I Confused by nonlocal models and relativity

[vanhees71]

Then why put in the extra word "local"? Particularly when it causes interminable arguments in threads like this, because the word "nonlocal" is commonly used to describe correlations that violate the Bell inequalities?

The problem is that this terminology is used all the time. It's hopeless to change terminology which is established for nearly 100 years. That makes the debates about the foundations so difficult.

 

[vanhees71]

1. Finally!

2. Agreed.

3. No, and once again, please give a reference other than yourself. I have never seen such a [*] description in any entanglement swapping paper [**]. If the entanglement swap is not executed at 2 & 3, as I indicated above, the far separated 1 & 4 will not be entangled - contradicting your purely local [***] characterization.

Once 1 & 4 are entangled, they are mirrors of each other and have quantum properties that far exceed what 2 otherwise independently created particles could ever have. Of course, they are now part of a quantum system and are no longer separable. You could never construct such a system of 2 particles otherwise as you could never know that many non-commuting observables. Zeilinger says, of the 2 entangled particles that never interact:

"The aim is that the distant experimenter Bob [looking at photon 4] obtains an exact replica of that particle. It is evident that no measurement whatsoever Alice [looking at photon 1] might perform on the particle could reveal all necessary information to enable Bob to reconstruct its state."

That doesn't happen because of post-selection! That should be obvious. There are NO such 2 particles that can be independently created and later post selected (they must be entangled, and cannot be entangled with any other particle). That is strictly forbidden by the HUP. The mirror particles (the ones projected into the singlet state) have the mirroring values for non-commuting p and q, for example. They must be physically connected as part of a single, non-separable, quantum system. It's non-local in spatial extent.

4. The humorous element is that you completely ignore everything Zeilinger actually says, and then recast his viewpoint to match yours. Zeilinger does not claim to have an understanding of the mechanism by which quantum nonlocality operates (and I don't either). But he would never refer to QM as being local causal, and I certainly can't recall a respected paper of the last 20 years using any terminology similar to yours.

And please, despite our going back and forth on the subject, I hope you would not take our discussion as anything other than friendly. *Let's just say "contrived".
**And I've read a few.
*** Seriously, it's 2019 my friend. Quantum non-locality was generally accepted some time ago.

For sure, I think this is a completely friendly discussion, and I think all there is is a misunderstanding between our points of view due to different understanding of unsharply defined words.

The most puzzling thing for me is our disagreement about 3. I also don't see that my viewpoint is any different from what's written in the paper by Zeilinger et al which we discuss here.

Again ad 3). In the paper they emphasize themselves that in order to get a preparation of a subensemble, where the pair 1&4 is entangled is the sufficient locality of the manipulations/measurements on the pair 2&3. The Bell measurement of 2&3 must be made such that it's happening in a sufficiently small space-time region to be within the temporal and spatial coherence lengths of the photons. Thus I agree with both you and the authors of the paper that the entanglement swapping won't work if you don't match this constraint.

The photons 1&4 have never causally interacting and are nevertheless entangled after the entanglement-swapping procedure. We also agree on this, and I never denied that quantum states can describe "non-local correlations through entanglement". I emphasize however, that it describes "correlations" not "causal connections". As I said, I think our mutual misunderstanding is due to the unsharply defined meaning of these words.

Finally, I don't believe that physics is about understanding some "mechanism". Whatever that might be. Quantum theory as any physical theory describes (admittedly in a quite formal way) phenomena, and all there is to understand is this formalism and how it's applied to phenomena. The very fact that Zeilinger et al can invent all their beautiful experiments which finally all confirm QT shows that they have very well understood QT. There's nothing more to understand! Just take the formalism seriously, and this formalism is in some sense a miracle, making the long-range correlations described by entanglement and the implied "inseparability" on the one hand consistent with Einstein causality through the microcausality constraint of relativistic QFT on the other hand!

 

[akvadrako]

That doesn't happen because of post-selection! That should be obvious. There are NO such 2 particles that can be independently created and later post selected (they must be entangled, and cannot be entangled with any other particle). That is strictly forbidden by the HUP.

Why's it obvious that entanglement can't be created via a quantum post-selection procedure?

Imagine that you've already performed some Bell tests on 1&4 and you have the results in front of you. With those results you should be able to classically select pairs so that those results seem to violate a Bell inequality. However, because you've measured them, at this point the entanglement correlations are broken.

I think what's happening in this experiment is almost the same thing but unlike with the classical example, it doesn't reveal the measurement results for 1&4, so they can maintain their entanglement. Initially, even without any interaction, there is a sub-ensemble of 1&4 which is entangled along a chosen direction. Maybe it's correct to say every pair of identical particles is entangled along a random direction. Then you use the quantum post-selection procedure on pairs 2&3 to identify an appropriate sub-ensemble of 1&4.

 

[vanhees71]

Exactly!

In other words: You can post-select the subensemble 100 years after the experiment was done provided you have a sufficiently complete measurement protocol. There's nothing mysterious in this as long as you don't insist on the collapse interpretation in the sense of a causal action at a distance as some Copenhagen flavored interpretations insist upon but interpret entanglement as a description of very strong correlations between parts of a quantum system.

 

[microsansfil]

*For example: The entanglement swap can occur such that the entangled photons never co-exist. So obviously the entanglement did not occur at their creation - they were not created together (as you proposed). Variations on entanglement swapping wreck attempts to describe in terms of locality and/or (micro)causality.

Entanglement Between Photons That Have Never Co-existed

When photon 1 is measured in a certain basis the correlation with photon 2 is break.
Photon 2 is delayed until a second pair (3–4) is created and photons 2 and 3 are projected onto the Bell basis.

When photon 2 is projected, with photon 3, onto bell basis (Bell measurement), will the entanglement swapping still be realized ? Since photon 2 has lost its correlation with photon 1.

/Patrick

 

[vanhees71]

Then it won't be realized. That's the whole point of the discussion! To get entanglement swapping it is necessary to measure "locally (in space and time!) enough" to be within the coherence lengths of the photons. If you perform the measurments on 2&3 at a time where 2 is no longer entangled with 1 and/or 3 no longer entangled with 4, all you get are uncorrelated photons 1&4, no matter what you meaure on photons 2&3.

 

[DrChinese]

Why's it obvious that entanglement can't be created via a quantum post-selection procedure?

Ha, perhaps not obvious because of my poor description.

They can't be created by post-selection! Post-selection (as an explanation for what is occurring) implies that these 2 photons - 1 & 4 - are occasionally and randomly entangled (with each other); and then post-selection simply reveals that entanglement. That's a reasonable hypothesis, but here's why that is absolutely impossible.

A. You can create 2 photons that have the same polarization (at a specific angle), for example light from a laser, but a test for entanglement will fail on those. There are a number of mechanisms for creating entangled pairs; here, pair 1 & 2 are entangled via PDC and 3 & 4 are as well. In fact they are maximally entangled. You may recall there is something called "monogamy of entanglement". That says that if photon 1 is maximally entangled with photon 2, then it CANNOT be entangled with photon 4 or with any other particle in the universe.

B. Now you run into our problem: what happened to cause 1 & 4 to become entangled - meaning that ANY observation on one tells you the matching value of an observable on the other? That state for 1 & 4 only occurs IF they were entangled, there is no other quantum state that yields the same results. So what could possibly have occurred to cause this state? "Something" must have happened to change all that!

C. I say (and this simply follows the rules of entanglement swapping, see the cited paper for more detail):
- Photons 1 & 4 were entangled as a result of a decision to cast them into a Bell State (by action on photons 2 & 3), else they weren't entangled at all.
- The mechanism for entangling 1 & 4 is to bring 2 & 3 together in the Bell State Analyzer (BSA) and perform a Bell State Measurement (BSM) on them. Some of the 2 & 3 pairs will randomly be cast into a Bell State which indicates that 1 & 4 are now entangled.
- Such only happens if 2 & 3 are completely indistinguishable. In the experiment, that occurs when they arrive at the BSA within a very small time window, perhaps within 5-10 picoseconds. They must also show up in different arms (different PBS) of the BSA, after passing through a common Beam Splitter (BS), as that indicates a Bell State.

D. If the vanhees hypothesis were correct (local causality, no physical collapse, his minimal interpretation where observations reveal pre-existing attributes):

- Photons 2 & 3 are speeding towards the BSA and whatever happens (or doesn't happen) at the BSA cannot change photons 1 & 4 because they are spacelike separated from the BSA.
- Photons 1 & 4 are NOT yet entangled with each other, because they are entangled with 2 & 3 respectively.
- The 2 & 3 photons enter the BSA around the same time (within a very small window), but they generally cannot interfere or otherwise interact with each other. So presumably, whether they are going to register as meeting the conditions for a Bell State (psi+ or psi-) has already been determined and the BSA reveals the appropriate detector clicks to so indicate.

E. And now we have big problems with no good answers (although you can try):
i) How (and when) did photon 1 lose its entangled connection to photon 2? Presumably that occurs when photon 2 is measured, correct? But then it no longer exists!
ii) How (and when) did photon 1 gain an entangled connection to photon 4? After all, we have postulated it was previously entangled with photon 2 and photon 2 alone (due to monogamy). And nothing is changing for its state, as it is too far away.
iii) More importantly, why would photon 4 - out of all the particles in the universe - suddenly have this unique and monogamous connection to photon 1? (Remember: attributes such as momentum (frequency), polarization, etc. are all part of the entanglement.)

I would hope these problems would convince you of the futility of the hypothesis. There is no narrative described in any paper I have read that remotely matches the vanhees hypothesis (I've asked and asked without any success for a reference). But if E. didn't convince you...

F. Furthermore: If you accept the vanhees hypothesis, then the detector clicks at the BSA are revealing pre-existing attributes of the 2 & 3 pair which is to be used to identify Bell States. And critically, photons 2 & 3 do not interact in any way, as mentioned above. So if we were to delay photon 2 from arriving at the BSA by (say) 100 ps, that should not in any way affect the detector click outcomes at the BSA other than to have one of the clicks occur about 100 ps later than the other. Here's how it might look for the relative detection time stamps, and I am making up simple time stamps for purposes of illustration:

No delay:
Detector 1V: 1000000ps (photon 1)
Detector 2H: 1000003ps (either photon 2 or 3, not sure which)
Detector 3H: 1000004ps (either photon 2 or 3, not sure which)
Detector 4V: 1000002ps (photon 4)

Add in a 100ps delay to the photon 2 path to make it distinguishable from photon 3:
Detector 1V: 1000000ps (photon 1)
Detector 2H: 1000003ps (either photon 2 or 3, not sure which)
Detector 3H: 1000104ps (this must be photon 2, which now makes the 2H detector click due to photon 3)
Detector 4V: 1000002ps (photon 4)

You can see that this should NOT identify different 2 & 3 pairs if the BSA is revealing pre-existing properties of those photons. The only difference is that 2 is easily identified. To put this in perspective: 4-fold coincidences similar to the above only occur every few seconds on the average. That would place the next occurrence perhaps 1000000000000+ ps later than my example. Not much chance to get confused about which clicks belong together.

Of course: if 2 & 3 are distinguishable, the rule is that there is no entanglement swap. So 1 & 4 are not entangled, and now demostrate Product State statistics which are clearly different than Entangled State statistics. But we postulated their polarizations were simply being revealed, and nothing occurring at the BSA changed anything. But actually: choosing to add a delay to the photon 2 path does change the 1 & 4 statistics, and that occurs both non-locally and without any causal direction in time. QED.

 

[PeterDonis]

The problem is that this terminology is used all the time.

Really? Everybody uses "local" to mean "microcausal"?

That certainly isn't true of Bell's original paper or the copious literature it has spawned; in that literature, "local" means what Bell defined in his original paper (that the joint probability function factorizes). That definition has nothing whatever to do with causality, or with QFT.

 

[vanhees71]

Ha, perhaps not obvious because of my poor description.

They can't be created by post-selection! Post-selection (as an explanation for what is occurring) implies that these 2 photons - 1 & 4 - are occasionally and randomly entangled (with each other); and then post-selection simply reveals that entanglement. That's a reasonable hypothesis, but here's why that is absolutely impossible.

So you say the cited paper by Zeilinger et al is fake? I don't believe that!

Again: Before the described selection by the (local) manipulations of photons 2&3 the photons 1&4 were not entangled because the initial state the four photons are prepared in are factorizing in the following way
$$|\Psi_{1234} \rangle = |\Psi_{12} \rangle \otimes |\Psi_{34} \rangle.$$
The two-photon states $|\Psi_{12} \rangle$ and $|\Psi_{34} \rangle$ are maximally entangled (Bell states) but the pair 1&4 are not. This state now describes and ensemble of equally prepared four photons, and this preparation is described by this state and nothing else.

Now if you do the described manipulations on photons 2&3, however, and select (or post-select, which doesn't matter at all) an subensemble, i.e., after choosing only those photon pairs 1&4, for which the pair 2&3 was found in one of the maximally entangled Bell states, then this subensemble of photon pairs 1&4 is described by a maximally entangled Bell state $|\Psi_{14} \rangle$.

The subensemble can be chosen whenever you like after the experiment is done and an appropriate measurement protocol is taken. The possibility of postselection due to entanglement is more explicit in the famous quantum-erasure experiments a la Wheeler, now realized several times with photons (e.g., Kim et al or Walborn et al).

 

[vanhees71]

Really? Everybody uses "local" to mean "microcausal"?

That certainly isn't true of Bell's original paper or the copious literature it has spawned; in that literature, "local" means what Bell defined in his original paper (that the joint probability function factorizes). That definition has nothing whatever to do with causality, or with QFT.

That's precisely what I mean. Bell talks about correlations and (in)separability, while in QFT locality has a different meaning, namely locality of interactions and thus microcausality. That's what's confusing, and that's why one has to read each paper in context. This confusion is why some people think Bell's non-locality would contradict the QFT-meaning of locality, but that's NOT the case!

The most accurate experiments are done with entangled-photon state, and if anything gets relativistic it's photons. The experiments are analyzed with standard QED, which is a microcausal QFT, and as long as there's no contradiction between experiment and QED I believe that relativistic QFT is consistent with both locality of interactions (microcausality and thus Einstein causality) and the fact that there are non-local correlations described by entanglement and inseparability.

What's not so clear to me is whether Bell was convinced that QT (no matter whether relativistic QFT or non-relativistic QM) is wrong and there's some local hidden-variable theory being right and QT being wrong or not. Before Aspect that could well have been possible, but after his experiments and the much more accurate ones possible since then, I think that's out of the question.

 

[PeterDonis]

in QFT locality has a different meaning, namely locality of interactions and thus microcausality

"Microcausality" in QFT means operators at spacelike separated events commute. That in itself does not mean the same thing as "locality of interactions". You could have as many nonlocal interactions as you like, as long as the outcomes of spacelike separated measurements do not depend on the order in which they are performed.

 

[vanhees71]

Then define what you mean by "locality of interactions". The very reason to use the constraint of microcausality in fact is to have local interactions only, i.e., you build the interaction Lagrangians as integrals over local operators obeying the microcausality contraint. This is at least sufficient for locality. I'm not sure whether it's also necessary, but the Standard model, including QED, is using the microcausality constraint anyway.

 

[PeterDonis]

Then define what you mean by "locality of interactions".

I didn't introduce the term so I feel no need to define it.

I already gave my definition of "locality": it's the one Bell used in his paper.

The very reason to use the constraint of microcausality in fact is to have local interactions only, i.e., you build the interaction Lagrangians as integrals over local operators obeying the microcausality contraint.

But those operators also have to obey a nonlocal constraint: they have to commute with other operators at spacelike separated events.

 

[vanhees71]

This is of course fulfilled either, because you build the local observables from quantum fields obeying bosonic or fermionic commutation or anticommutation relations, respectively. Then the observables built up from them are all obeying the microcausality constraints.

Again, the only point I want to make is that you have to clearly specify whether you mean locality in the sense of interactions/microcausality or in Bell's sense, where it means separability.

I really don't understand what you are after.

 

[DrChinese]

So you say the cited paper by Zeilinger et al is fake?

I don't get this, where do I say the paper I cited is fake? I realize that English may not be your first language, but this is a bit extreme.

Post selection identifies the 4-fold events to be analyzed. What I said is that the post selection process itself does NOT create the entanglement. Zeilinger says nothing different, and if he does, feel free to point that out.

And I again call for a narrative from ANY entanglement swapping experiment that describes the swapping action as you do. Specifically: your opinion that it is local and causal, nothing happening at the BSA that causes the swap.

Entanglement swapping IS due to the Bell state cast which non-locally affects photons 1 & 4 (changing Product state stats to Entangled state stats), and the entire process lacks any semblance of a causal direction. Ordering has no bearing on the outcomes.

 

[PeterDonis]

I really don't understand what you are after.

You were arguing with @DrChinese about whether QFT is "local". You were actually in violent agreement with him, because he was using "local" the way I am using it (Bell's definition), but you were using "local" to mean "microcausal", and both are true; QFT is microcausal, but it violates the Bell inequalities. If you had just left out the word "local", there would have been no argument.

 

[DrChinese]

1. Now if you do the described manipulations on photons 2&3, however, and select (or post-select, which doesn't matter at all) an subensemble, i.e., after choosing only those photon pairs 1&4, for which the pair 2&3 was found in one of the maximally entangled Bell states, then this subensemble of photon pairs 1&4 is described by a maximally entangled Bell state $|\Psi_{14} \rangle$.

2. The possibility of postselection due to entanglement is more explicit in the famous quantum-erasure experiments a la Wheeler, now realized several times with photons (e.g., Kim et al or Walborn et al).

1. There are no papers that say that 4-fold coincidences simply "reveal" entanglement properties of 1 & 4 that were pre-existing. They all say that decision to project them into a Bell state - or not - is what is responsible for 1 & 4 entanglement. The below quote from the cited paper is a good example that confirms my description and rejects yours:

"We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."

That is diametrically the opposite of what you describe, which is that 1 & 4 are correlated if 2 & 3 click a certain way. They aren't, the swap must occur for that to happen. Please note that the action is called "entanglement swapping" because photon 1's entangled partner changes from photon 2 to photon 4. Nowhere is the process of projection, casting, swapping referred to in terms that imply pre-existing relationships are being "revealed".

And if you can address my example F. in my post #57, that would be on target. Ditto for explaining why entanglement monogamy doesn't prevent 1 & 4 from being entangled while 1 & 2 are. I look forward to that.

2. Try referencing something a little more modern... and relevant. We are not discussing quantum erasers in this thread. We are discussing entanglement swapping using independent PDC sources.Again, please QUOTE a suitable citation for your position - or retract it. If you are correct, and this is standard QFT, such quotes must be everywhere. I would let this drop (since I know I won't change your opinion regardless of what I cite) but there are plenty of others who are following who are drawing a completely wrong picture of things because of what you are saying. People are drawn to local causality, but the whole point of entanglement swapping experiments is to show in the strongest of terms that position is not tenable in any form.

 

[akvadrako]

And if you can address my example F. in my post #57, that would be on target. Ditto for explaining why entanglement monogamy doesn't prevent 1 & 4 from being entangled while 1 & 2 are. I look forward to that.

This is also something I would like to know. At the very least, it should be possible for 1 to be entangled with 2, while (1&2) is entangled with (3&4), but that doesn't seem like this case. Maybe monogamy of entanglement is only about "known" entanglement; after all, having two qubits entangled along random directions isn't a useful resource.

People are drawn to local causality, but the whole point of entanglement swapping experiments is to show in the strongest of terms that position is not tenable in any form.

Regardless of the outcome of this discussion, this really hasn't been shown in a convincing manner. Some MWI and anti-realist proponents say QM has been shown to be locally causal. Not everyone agrees those proofs are convincing, but the opposite also hasn't been generally accepted either. If entanglement swapping provides a clear argument against local causality, it should be better explained.

 

[DrChinese]

1. This is also something I would like to know. At the very least, it should be possible for 1 to be entangled with 2, while (1&2) is entangled with (3&4), but that doesn't seem like this case. Maybe monogamy of entanglement is only about "known" entanglement; after all, having two qubits entangled along random directions isn't a useful resource.

2. Regardless of the outcome of this discussion, this really hasn't been shown in a convincing manner. Some MWI and anti-realist proponents say QM has been shown to be locally causal. Not everyone agrees those proofs are convincing, but the opposite also hasn't been generally accepted either.

1. No, absolutely not possible if 1 & 2 are maximally entangled (which they are when exiting the PDC crystal). You can entangle N number of quantum particles (no specific limit), but they will not be maximally entangled in that case. In fact, PDC occasionally produces 4 entangled photons - but again, no 2 are maximally entangled.

2. Post Bell, local realism has been roundly excluded along with most variations of same (depending on your particular exact definition, of course: local causality, local determinism). And yet many physicists are completely unaware of swapping, and how far the swapping experiments have come. There's no one that "needs" to be convinced, but what I am saying is a direct reflection of the mainstream. As a note: Because I am a Science Advisor, I try to label any non-standard opinion I hold as such. Of course, like vanhees71, I still think my personal opinions are correct too.

 

[microsansfil]

Then it won't be realized.

The document has been published at PHYSICAL REVIEW LETTERS

Here it is write :

To prove it, the researchers first used a laser to cause entanglement between a pair of photons, P1, P2. They then measured the polarization of P1, which was immediately followed by the entangling of another pair of photons, P3, P4. This was followed by measuring P2 and P3 simultaneously and causing them to become entangled with one another—a process known as projective measurement. Then, P4 was measured. Measuring P1 caused its demise of course—before P4 was born—but the measurement of P4 showed that it had become entangled with P1 nevertheless, if only for a very short period of time.

No one said anything?

/Patrick

 

[vanhees71]

I don't get this, where do I say the paper I cited is fake? I realize that English may not be your first language, but this is a bit extreme.

Post selection identifies the 4-fold events to be analyzed. What I said is that the post selection process itself does NOT create the entanglement. Zeilinger says nothing different, and if he does, feel free to point that out.

And I again call for a narrative from ANY entanglement swapping experiment that describes the swapping action as you do. Specifically: your opinion that it is local and causal, nothing happening at the BSA that causes the swap.

Entanglement swapping IS due to the Bell state cast which non-locally affects photons 1 & 4 (changing Product state stats to Entangled state stats), and the entire process lacks any semblance of a causal direction. Ordering has no bearing on the outcomes.

Maybe it's my lack of English that we are running in circles. First of all let me again stress that one cannot describe ANY entanglement-swapping experiment at once, but one has to concentrate carefully in any specific case. So let's discuss the experiment by Zeilinger again in detail, because that's what we are pondering for most of the time in this thread by now. You started with another one, where also time delays are involved, and we can analyze this too again. Also in this experiment there's nothing I can find contradicting my very standard minimal interpretation of local relativistic QFT point of view either (though I don't agree with some jargon in this paper indicating some "retrocausality argument" and at the same time stating this interpretation doesn't contradict standard relativistic QFT, which is for me a contradiction in itself).

So let's first concentrate again on the paper by Pan, Zeilinger et al, i.e.,

https://doi.org/10.1103/PhysRevLett.80.3891
Since it seems not to be available from free legal sources, I'll try to summarize it completely. In quotation marks I write literal quotes from the paper, which I may also comment to make my terminology clear again.

First of all let's quote the abstract:

"We experimentally entangle freely propagating particles that never physically interacted with one another or which have never been dynamically coupled by any other means. This demonstrates that quantum entanglement requires the entangled particles neither to come from a common source nor to have interacted in the past. In our experiment we take two pairs of polarization entangled photons and subject one photon from each pair to a Bell-state measurement. This results in projecting the other two outgoing photons into an entangled state."

Maybe my English is too bad, but for me it's clearly stated that at the end of some manipulations two "particles" (though the authors use photons, but that's usual jargon and not too critical) ARE (sic!) entangled though they have never interacted nor are from a common source.

Now let's describe the experiment in mathematically clear ways (taken also from the paper). The authors create two polarization entangled photon pairs in the following state
$$|\psi_{1234} \rangle = \frac{1}{2} (|H_1 V_2 \rangle-|V_1 H_2 \rangle) \otimes (|H_3 V_4 \rangle-|V_3 H_4 \rangle).$$
Note that here the labels 1...4 can be interpreted to indicate the momentum part of the state which translates by geometry to the places where the various interactions with optical elements like beam splitters, polarizers, and photo detectors etc.

Defining the complete CONS of Bell states of photon pairs (with momenta labeled by a,b)
$$|\phi_{ab}^{\pm} \rangle = \frac{1}{\sqrt{2}} (|H_a H_b \rangle \pm |V_a V_b \rangle),\\
|\psi_{ab}^{\pm} \rangle = \frac{1}{\sqrt{2}} (|H_a V_b \rangle \pm |V_a H_b \rangle),$$
there's a typo in the paper concerning Eq. (3) which should read
$$|\psi_{1234} \rangle = \frac{1}{2} (|\psi_{14}^+\rangle \otimes \psi_{23}^+ \rangle - |\psi_{14}^- \rangle \otimes |psi_{23}^- \rangle - |\phi_{14}^+ \rangle \otimes \phi_{23}^+ \rangle + |\phi_{14}^{-}\rangle \otimes |\phi_{23}^{-} \rangle). \qquad (3^{\text{corrected}})$$
This of course doesn't change anything concerning the outcome of the measurement, i.e., projecting the pair 2&3 to the Bell state $|\psi_{23}^- \rangle$ leads necessarily to a preparation of the pair 1&4. Note that this projection only acts on photons 2&3, i.e., the corresponding projection operator on the four-photon state is described by
$$\hat{P}_{\psi_23^-}= |\psi_{23}^- \rangle \langle \psi_{23}| \otimes \hat{1}_{14},$$
i.e. NOTHING (sic!) happens to the pair 1&4.
Applying this projector to the corrected Eq. (3) above we get
$$\frac{1}{2} |\psi_{23}^- \rangle \otimes \psi_{14}^- \rangle. \qquqad (\text{Projector})$$
This implies, by the way, that only 1/4 of the four photons are left in the ensemble after this SELECTION.

To verify that pair 1&4 in this partial ensemble is indeed in the expected entangled state the authors verify by doing the coincidence measurements on polarization states of the photons in the pair 1&4 and they precisely verify the expectation.

The authors emphasize all the very points I'm making, particularly that you have to measure coincently the four photons:

Concerning the measurement of the pair 2&3 enabling the wanted projection:

"One, therefore, has to guarantee good spatial and temporal overlap at
the beam splitter and, above all, one has to erase all kinds
of path information for photon 2 and for photon 3."

Then the authors describe how they achieved this goal (here and in the following I do not explain this in detail; if necessary, I can try to do also this, but it's all standard textbook stuff concerning standard optical elements like half-wave plates, polarizers, (coincidence) photo detectors).

Concerning the measurement on the pair 1&4 for state verification after the projection

"According to the entanglement swapping scheme, upon
projection of photons 2 and 3 into the $|\psi_{23}^- \rangle$ state, photons
1 and 4 should be projected into the $|\psi_{14}^- \rangle$ state. To
verify that this entangled state is obtained, we have to
analyze the polarization correlations between photons 1
and 4 conditioned on coincidences between the detectors
of the Bell-state analyzer."

and

Thus, indeed the authors state that by this procedure of coincidence measurments, i.e., the projection of the pair 2&3 to the said Bell state necessarily leads to entanglement of the pair 1&4 in the corresponding partial ensemble (which is the case in 1/4 of the cases, neglecting real-world inaccuracies of the equipment), and I agree with them. Note that the projection acts only on the photons in the pair 2&3 and NOT on those in the pair 1&4, as shown in Eq. (Projector). On pair 1&4 nothing at all is done in the analysis, as indicated by the unit operator in the second factor of the Kronecker product in Eq. (Projector), and this is so provided the locality of interactions is as described by standard QED based on the microcausality constraint, and thus the experiment indeed precisely verifies the predictions of QED (note that in the description above the authors as well as I never have used anything contradicting standard QED). Nowhere is a causal action at a distance which would be violating the very principles of relativity and also standard QED!

 

[vanhees71]

1. No, absolutely not possible if 1 & 2 are maximally entangled (which they are when exiting the PDC crystal). You can entangle N number of quantum particles (no specific limit), but they will not be maximally entangled in that case. In fact, PDC occasionally produces 4 entangled photons - but again, no 2 are maximally entangled.

2. Post Bell, local realism has been roundly excluded along with most variations of same (depending on your particular exact definition, of course: local causality, local determinism). And yet many physicists are completely unaware of swapping, and how far the swapping experiments have come. There's no one that "needs" to be convinced, but what I am saying is a direct reflection of the mainstream. As a note: Because I am a Science Advisor, I try to label any non-standard opinion I hold as such. Of course, like vanhees71, I still think my personal opinions are correct too.

Integerstingly, here I fully agree with @DrChinese ;-)). So now again it seems we share the same (pretty conservative!) view on the meaning of the QT (and particularly relativistic QFT) formalism.

Yes, and I claim as well that my point of view is the standard one. Maybe the discrepancies between my view and @DrChinese 's is also due to the fact that we are working in different communities. I don't know on what he is working. I'm in theoretical high-energy heavy-ion research, using equilibrium and non-equilibrium relativistic QFT. Quantum optics is only my hobby interest on another fascinating subject, and for me what quantum optics has shown over the recent years is confirming more and more the standard minimal interpretation of relativistic QFT. There's no need for additional interpretational elements like MWI (which cannot be checked anyway since all the parallel universes predicted are by construction unobservable), state collapse contradicting microcausality and locality of standard relativistic QFT, Bohmian mechanics (which is not convincingly generalized to standard relativistic QFT)...

 

[Mentz114]

1. No, absolutely not possible if 1 & 2 are maximally entangled (which they are when exiting the PDC crystal). You can entangle N number of quantum particles (no specific limit), but they will not be maximally entangled in that case. In fact, PDC occasionally produces 4 entangled photons - but again, no 2 are maximally entangled.

2. Post Bell, local realism has been roundly excluded along with most variations of same (depending on your particular exact definition, of course: local causality, local determinism). And yet many physicists are completely unaware of swapping, and how far the swapping experiments have come. There's no one that "needs" to be convinced, but what I am saying is a direct reflection of the mainstream. As a note: Because I am a Science Advisor, I try to label any non-standard opinion I hold as such. Of course, like vanhees71, I still think my personal opinions are correct too.

I have to say that the discussion between yourself and prof @vanhees71 is the most informative about EPRB ever !
I just want to clear up one point about the swapping experiment. You said or showed that adding a certain time delay to a path did not affect the statistics. Is this true of any delay that does not cause disentanglement ?
It seems to me that the one explanation for the outcomes is that between preparation and disentanglement everything happens at once . At the time of preparation the settings at A and B already exist. Nothing needs to communicate and no information goes backwards in time. This reminds me of Feynmans QED description.

 

[DrChinese]

1. First of all let me again stress that one cannot describe ANY entanglement-swapping experiment at once, but one has to concentrate carefully in any specific case. So let's discuss the experiment by Zeilinger again in detail, ...

2. Concerning the measurement on the pair 1&4 for state verification after the projection

"According to the entanglement swapping scheme, upon
projection of photons 2 and 3 into the $|\psi_{23}^- \rangle$ state, photons
1 and 4 should be projected into the $|\psi_{14}^- \rangle$ state. To
verify that this entangled state is obtained, we have to
analyze the polarization correlations between photons 1
and 4 conditioned on coincidences between the detectors
of the Bell-state analyzer."

and

View attachment 246043

Thus, indeed the authors state that by this procedure of coincidence measurments, i.e., the projection of the pair 2&3 to the said Bell state necessarily leads to entanglement of the pair 1&4 in the corresponding partial ensemble (which is the case in 1/4 of the cases, neglecting real-world inaccuracies of the equipment), and I agree with them. Note that the projection acts only on the photons in the pair 2&3 and NOT on those in the pair 1&4, as shown in Eq. (Projector).

3. On pair 1&4 nothing at all is done in the analysis, as indicated by the unit operator in the second factor of the Kronecker product in Eq. (Projector), and this is so provided the locality of interactions is as described by standard QED based on the microcausality constraint, and thus the experiment indeed precisely verifies the predictions of QED (note that in the description above the authors as well as I never have used anything contradicting standard QED).

4. Nowhere is a causal action at a distance which would be violating the very principles of relativity and also standard QED!

1. It makes it difficult for myself and readers to follow a paper behind a paywall, but I see that the paper I cited did not have the equation you presented. Here's an freely available similar one from Zeilinger et al which does:

Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping

2. Now, you failed to mention a key point of formula (3) in this reference: This does NOT describe the state prior to photons 2 & 3 arriving together at the beamsplitter. So your "conclusion" that "nothing changes" for 1 & 4 after selection is tainted by this omission. If entanglement swapping does not happen (for example 2 & 3 are not brought together), there is no entanglement between 1 & 4 (and that has nothing to do with post selection).

3. There is no microcausality constraint. And certainly none mentioned in any entanglement swapping paper. Again, you are not quoting the authors here, and this is one of the things I object to. Please don't put your words in their mouth. What the authors say in no way supports your position.

4. And now you are mangling my position as well: I don't assert there are causes which propagate FTL, although it is possible as Bohmian Mechanics is a viable interpretation. What I am saying is that the action narrative for entanglement swapping does not follow any clear causal description, precisely because the detection ordering is not relevant, and because the detectors are spacelike separated. I don't know any more than anyone else what is occurring under the quantum covers.

------------------

I notice you keep ignoring key points I am making:
a) Entanglement monogamy prevents photon 1 from being entangled with both 2 and 4 as you claim. It's one or the other, and I will challenge you to provide a reference to the contrary. That alone makes your description not viable.
b) My counter-example F from post #57. As mentioned previously, this counter-example is not theoretical: it is done as part of the tuning process for every entanglement swapping experiment. It must be performed, as this is how the 2 & 3 streams are calibrated so the the swap is enabled. It starts off with a timing difference and no swaps. As calibration improves, swaps occur and that continues until an optimal performance level is achieved. They simply don't publish those results because it is a null result (because 1 & 4 won't be entangled because no swap occurred).

 

[DrChinese]

1. I have to say that the discussion between yourself and prof @vanhees71 is the most informative about EPRB ever !

2. I just want to clear up one point about the swapping experiment. You said or showed that adding a certain time delay to a path did not affect the statistics. Is this true of any delay that does not cause disentanglement ?

3. It seems to me that the one explanation for the outcomes is that between preparation and disentanglement everything happens at once . At the time of preparation the settings at A and B already exist. Nothing needs to communicate and no information goes backwards in time. This reminds me of Feynmans QED description.

1. Yay!

2. Adding delay to change the ordering (sequence) does not change the statistics. The following can occur in any order:

a. Detection of photon 1.
b. Detection of photon 4.
c. Projection of the photons 2 & 3 into a Bell state via co-arrival at the beam splitter.
d. Creation of photons 1 & 2 (must precede a. and c. though).
e. Creation of photons 3 & 4 (must precede b. and c. though).

3. I don't know if it makes sense to refer to "everything happening at once" in a normal temporal sense. Precisely because there is no required order other than that photons must be created before they are detected, and photons 2 & 3 must be created prior to projection.

My "narrative" to describe entanglement swapping is as follows:

When photons 1 & 2 are created, they form an entangled system "X" which grows to have spatio-temporal extent. When photons 3 & 4 are created, they too form an entangled system "Y" which grows to have spatio-temporal extent. As elements of quantum systems X and Y intersect at the beam splitter, they split into 2 new systems that are likewise entangled, but consisting of different pairing of the photons. After the *beamsplitter* portion of the BSA, ALL 4 PHOTONS ARE STILL ENTANGLED: 1 & 4, and 2 & 3. And in some experimental versions, the 2 & 3 pair is in the singlet state and therefore otherwise has the same characteristics as the 1 & 4 pair. Both sets now exhibit perfect correlations.

a. What can't be described in this narrative is the nature of how systems with spatio-temporal extent "collapse", if indeed there is something that can be called collapse. Because of Bell: this implies that "something" changes non-locally, and it certainly appears that it is NOT the revealing of quantum properties that had preexisting values. Because entangled particles lack well-defined preexisting values until observation (again per Bell, and this particular characteristic appears one way or another in all interpretations).

b. When can it be said that 1 & 4 become entangled? They need not ever have been in causal contact, don't need to exist at the same time, don't need to even exist when they became entangled. And because of entanglement monogamy, they cannot remain entangled (as they were previously) with their birth twins.

c. Returning to the OP: special relativity does NOT in any way figure in, constrain, or otherwise involve itself in the quantum description. In fact, SR can be even considered time symmetric (just to add to the confusion).

 

[Lord Jestocost]

One should always keep in mind that “the Bell theorem furnishes a criterion to experimentally exclude the hypothesis that quantum correlations are established at the source (that is, to rule out an alternative description of quantum phenomena based on local variables).”

Valerio Scarani in “Quantum Physics: A First Encounter: Interference, Entanglement, and Reality”

 

[GlebKit]

Good day.
I have a question about using for nonlocal connection not individual entanglement particles but common beam.
The main approach is depicted at following figure:

Can we transmitt an information by means of distruction two photons entanglement in beams?
If we destroy entanglement (measure the polarization) before beam reaching the two slit wall then we will detect two peaks under the slits. Otherwise we will see an interference picture.

 

[vanhees71]

1. It makes it difficult for myself and readers to follow a paper behind a paywall, but I see that the paper I cited did not have the equation you presented. Here's an freely available similar one from Zeilinger et al which does:

Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping

2. Now, you failed to mention a key point of formula (3) in this reference: This does NOT describe the state prior to photons 2 & 3 arriving together at the beamsplitter. So your "conclusion" that "nothing changes" for 1 & 4 after selection is tainted by this omission. If entanglement swapping does not happen (for example 2 & 3 are not brought together), there is no entanglement between 1 & 4 (and that has nothing to do with post selection).

3. There is no microcausality constraint. And certainly none mentioned in any entanglement swapping paper. Again, you are not quoting the authors here, and this is one of the things I object to. Please don't put your words in their mouth. What the authors say in no way supports your position.

4. And now you are mangling my position as well: I don't assert there are causes which propagate FTL, although it is possible as Bohmian Mechanics is a viable interpretation. What I am saying is that the action narrative for entanglement swapping does not follow any clear causal description, precisely because the detection ordering is not relevant, and because the detectors are spacelike separated. I don't know any more than anyone else what is occurring under the quantum covers.

------------------

I notice you keep ignoring key points I am making:
a) Entanglement monogamy prevents photon 1 from being entangled with both 2 and 4 as you claim. It's one or the other, and I will challenge you to provide a reference to the contrary. That alone makes your description not viable.
b) My counter-example F from post #57. As mentioned previously, this counter-example is not theoretical: it is done as part of the tuning process for every entanglement swapping experiment. It must be performed, as this is how the 2 & 3 streams are calibrated so the the swap is enabled. It starts off with a timing difference and no swaps. As calibration improves, swaps occur and that continues until an optimal performance level is achieved. They simply don't publish those results because it is a null result (because 1 & 4 won't be entangled because no swap occurred).

Ok, let's discuss this paper (I use the PRL version however, since I hate revtex without the tightenlines switch envoked, but I guess it's identical with the arXiv version).

ad 2) The for our discussion crucial point is that, as the authors correctly state, (3) IS the prepared state of the four photons BEFORE any projections are done, and this time the authors got the signs right too. It's a bit of work to write it out, but indeed (3) is exactly the same vector as (1), it's just decomposed with respect to different bases.

I don't claim that nothing happens, but I claim that the projection accoring to A's finding of the pair 1&2 (note that now the photons are labelled differently from the paper we discussed before; instead of 1234 they now count 0123, everything else is identical) in one of the 4 maximally entangled (Bell) states, you get subensembles of the correspondingly entangled photon pair 0&3, though these two photons have not been entangled before nor have ever directly interacted with each other. The Bell-state measurement by A is local and doesn't causally influence photons 0&3, but due to the entanglement of the pairs 0&1 and 2&3 in the originally prepared 4-photon state each partial ensemble of the photon pair 0&3 is entangled due to the selection depending on the measurement outcome of A. Of course, all that has to be done is indeed to provide a measurement protocol to Victor with all the coincidence measurements properly, and you can sort the corresponding events into the four classes each showing the entanglement in each of the corresponding Bell states of the pair 0&3.

ad 3) Microcausality is a theoretical constraint on relativistic QFTs, and all in the paper is consistent with standard QED. That's why there's no contradiction between the experimental findings and microcausality.

ad 4) Good. Then at least in this point we agree. There's no FTL propagation, and this newer paper even underlines this again with the variant, where the choice of the state of Bob's photon pair 0&3 through Alice's Bell measurement on photons 1&2 is done after Bob has measured his photons.

Then I don't understand what you are saying in point a). By the preparation 0&1 are entangled as well as 2&3 but not 0&2 and 1&3. The whole point of the paper is that through the (post-)selection via A's measurements the pair 0&3 are entangled in the same state at which Alice found her pair 1&2. They even proved entanglement of photons 0&3 in $|\psi_{03}^- \rangle$ for the partial ensemble, for which Alice found her photons 1&2 in the state $|\psi_{12}^-\rangle$.

I think I answered also b) with this. Note that I refer now to the labelling of the photon states according to the new paper, discussed in this posting, while you of course referred to the before discussed older paper.

The important point of the minimal interpretation is that the quantum state describes statistical properties of ensembles and that of course in the full ensemble of four photons 0123 only 0&1 and 2&3 are entangled. For the subensemble, where Alice found photons 1&2 in the state $|\psi_{12}^- \rangle$ the photons 0&3 are in the maximally entangled Bell state $|\psi_{03}^- \rangle$ either. That's the whole point of this great experiment, and that's what's called entanglement swapping and is a strong form of teleportation either as the authors stress in their paper too.

 

[Lord Jestocost]

The important point of the minimal interpretation is that the quantum state describes statistical properties of ensembles...

Allow me a comment on the side, in Abner Shimony’s words (in “Symposia on the Foundations of Modern Physics 1992 - The Copenhagen Interpretation and Wolfgang Pauli” (edited by K. V. Laurikainen and C. Montonen))

“There is, for example, Ballentine, whom I mentioned yesterday. He says: ‘I am not a hidden variable theorist, I am only saying that quantum mechanics applies not to individual systems but to ensembles.’ I didn't put this down separately because I simply do not understand that position. Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables. So I fail to see how one can have Ballentine's interpretation consistently. That is, one can always stop talking and not answer questions, but that is not the way to have a coherent formulation of a point of view. But to carry out the coherent formulation of a point of view, as I think Einstein had in mind, you certainly have to supplement the quantum description with some hypothetical extra variables.”

 

[vanhees71]

The members of the ensemble in the described experiment are easily differentiated simply by the time of the registration of the four photons for each prepared four-photon state. It's not about stopping talking (we talk a lot in fact ;-)), but it's the interpretation which just boils it down to what's described and what's observed (at least in experiments like the one we discuss here). I don't understand what "hypothetical extra variables" one "certainly has to supplement the quantum description with". Maybe at Einstein's time you might have the idea that QT is incomplete because of the inseparability and Einstein's quibbles with this implication of the QT formalism, but today where we are 84 years further in investigating it, it seems as if there's nothing of this kind to add since Q(F)T describes all observations accurately, including the one we are discussing here and which is a great example for the fact that the inseparability/entanglement is what's the case in nature. Einstein's gut feeling about the quibbles were put into a clearly observable prediction of an entire class of local deterministic hidden-variable theories by Bell, and then starting with Aspect's experiment and with many more until today, including the one we discuss here, clearly show that Q(F)T is the correct description. You may like it or not, it's a fact of nature revealed by hard work of many physicists, theorticians and experimentalists alike, and one has to accept it as a fact.

Whether there is some more comprehensive theory than Q(F)T, I don't know. From the here discussed kinds of experiments, I don't see the need for any such thing, but who knows, what a hopefully some day found solution of the puzzle of quantum gravity may come up with?

 

[DrChinese]

Good day.
I have a question about using for nonlocal connection not individual entanglement particles but common beam.
The main approach is depicted at following figure:
View attachment 246141

Can we transmitt an information by means of distruction two photons entanglement in beams?
If we destroy entanglement (measure the polarization) before beam reaching the two slit wall then we will detect two peaks under the slits. Otherwise we will see an interference picture.

You might be surprised to learn that entangled photons do NOT produce interference as one might otherwise expect. You must stop the entanglement first. Once you do that, the ability to carry out the rest of your idea is lost. See Figure 2 in this great summary paper by Zeilinger:

https://pdfs.semanticscholar.org/3644/6f15507880c629e06391adf9d21aa6d76015.pdf

 

[DrChinese]

2) The for our discussion crucial point is that, as the authors correctly state, (3) IS the prepared state of the four photons BEFORE any projections are done, and this time the authors got the signs right too. It's a bit of work to write it out, but indeed (3) is exactly the same vector as (1), it's just decomposed with respect to different bases. 1.
...

ad 3) Microcausality is a theoretical constraint on relativistic QFTs, and all in the paper is consistent with standard QED. ...

ad 4) Good. Then at least in this point we agree. There's no FTL propagation, and this newer paper even underlines this again with the variant, where the choice of the state of Bob's photon pair 0&3 through Alice's Bell measurement on photons 1&2 is done after Bob has measured his photons.

Then I don't understand what you are saying in point a). By the preparation 0&1 are entangled as well as 2&3 but not 0&2 and 1&3. The whole point of the paper is that through the (post-)selection via A's measurements the pair 0&3 are entangled in the same state at which Alice found her pair 1&2. They even proved entanglement of photons 0&3 in $|\psi_{03}^- \rangle$ for the partial ensemble, for which Alice found her photons 1&2 in the state $|\psi_{12}^-\rangle$.

I notice you keep ignoring key points I am making:
a) Entanglement monogamy prevents photon 1 from being entangled with both 2 and 4 as you claim. It's one or the other, and I will challenge you to provide a reference to the contrary. That alone makes your description not viable.
b) My counter-example F from post #57. As mentioned previously, this counter-example is not theoretical: it is done as part of the tuning process for every entanglement swapping experiment. It must be performed, as this is how the 2 & 3 streams are calibrated so the the swap is enabled. It starts off with a timing difference and no swaps. As calibration improves, swaps occur and that continues until an optimal performance level is achieved. They simply don't publish those results because it is a null result (because 1 & 4 won't be entangled because no swap occurred).

2. This is incorrect, and does not express what you claim. It assumes a swap occurs (i.e. 2 of the photons are indistinguishable). If no swap occurs, then the 0 and 3 photons (numbered per this paper) are NOT entangled on any basis (and in this form, they are entangled on one basis). The authors say the following in their conclusion (and notice how I quote the authors to support my statement):

"Thus depending on Alice’s later measurement [or choice not to measure], Bob’s earlier results either indicate that photons 0 and 3 were entangled or photons 0 and 1 and photons 2 and 3. This means that the physical interpretation of his results depends on Alice’s later decision."

3. You keep quoting yourself. Microcausality is not a restriction on QFT. There are considerations for special relativity, of course. But as I keep repeating, quantum mechanics post-Bell is NOT local causal, and this is beyond contention. There is nothing different in QFT, and I challenge you for the nth time to produce a suitable quote from someone else that supports your position regarding causality in QFT.

4. We don't agree on this! I say there are no FTL causes because there is no causality! There is no causal direction for anything in these experiments. And if there are, then it is FTL (which is viable in some interpretations). Either way, we don't agree.

 

[vanhees71]

I'm not ignoring the points you are making, but I just quote the results of the very paper (PRL 88, 017903, 2002) you discuss to contradict you. Maybe I do not understand what you want to say. I try one last time:

ad a) The full ensemble of photons is described by the state in Eq. (2) which is indeed exactly the same as Eq. (3) is prepared such (as can be read off immediately in the form of Eq. (2)) that the photon pair 0&1 and the photon pair 2&3 are entangled, while neither the pair 0&2 nor the pair 1&3 are entangled (that's the meaning of a product state vs. a superposition of product states), and the entanglement for the pairs 0&1 and 2&3 is maximal, i.e., you have a Bell state. Now Alice projects the pair of photons 1&2 to the state $|\psi_{12}^{-} \rangle$. As you can immediately read off of the state written in the form of Eq. (3) the photons 0&3 of this particularly partial ensemble (on average 1/4 of all measured four-photon states) are entangled, i.e., described by the state $|psi_{03}^- \rangle$. That's precisely what the authors have demonstrated, and that's entanglement swapping and a particular nice example for quantum teleportation. The authors demonstrate that the pair 0&3 of the partial ensemble is really entangled even by proving the violation of the Bell inequality. They also demonstrate that there's no causal effect of Alice's measurement process on the pair 0&3 since the pairs 0&3 can be post-selected through A's measurement, i.e., A can do her measurement after the pair 0&3 is measured with the same result. As the authors also emphasize, all that's needed is a complete measurment protocol on an event-by-event basis, i.e., only Victor can choose the partial ensemble based on A's mesurement.

ad b) now you jump again to the other paper, but there's nothing different (only the labelling of the photons with 1234 rather than 0123). Thus b) is answered with a), and it's not answered by me but by the authors and the outcome of their real-lab experiment!

2) what do you mean by "the swap occurs"? As already expolained under a): You deny the very result of the paper! Based on Alice measurement Victor is able to choose the partial ensemble, for which photons 0&3 are entangled, and that's what the authors have shown experimentally and that's the whole purpose of this experiment, and that's what's called entanglement swapping and teleportation. I don't understand why you deny the main intention and conclusion of the very paper you yourself have chosen to discuss here.

3) Come on! Read any decent textbook on standard QED. There microcauality is in the very construction of the theory: You start with field operators which transform locally under the Poincare group as their classical analogues, and then you write down a Poincare invariant action with a Lagrangian consisting of a sum over local field monomials and this guarantees by construction the microcausality condition, i.e., if you have a local observable $\hat{O}(x)$, then it commutes with the Hamilton density $\hat{\mathcal{H}}(y)$ at space-like separation
$$[\hat{O}(x),\hat{\mathcal{H}}(y)]=0 \quad \text{if} \quad (x-y)^2=(x^0-y_0)^2-(\vec{x}-\vec{y})^2<0.$$
This ensures that there are no spooky actions at a distance and formally that the time ordering in the Dyson series of perturbation theory is frame-independent and thus leads to Poincare-invariant S-matrix elements. It's a very fundamental property of all successful relativistic QFTs (including the Standard Model) and it's taught almost in the first lecture of the introductory QFT lecture worldwide!

4) Ok, since you don't understand the meaning of fundamental mathematical facts of QFT, as the microcausality principle, it's cear that you are not able to understand my argument either. Everything of the experiment is in perfect agreement with the predictions of QED. The whole experimental setup is based on QED and confirms it. For sure there are no spooky actions at a distance, and everything is about correlations described by the state given in Eq. (2), which is the same as given in Eq. (3), of the paper.

 

[DrChinese]

1. I'm not ignoring the points you are making, but I just quote the results of the very paper (PRL 88, 017903, 2002) you discuss to contradict you. Maybe I do not understand what you want to say. I try one last time:

2. ad a) The full ensemble of photons is described by the state in Eq. (2) which is indeed exactly the same as Eq. (3) is prepared such (as can be read off immediately in the form of Eq. (2)) that the photon pair 0&1 and the photon pair 2&3 are entangled, while neither the pair 0&2 nor the pair 1&3 are entangled (that's the meaning of a product state vs. a superposition of product states), and the entanglement for the pairs 0&1 and 2&3 is maximal, i.e., you have a Bell state.

1. Referencing an entire paper - one that doesn't say anything like what your position is - well, that's not responsive. Every entanglement swap paper says something like one of the two statements below:

a. Your position: post selection identifies a state which already existed and was simply revealed, nothing changed in the state for photons 0 & 3.
b. My position: the swap changes the states of the 2 separate systems (pair 0 & 1 and pair 2 & 3) such that photons 0 & 3 (previously uncorrelated) are entangled. That change to the state of 0 & 3 is nonlocal.

To help clarify which of above matches standard science:

https://arxiv.org/pdf/0809.3991.pdf"We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons [0 & 3]. Violation of a CHSH inequality is not only of fundamental interest because it rules out local-hidden variable theories. It also proves that the swapped states are strongly entangled and, as a result, distillable [40]. The specific state of photons 1 and 4 after entanglement swapping depends on the result of the BSM, which can either be ψ + or ψ −."

https://arxiv.org/pdf/quant-ph/0201134.pdf"Initially, the system is composed of two independent entangled states... Alice subjects photons 1 and 2 to a measurement in a Bell-state analyzer (BSA), and if she finds them in the state |Ψ−>12, then photons 0 and 3 measured by Bob, will be in the entangled state |Ψ−>03. If Alice observes any of the other Bell-states for photons 1 and 2, photons 0 and 3 will also be perfectly entangled correspondingly. We stress that photons 0 and 3 will be perfectly entangled for any result of the BSA... [after the swap].

None of the above, or anything else in these papers, remotely supports your characterization.2. Your narrative omits the key point that photons 0 & 3 are not entangled before the swap. I agree with your statements that 0 & 1 and 2 & 3 are entangled before the swap, and that 0 & 2 and 1 & 3 are not entangled before the swap. This is the correct state BEFORE the swap:

a. Before swap:
|Ψtotal> =
|Ψ −>01 ⊗ |Ψ −>23 =
1/2 [ |H0V1> |H2V3> + |V0H1> |H2V3> + |H0V1> |V2H3> + |V0H1> |V2H3>
[none of which terms can be recombined into any state where photons 0 & 3 are in an entangled state]

Where we agree that the state after the swap is as you describe.

b. After swap:
|Ψtotal> = 1/2 [|Ψ+>03|Ψ+>12 − |Ψ−>i03|Ψ−>12 − |Φ+>03|Φ+>12 + |Φ−>03|Φ−>12].

You need to be able to make photons 1 and 2 indistinguishable before you can move to state b. If they are distinguishable, they remain in state a. That's the whole point, that the state of 0 & 3 change as a result of the swap. And the statistical results change too!

The change (resulting from the swap action) to photons 0 & 3 is quantum nonlocal, and is not subject to a microcausality constraint. First, there is the demonstrated quantum nonlocality ruining the locality principle here. And second, the ordering of events prevents a discrete "cause" and a discrete "effect" from being identified. Which then ruins any notion of causality. Local causality (which should already have been thrown out post-Bell) is easily disproven with this experiment, and again, that is the [paradoxical] point. Photons from independent sources can be entangled by a remote action, and that action can occur before or after the detection of those photons.

Of course, all of this is standard QM/QFT. Relativity does not factor in other than everyone agrees there is no possibility of sending a message FTL. However, the relevance to quantum computing is that you can clone a quantum state FTL. This is a demonstration of spooky action at a distance. (Which is exactly the opposite of your position: that it is forbidden by construction.)

 

[vanhees71]

I think it's impossible to discuss this with you. You are simply not reading carefully what I'm writing and sometimes claim the opposite what I said!

What you claim to be my statement a) I've never said. I say:

The total ensemble is described by the state ket given in Eq. (2) by the authors (of course, I don't contradict the authors, because I want to discuss their paper and not something else). The state ket in Eq. (3) is exactly the same (also what the authors say). The pairs 0&1 and 2&3 are entangled but not 1&2 and 0&3 (that's what (2) directly implies).

I cannot read your formlae. So here are the facts from the paper, written out in LaTeX again:
$$|\psi_-^{12} \rangle \otimes |\psi_{03}^- \rangle.$$
For the following we need this in the form written as Eq. (3) by the authors:
$$|\Psi \rangle=\frac{1}{2} (|\psi_{03}^+ \rangle \otimes |\psi_{12}^+ \rangle - |\psi_{03}^- \rangle \otimes |\psi_{12}^- \rangle -\frac{1}{2} (|\phi_{03}^- \rangle \otimes |\phi_{12}^+ \rangle + |\phi_{03}^- \rangle \otimes |\phi_{12}^- \rangle).$$
Let me stress again this is mathematically identical and thus both formulae describe precisely the same state the four photons are prepared in before any measurement by Alice and/or Bob is made and no choice of an subensemble is made either. That comes now:

With the so prepared four-photon state Alice performs a Bell measurement on Photons 1&2, i.e., she chooses a partial ensemble by filtering out all findings except when she finds photons 1&2 to be in the Bell state $|\psi_{12}^{-} \rangle$ which is chosen for technical reasons: It's the one which is most simple to detect.

This is explained in the paper too, to understand this one must remember that the notation of the states above is a bit sloppy to simplify the explanation; in fact to understand how Alice filters out the specific entangled state of the pair 1&2, one has to take into account here that the photons are indistinguishable bosons and that thus $|\psi_{12}^{-}$ is the state where the spatial (momentum) part of the photon states is anti-symmetric and thus also the polarization part must be antisymmetric, and thus it's the very one of the four possible Bell states state, where at the beam splitter you have coincident detections in the detectors D1 and D2 at Alice's site, as drawn in Fig. 2 of the paper). To be clear, the correct notation for the states are rather like this (using photon creation and annihilation operators and the vacuum state $\Omega \rangle$):
$$|\psi_{12}^- \rangle = \frac{1}{2} (\hat{a}_{1H}^{\dagger} \hat{a}_{2V}^{\dagger} - \hat{a}_{1V}^{\dagger} \hat{a}_{2H}^{\dagger}.$$
Anyway, it's clear that whenever Alice has a coincident click at both detectors D1 and D2 her photons are in the state $|\psi_{12}^- \rangle$ and thus due to the state preparation of the four-photon state, the corresponding partial ensemble must be described by the corresponding component:
$$|\Psi_' \rangle=- |\psi_{03}^- \rangle \otimes |\psi_{12}^- \rangle.$$
This clearly tells you that for this partial ensemble the photon pair 03 is maximally entangled and described by the state $|\psi_{03}^- \rangle$. Alice will have such coincident clicks of her detectors D1 and D2 with probability
$$|\langle \Psi'|\Psi \rangle|^2=1/4.$$
The entanglement of photons 0&3 for this partial ensemble is clearly demonstrated by this experiment. The experimentalists even verified the violation of Bell's inequality which is a clear indication for entanglement.

That it cannot be Alices measurement/manipulations of photons 1&2 that causes the pair 0&3 being entangled when the above described subensemble is chosen, is also proven in the experiment: When A's photons are delayed such that the mesurements on the pair 0&3 are already finished and fixed when A is doing here measurement, precisely the entanglement of the pair 0&3 is still observed for this partial ensemble. The interaction of each photon with optical devices is local (according to QFT in the specific sense implemented by microcausality). What's nonlocal in a specific quantum sense is the correlation of the entangled pairs (0&1 as well as 2&3 for the initial total ensemble at the beginning of the experiment and 1&2 and 0&3 in the selected partial ensemble at the end of the experiment) described by entanglement. Nothing is contradicting standard QFT, nothing is faster-than-light action at a distance, and nothing violates causality in any way. The teleportation or entanglement swapping also cannot achieve faster-than-light communication, because to choose the partial ensemble you have to communicate about the measurement outcome about Alice's photon pair 1&2 before Bob can know that his photons 0&3 are in fact entangled, i.e., in the state $|\psi_{03}^- \rangle$ after choosing to consider only the pairs of that specific partial ensemble, where Alice had coincident clicks of her detectors D1 and D2 and thus has ensured that her photon pair 1&2 is in the state $|\psi_{12}^{-} \rangle$.

So indeed by (post-)selecting the states as described the two photons 0&3 are to be described by the entangled state $|\psi_{03}^- \rangle$ though they never have been interacted or where in any "causal contact" with each other.

As you also see, I always even stress that the photons 0&3 have not been entangled before selecting the partial ensemble. That's indeed the key point of the entire paper, successfully aiming at entanglement swapping/teleportation of entangled states.

Last but not least there's no way to clone a quantum state. That's also true in the experiment here: The subensemble choosen by A is described by $|\Psi' \rangle$. This clearly shows that in this subensemble the pairs 0&1 and 2&3 are NOT entangled at all. So by the very measurement enable entanglement swapping you destroy the original entanglement of these pairs 0&1 and 2&3. The correct term is not cloning but teleportation, as it is written in the paper. That's no surprise since Zeilinger and his group was indeed the first who demonstrated teleportation (in a somewhat simpler experiment) in the 1990ies. I'm sure you find the papers cited in his APS centennial RMP contribution you quoted above.

 

[DrChinese]

1. I think it's impossible to discuss this with you. ...

2. ... nothing is faster-than-light action at a distance, and nothing violates causality in any way. ...

3. Last but not least there's no way to clone a quantum state. ...

1. Yes, and we may as well stop now as we are talking past each other. You have yet to cite a statement matching any of your [wrong] statements other than quoting yourself:

- Swapping does not change the state of photons 0 & 3 from uncorrelated to entangled. [incorrect]
- QM/QFT is causal. [incorrect]
- The authors agree with you and not with me. [incorrect]
etc.

2. This is exactly opposite of every swapping paper. There is no causal direction, and the action is quantum nonlocal.

3. What is "cloned" is a superposition. Particle 3 will now contain more information about 0 (which it never interacted with) than any preparation could otherwise do (unless it's entangled).

-------------

I have already quoted chapter and verse over and over again from the cited papers, and explained that actual experiments verify everything I said (per my post #57, 6F example) that clearly proves that swapping changes the statistical outcomes. I have nothing left to add on the matter, and will not respond further. So I will simply say "cheers" and move on.

 

[akvadrako]

1. No, absolutely not possible if 1 & 2 are maximally entangled (which they are when exiting the PDC crystal). You can entangle N number of quantum particles (no specific limit), but they will not be maximally entangled in that case. In fact, PDC occasionally produces 4 entangled photons - but again, no 2 are maximally entangled.

I think part of the confusion comes from the way the word entanglement is used. Saying 1&4 are entangled seems to imply that it's some objective property of qubits 1&4, but it's only a property of the observer's view of 1&4. Before measuring 2&3, he doesn't know how to see 1&4 as entangled, so he says "they are not entangled". After measuring he does, so he says they are. Then if he throws away that information he gained, they "become unentangled" again. Nothing about 1&4 is changing, just his perspective.

To empathise the point, If another observer $(O_B)$ is casually disconnected from the 2&3 measuring observer $(O_A)$, then 1&4 will never be entangled according to $O_B$. Nothing $O_A$ can do will change that.

So entanglement is really about "known" or "knowable" correlations and the monogamy principle says that it's impossible to simultaneously see 1&2 and 1&4 as fully entangled – no view is compatible with both.

2. Post Bell, local realism has been roundly excluded along with most variations of same (depending on your particular exact definition, of course: local causality, local determinism).

It's possible to show step by step how Bell inequalities can be violated with local operations if you invoke many worlds. His theorem assumes single outcomes – that's why it doesn't apply. The interesting question about this experiment is if the entanglement swapping (not the CHSH test) can be explained locally within a single world.

 

[Tendex]

2. ... nothing is faster-than-light action at a distance, and nothing violates causality in any way. ...

- QM/QFT is causal. [incorrect]2. This is exactly opposite of every swapping paper. There is no causal direction, and the action is quantum nonlocal.

As interesting as this discussion is I think (like an earlier poster) that it would benefit from some terminology clarification as it seems to me that the terms "microcausality" and "local causality" are still being interpreted differently by vanhees71 and DrChinese and for different aspects in both QFT and the experiments .

In fact there is one important additional subtlety in QFT with respect to Bell's mathematization of locality and causality, that is given by the use of the indefinite signature to discern different types of intervals, while in Bell's setting this distinction about which type of intervals should the nonlocality be attributed to gets lost.
And so in QFT microcausality is as much a nonlocal condition(on spacelike-separated operators) as can be interpreted as a local causal condition for timelike ones(time-ordered products) without contradiction wheras in Bell's formulation not having this distinction,

 

[Tendex]

Continued) there is no way to have both quantum nonlocality and causal locality without contradiction, mathematically nonlocality must violate Bell's inequalities based on causal locality.

 

[DrChinese]

1. Nothing about 1&4 is changing... the monogamy principle says that it's impossible to simultaneously see 1&2 and 1&4 as fully entangled – no view is compatible with both.

2. It's possible to show step by step how Bell inequalities can be violated with local operations if you invoke many worlds.

1. Logically, monogamy should convince you that a physical change to the state of 1 & 4 must occur along with the swap. The statistics change depending on whether the system of 1 & 2 is allowed to interact with the system of 3 & 4. If they interact, then 1 & 4 well definitely become entangled as one of the four possible Bell states.

2. I have no disagreement with MWI or any other generally accepted interpretation. (I realize that MWI claims to be local, but it would be difficult to refer to it as causal in any meaningful manner.)

 

[PeterDonis]

Microcausality is not a restriction on QFT.

I'm not sure what you mean by this. The fact that quantum field operators at spacelike separated events have to commute, which is what "microcausality" is being used to mean in this discussion, most certainly is a "restriction" on QFT, since QFT satisfies it.

The change (resulting from the swap action) to photons 0 & 3 is quantum nonlocal, and is not subject to a microcausality constraint.

Are the events in question spacelike separated? If so, they have to commute--what happens at them cannot depend on the order in which they happen. And that is a microcausality constraint--see above.

Relativity does not factor in other than everyone agrees there is no possibility of sending a message FTL.

Why is this true? It's because spacelike separated measurements commute. So microcausality is a factor.

QM/QFT is causal. [incorrect]

I think you need to clarify what you mean by "causal". See above.

 

[DrChinese]

1. I think you need to clarify what you mean by "causal". See above.

2. I'm not sure what you mean by this. The fact that quantum field operators at spacelike separated events have to commute, which is what "microcausality" is being used to mean in this discussion, most certainly is a "restriction" on QFT, since QFT satisfies it.

1. vanhees71 earlier (#38*) specified that "microcausal" was a normal use of the word as it applies to commuting of spacelike operators, same as you. But he then switches usage of the word "causal" in a different context. If there is a causal constraint, where A causes B, then A must precede B. In an entanglement swapping experiment, there is no clear causal direction but: A still causes B. The swap (which creates a new entangled pair - let's call that A) can occur before *or* after the entangled pair is detected (let's call that B). Ergo, there is no causal direction, and there is no description of this that contains causality as the word is normally used. That being: Cause A must precede effect B. Causality fails (if locality holds).

2. Now, if you say that "microcausal" in QFT means spacelike operators commute: well that would also mean that the order of results does *not* matter. Certainly not an issue in a swapping experiment, where the order of events does not matter (the only requirement is that the swap requires all 4 particles to be previously created). But he did not restrict his usage in that manner. He extended it to mean: local microcausality. And he further extends the meaning to say there is only quantum local action occurring. That extension is not a deduction from microcausality, and I'd again challenge anyone to provide a quote that says: QFT requires both that a) all causes must precede the effect, and b) also denies the existence of quantum nonlocal action such as swapping entails.

With entanglement swapping: There is a physical state change (if the remote systems interact), it is not quantum local, and the order of events is not relevant. Virtually every entanglement swapping paper more or less says this exact thing somewhere in the text. So it is not me that is mangling the use of the word "causality". I think I have been pretty clear in every post to indicate that I am referring to a post-Bell world, in which local causality is rejected, and it is that I object to. One should not say QM/QFT is local causal, and I think my reasoning is the norm.

If everyone agrees with my characterization of entanglement swapping, but also agrees with PeterDonis' definition of "microcausality", then we're all good.

So if someone wants to say that QFT requires that there be commuting between spacelike separated operators, fine. To me, that means they are separable. How that possibly applies to an entanglement swap, I don't know, because commuting is never mentioned in these papers - and Entangled state statistics are well different than separable Product state statistics. Entangled particles do not commute when measured, as they are not separable (the HUP applies).

This thread is about whether relativity restricts quantum actions to c. Since a swap can take previously uncorrelated spacelike separated particles and change them into a state in which the spooky action at a distance of entanglement occurs, and measurements on them are both correlated and do not commute, I would say the answer is NO. I am not saying that relativity is not relevant to QM, of course it is**. But you can't frame that as vanhees71 is doing in a post Bell world. * In post #33, in reference to causality, vanhees71 says: "No spacelike separated events can be causally connected in any way." This is the assertion I object to, and I think he has been steady in standing by that. In the cited papers: We have spacelike separated events that depend on the decision to bring 2 independent systems together so they interact. The resulting statistics change for the newly entangled pair 0 & 3 [1 & 4 in some papers], which are in fact spacelike separated when they cease from being monogamously entangled to their birth partners. If you don't like Zeilinger et al's characterization of things, please consider the groundbreaking experiment of Henson et al, which uses swapping to simultaneously address multiple loopholes. Here the swap precedes detection, but every element is rigorously spacelike separated from the other. They confirm spooky action at a distance a la Bell, and it is not simply revealing "pre-existing" attributes. The entanglement generation (0 and 3, locations A and B) is caused by action at C on photons 1 & 2. They say:
"We generate entanglement between the two distant spins by entanglement swapping in the Barrett-Kok scheme using a third location C (roughly midway between A and B, see Fig. 1e). First we entangle each spin with the emission time of a single photon (timebin encoding). The two photons are then sent to location C, where they are overlapped on a beam-splitter and subsequently detected. If the photons are indistinguishable in all degrees of freedom, the observation of one early and one late photon in different output ports projects the spins at A and B into the maximally entangled state |ψ −> ... These detections herald the successful preparation and play the role of the event-ready signal in Bell’s proposed setup."
https://arxiv.org/abs/1508.05949Nothing here about relativity preventing a causal (physical) connection between spacelike separated events.

**Keep in mind I am not a Bohmian, not that it should matter to this discussion.

 

[PeterDonis]

if you say that "microcausal" in QFT means spacelike operators commute: well that would also mean that the order of results does *not* matter

Yes. And it appears that you agree with that.

There is a physical state change (if the remote systems interact), it is not quantum local, and the order of events is not relevant.

Does "not quantum local" mean "violates the Bell inequalities"?

 

[GlebKit]

You might be surprised to learn that entangled photons do NOT produce interference as one might otherwise expect. You must stop the entanglement first. Once you do that, the ability to carry out the rest of your idea is lost. See Figure 2 in this great summary paper by Zeilinger:

https://pdfs.semanticscholar.org/3644/6f15507880c629e06391adf9d21aa6d76015.pdf

Thank you a lot for a precise remark. Indeed we will not detect interference at receive side as for entangled particles common function is sum of multiplications thus ortogonal addend (corresponding to slit path) will not give interference picture.
But what will be if we modify experement in the following way?
If 1 is transmitted then before beam arrival transmiited side measure polarization under two projections that have angle θ1.
For 0 transmissions we use axis θ0 for detection.
In all cases before arriving to double slit wall all particles will have their own independed fuction (no entanglement). In one case the beam will consist of two groups with eigenvalues for axis θ1 and in anouther from groups with eigenvalues for axis θ0. Angles are related to slit polarizers that have angels 0 and 90°.
I think that these two different cases give different interferences pictures.

 

[PeterDonis]

Entangled particles do not commute when measured

They don't? The results depend on the order in which they are measured? Bear in mind we are talking about spacelike separated measurements.

 

[microsansfil]

If so, they have to commute--what happens at them cannot depend on the order in which they happen. And that is a microcausality constraint--see above.

Does this mean that if you apply operators that don't commute ([X, Y] ≠ 0) to a spacelike separated event (in which the order of application of the operators X and Y no longer makes sense), the opération must commute (The same result is obtained regardless of the order in which the operators are applied)?

/Patrick

 

[PeterDonis]

operators that don't commute ([X, Y] ≠ 0)

Operators that don't commute when applied to the same individual particle. But here we are talking about two spacelike separated operators applied to two different particles. Not the same thing.

 

[microsansfil]

Operators that don't commute when applied to the same individual particle. But here we are talking about two spacelike separated operators applied to two different particles. Not the same thing.

Ok. It is about tensor product of operators (in particular here two spacelike separated operators applied on entangled (which is considered inseparable) particles or not entangled (factorizable into a tensor product of the state of the two particles) ) ? Thus the tensor product of these operators must commute [X₁ x I₂, I₁ x Y₂] = 0?

Not being a specialist in the field of quantum physics, it is a matter of understanding.

/Patrick

 

[vanhees71]

1. Yes, and we may as well stop now as we are talking past each other. You have yet to cite a statement matching any of your [wrong] statements other than quoting yourself:

- Swapping does not change the state of photons 0 & 3 from uncorrelated to entangled. [incorrect]
- QM/QFT is causal. [incorrect]
- The authors agree with you and not with me. [incorrect]
etc.

2. This is exactly opposite of every swapping paper. There is no causal direction, and the action is quantum nonlocal.

3. What is "cloned" is a superposition. Particle 3 will now contain more information about 0 (which it never interacted with) than any preparation could otherwise do (unless it's entangled).

-------------

I have already quoted chapter and verse over and over again from the cited papers, and explained that actual experiments verify everything I said (per my post #57, 6F example) that clearly proves that swapping changes the statistical outcomes. I have nothing left to add on the matter, and will not respond further. So I will simply say "cheers" and move on.

Ad 1) You always claim I'm saying the opposite of what I said. I said by projection you change the state of photons 0&3 to be entangled. You claim the opposite. Why are you doing this. Is it, because I'm a bit more careful in formulating it? I say

The partial ensemble chosen by the measurement of Alice (in short the "projection") is described by an entangled state of photons 0&3.

So indeed the state is changed but, there's no action at a distance it's just the selection of a partial ensemble out of the full ensemble.

Ad 2) QM/QFT is causal by construction. Read a textbook, before you claim esoteric ideas!

Ad 3) There's nothing cloned. It's a mathematical theorem that cloning is impossible. Also this you can read in many QM textbooks (e.g., Ballentine).

What do you mean by "particle 3 will now contain more information about 0"? First of all it's a photon, not a particle. The information about a system is described by the state the system is prepared in.

 

[vanhees71]

They don't? The results depend on the order in which they are measured? Bear in mind we are talking about spacelike separated measurements.

It's of course utter nonsense. The very experiment we discuss here proves him wrong. The temporal order of the measurements on the pairs 0&3 and 1&2 to project to the state $|\psi_{03}^- \rangle \otimes |\psi_{12}^- \rangle$ is irrelevant for this description. This was explicitly shown by this experiment. I don't know, why @DrChinese is claiming the opposite (sometimes he agrees).