, together with the fulfillment of the relativistic causality principle (i.e., no FTL signalling possible), this possibility is ruled out by the very argument leading to Bell's inequalities within such "local realistic HV theories" and the empirical finding that indeed these inequalities are precisely violated in the way predicted by relativistic QFT, which by construction fulfills the locality constraint (i.e., no FTL signalling possible) via the microcausality constraint on local observable-operators.

 

[mattt]

Please see my post #58, where I analyze the psi- case specifically.

When the experimenter fails the swap, he still gets the same information about the Bell state that would have been been obtained had the swap succeeded. There’s no difference in which detectors are triggered. The only change is distinguishability, which fails the swap but still allows the Bell state to be identified (if the swap had succeeded).

You are assuming that, in a single run where the experimenter fails to do the swap, we know what would have happened exactly (wrt output ports, polarization outputs, phi+, phi-) if he hadn't failed to do the swap.

 

[PeterDonis]

Thread closed for moderation.

 

[berkeman]

Thread reopened after a cleanup of misinformation and a thread band for @Simple question

 

[DrChinese]

Indeed, this is why I thought it would be the best example to better understand your claim.From the paper I read this to mean, when distinguishability is established, the apparatus can no longer project onto |φ+〉 or |φ−〉 and instead projects onto some state $a|\phi^+\rangle\langle\phi^+| + b|\phi^-\rangle\langle\phi^-|$. How do you square this with your claim because it sounds like you lose the ability to identify phi+ or phi- and must settle for a mixture. The caption under figure 3c calls this case a failure to project.

Sure, the same detectors are present, and so that data becomes available just as when a swap occurs. It shows which Bell state would’ve been identified, if the swap had actually occurred. Of course, no swap… no true Bell state. From the paper:

One can also choose to introduce distinguishability between the two projected photons. In this case, the phase between the two terms of the |φ⟩ projected state is un- defined, resulting in a mixture of |φ+⟩ and |φ−⟩ in the projected state, and the first and last photons do not become quantum entangled but classically correlated. We observed this when we introduced a sufficient temporal delay between the two projected photons (see Fig. 3c). It is also evidence that the first and last photons did not somehow share any entanglement before the projection of the middle photons.

I would say their result is unambiguously objective and physical. A decision by an experimenter to execute (or fail) a set of swaps causes distant photons 1,4 to be entangled (or not be entangled at all). The Bell state measurement does not reveal pre-existing entanglement. It causes it (again, without violating signal locality).