Hidden Assumptions in Bell's Theorem?

[Jarvis323]

There has been a lot of discussion on Bell's theorem here lately. Superdeterminism as a Bell's theorem loophole has been discussed extensively. But I have not seen discussion about Karl Hess, Hans De Raedt, and Kristel Michielsen's ideas, which essentially suggest that there are several hidden assumptions in Bell's theorem, such as no time dependence, and that the mathematical abstractions follow the algebra of real numbers.

I am not sure how to interpret these ideas. First, are the primary claims about the hidden assumptions correct as stated and are the claimed implications valid? Secondly, how confident should we be that e.g., "the mathematical abstractions follow the algebra of real numbers." How plausible are alternative abstractions which don't, or which don't and support locality. Thirdly, if we assume Hess's primary claims are correct, and that Bell's theorem does include these hidden assumptions, leaving a space of local hidden variables theoretically possible, how plausible would such local variables be, and would they still be theoretically unmeasurable? Last, has any work by now ruled out any of these ideas?

Hidden assumptions in the derivation of the theorem of Bell​

...
Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein–Podolsky–Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra...

https://iopscience.iop.org/article/..._cwgK-_RU121lppqoyf9ASh6jo-6BxNavVNAOfJ8_qWnA

For additional context, Hess has been advocating for years the idea that Einstein was right about QM.
https://en.wikipedia.org/wiki/Karl_Hess_(scientist)

Einstein was right!
https://books.google.com/books?hl=e...Ozj2x9NoQGlc3r3EiRIBST5es#v=onepage&q&f=false

Here are a few of Hess's prior works.

Bell's theorem and the problem of decidability between the views of Einstein and Bohr (2001)​

...We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.
...
Note that, unlike other theorems used in physical arguments, the Bell inequality has no experimental basis and actually contradicts all known experiments. It stands on its correctness as a mathematical theorem alone.
...
We confirm this suggestion by a broad mathematical proof and show that the mathematical model of Bell is not general enough to cover all the physics that may be involved in EPR experiments...

https://www.pnas.org/doi/abs/10.1073/pnas.251525098

Exclusion of time in the theorem of Bell (2002)​

https://iopscience.iop.org/article/...k67wg09y6eMHCgYFiIX72DZr7biGhFBvlbOS0-4xIoDZw

​

 

[Demystifier]

Exclusion of time in the theorem of Bell (2002)​

https://iopscience.iop.org/article/...k67wg09y6eMHCgYFiIX72DZr7biGhFBvlbOS0-4xIoDZw

I don't have access to this paper, but a critique of it is on arXiv.
https://arxiv.org/abs/quant-ph/0204169

 

[Lord Jestocost]

No time loophole in Bell’s theorem: The Hess–Philipp model is nonlocal
by R. D. Gill, G. Weihs, A. Zeilinger and M. Zukowski
https://www.pnas.org/doi/full/10.1073/pnas.182536499

 

[Demystifier]

Those models remind me of superdeterministic models by 't Hooft, Hossenfelder and others which, when analyzed carefully, are also nonlocal.

 

[DrChinese]

The team of Hans De Raedt, Karl Hess, and Kristel Michielsen - individually and collectively and along with others - has attempted to put together computer models which purport to show how classical mechanisms (i.e. local realistic ones) can yield results which violate Bell inequalities.

https://arxiv.org/abs/0712.3693 (2007)
Event-by-event simulation of Einstein-Podolsky-Rosen-Bohm experiments
We construct an event-based computer simulation model of the Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a one-to-one copy of the data gathering and analysis procedures used in real laboratory experiments. We consider two types of experiments, those with a source emitting photons with opposite but otherwise unpredictable polarization and those with a source emitting photons with fixed polarization. In the simulation, the choice of the direction of polarization measurement for each detection event is arbitrary. We use three different procedures to identify pairs of photons and compute the frequency of coincidences by analyzing experimental data and simulation data. The model strictly satisfies Einstein’s criteria of local causality, does not rely on any concept of quantum theory and reproduces the results of quantum theory for both types of experiments. We give a rigorous proof that the probabilistic description of the simulation model yields the quantum theoretical expressions for the single- and two-particle expectation values.

There are a number of problems with these attacks on Bell tests:

1. You don't need a computer model to demonstrate to yourself that it is not possible to accomplish what they claim. You cannot even hand pick outcomes that will yield predictions identical to the QM expectation (i.e. to match experiment) unless you know what the measurement settings are in advance.

2. Their simulations are very sophisticated, and they have some interesting properties. However, they cherry pick elements that they want to simulate and place a number of assumptions around those. I would not say they faithfully match to actual Bell tests. On the other hand, I have not personally been able to locate the "smoking gun" flaw in their approach (and I have spent a little time looking at it).

3. A critical flaw: their approach focuses on the trees and misses the forest. The original EPR-B approach considers a pair of entangled particles created within a local source (such as PDC). The entangled particles are created as part of a common interaction. EPR says essentially that perfect correlations arise from this act of creation, there is nothing spooky involved. Forgetting Bell for the moment: in more modern experiments, entanglement is created from particle pairs that have never co-existed in a common light cone (unlike the EPR thought experiment). In a local realistic world, you cannot possibly explain such perfect correlations - as is seen in swapping experiments. Because there needs to be a nonlocal mechanism present to generate correlations between distant particles.

 

[vanhees71]

3. A critical flaw: their approach focuses on the trees and misses the forest. The original EPR-B approach considers a pair of entangled particles created within a local source (such as PDC). The entangled particles are created as part of a common interaction. EPR says essentially that perfect correlations arise from this act of creation, there is nothing spooky involved. Forgetting Bell for the moment: in more modern experiments, entanglement is created from particle pairs that have never co-existed in a common light cone (unlike the EPR thought experiment). In a local realistic world, you cannot possibly explain such perfect correlations - as is seen in swapping experiments. Because there needs to be a nonlocal mechanism present to generate correlations between distant particles.

Once more (however for the first time in the new year ;-)):

Entanglement swapping, is however also possible only due to the entanglement of each of the two pairs of photons used to achieve it. It's all with local interactions and well described within local (=microcausal) QED!

 

[DrChinese]

Once more (however for the first time in the new year ;-)):

Entanglement swapping, is however also possible only due to the entanglement of each of the two pairs of photons used to achieve it. It's all with local interactions and well described within local (=microcausal) QED!

And once more: the pairs subjected to the Bell test have never co-existed in a common light cone. Period. So no, they are not created by local interactions because they were never close enough.

Yes, it is described by QED. The theory that everyone else says demonstrates "quantum nonlocality" and not "locality", as I have provided quotes saying the same so many times previously. We can simply allow our 2 posts to speak for themselves, without further discussion of what is clearly a difference of opinion that will not soon go away.

And going back to the subject of this thread: the De Raedt team misses the boat because they cannot possibly make a local realistic model that explains entanglement of particles that have never existed in a local context. Since experiments evidence the QM predictions in that context, their methodology cannot be correct.

 

[Demystifier]

And once more: the pairs subjected to the Bell test have never co-existed in a common light cone. Period. So no, they are not created by local interactions because they were never close enough.

But each of them was close enough to one of the originally entangled particles, which, in turn, were close enough once in the past. In this sense, entanglement swapping is not any stronger argument for non-locality than the ordinary entanglement is.

Let me use a classical analogy. Suppose that we have twin sisters with identical (hence correlated) genes. When they grow up, they separate and never interact again. Finally, when each of them makes his own child, the two children have correlated genes even though they never interacted. Clearly, no non-local mechanism in this correlation is involved.

 

[martinbn]

And once more: the pairs subjected to the Bell test have never co-existed in a common light cone. Period.

As I've remarked before, whenever you say this you are very unclear. As written it is simply wrong. Period. You may want to rephrase it.

So no, they are not created by local interactions because they were never close enough.

Which "they"? The particles or the correlations? And saying that they are not created by local interactions imply (or at least can be inderstood that way) that there are some other interactions. What are they? All interactions in the standard model are local, gravity is local too. So, you may want to be more precise here too.

 

[vanhees71]

And once more: the pairs subjected to the Bell test have never co-existed in a common light cone. Period. So no, they are not created by local interactions because they were never close enough.

They are! You prepare two independent entangled photon pairs, (12) and (34), each of which is a local event (parametric down conversion of pair (12) and (34) at maybe far distant places), then you make a projective measurement to a Bell state of (23), which also is a local event. Then, for this sub-enemble, also photons (14) are entangled though these 2 photons weren't in any "causal contact", but still the entanglement is only possible to be prepared in this way, because (12) as well as (34) have been prepared as equal pairs. There's no acausal spooky action at a distance involved anywhere. Everything is describable within standard microcausal QED.

Yes, it is described by QED. The theory that everyone else says demonstrates "quantum nonlocality" and not "locality", as I have provided quotes saying the same so many times previously. We can simply allow our 2 posts to speak for themselves, without further discussion of what is clearly a difference of opinion that will not soon go away.

Again QED is by construction a local relativistic QFT. What's demonstrated are correlations between far-distant parts of an entangled system.

And going back to the subject of this thread: the De Raedt team misses the boat because they cannot possibly make a local realistic model that explains entanglement of particles that have never existed in a local context. Since experiments evidence the QM predictions in that context, their methodology cannot be correct.

Of course they can't, because entanglement cannot be described by "local realistic theories", which is the content of Bell's theorem.

 

[DrChinese]

1. But each of them was close enough to one of the originally entangled particles, which, in turn, were close enough once in the past. In this sense, entanglement swapping is not any stronger argument for non-locality than the ordinary entanglement is.

2. Let me use a classical analogy. Suppose that we have twin sisters with identical (hence correlated) genes. When they grow up, they separate and never interact again. Finally, when each of them makes his own child, the two children have correlated genes even though they never interacted. Clearly, no non-local mechanism in this correlation is involved.

3. As I've remarked before, whenever you say this you are very unclear. As written it is simply wrong. Period. You may want to rephrase it.

[DrChinese had said: "And once more: the pairs subjected to the Bell test have never co-existed in a common light cone. Period."]

4. They are [local]! You prepare two independent entangled photon pairs, (12) and (34), each of which is a local event (parametric down conversion of pair (12) and (34) at maybe far distant places), then you make a projective measurement to a Bell state of (23), which also is a local event. Then, for this sub-enemble, also photons (14) are entangled though these 2 photons weren't in any "causal contact", but still the entanglement is only possible to be prepared in this way, because (12) as well as (34) have been prepared as equal pairs. There's no acausal spooky action at a distance involved anywhere. Everything is describable within standard microcausal QED.

5. Again QED is by construction a local relativistic QFT. What's demonstrated are correlations between far-distant parts of an entangled system.

@Demystifier :
1. Close enough in the past? There is no such requirement. The entangled Bell pair (distant from each other) can be detected when the Bell State Measurement pair is also distant (which can be either before or after the Bell test occurs).

2. You cannot use an analogy which is not... a reasonably matching analogy. Especially in QM! You can see the problem here:

A pair of identical twins are born, Alice and Berta, who have identical DNA. Another pair of identical twins are born, Charles and Dave, who also have identical DNA. Alice goes to the US where she perishes in an accident. Dave goes to Thailand, where he also perishes in an accident. Berta and Charles meet in a cafe in Paris and fall in love. They are shocked (after autopsies on their siblings) to discover that the deceased Alice and Dave have the same DNA.

That's the quantum analogy. Due to monogamy of entanglement, Alice cannot have the same DNA as both Berta and Dave. And yet, in the quantum world: Alice's DNA matches Berta's at one point in time, and later matches Dave's instead. The event (quantum interaction) which is responsible for that change in Alice's DNA is the distant meeting of Berta and Charles. That meeting, in Paris, can occur before or after (or nearly simultaneous with) the deaths of Alice and Dave.

@martinbn :
3. Hmmm, what's not clear... Well, the title of one paper is: "Characterizing the nonlocal correlations of particles that never interacted". And the other is: "Entanglement Between Photons that have Never Coexisted". So I would say my statement ("the pairs subjected to the Bell test have never co-existed in a common light cone") is pretty close to these:

https://arxiv.org/abs/1209.4191
https://arxiv.org/abs/0911.1314

@vanhees71 :
4. Apparently your definition of "local" is quite different than mine. (Labeling below assumes we start with entangled photon pair 1 & 2, and another pair 3 & 4, and end up after the swap with entangled pair 1 & 4.)

a) You of course agree that the 2 Bell test photons are not tested local to each other in the cited experiments, they are tested each outside the light cone of the other and would show perfect correlations.

b) You of course agree that the projective BSA measurement can be performed at any time and any place, where the time and place can be suitably distant to both of the Bell test photons. So there can be no classically causal effect from photon 2 to photon 1 (or photon 3 to photon 4) which exceeds c.

c) And regardless of whether you think the projective BSA measurement is merely "post-selection" (as you do) or a necessary event which actually changes the distant Bell pair and is evidence of quantum nonlocality (as I do): You of course also agree that unless that projective measurement is performed, and due to monogamy of entanglement: the 1 & 4 photons cannot be entangled with each other when they are already maximally entangled (1 with 2, and 3 with 4).

So how can the measurements on 1, 2, 3, and 4 be considered local? Only the measurements on 2 & 3 are local, the 1 & 4 measurements are distant and 1 & 4 have never been in classical causal contact. In the reference above, they clearly refer to nonlocality in their abstract:

"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. "

5. Apparently, the members of this scientific team (Eisenberg et al) are completely unaware of the existence of your "local" QFT. Otherwise they would agree with you and not me.

 

[vanhees71]

@vanhees71 :
4. Apparently your definition of "local" is quite different than mine. (Labeling below assumes we start with entangled photon pair 1 & 2, and another pair 3 & 4, and end up after the swap with entangled pair 1 & 4.)

I have a definition of local as used in my scientific community, using relativistic QFT, where the Hamiltonian is build from a hamiltonian density which is expressed in terms of quantum-field operators that transform due to a "local" representation of the proper orthochronous Poincare group and fulfill the canonical equal-time (anti-)commutation relation, and this implies that the local operators that represent local observables commute at space-like separated arguments. This implies that there are no causal connections between space-like separated events.

You start with the photon pair (12), which is created, e.g., by parametric down-conversion, i.e., the interaction of a laser beam with a BBO at some place (described by local interactions) and the same for a photon pair (34) at some other (maybe far distant) place. The two pairs are by assumption uncorrelated and were in no causal connection between each other, which can be guaranteed (arguing exactly within local (!) QED) by ensuring that the "creation events" are space-like separated.

Then you let these pairs freely propagate and then you make an again local (!) projective Bell measurement at the two photons (23), and you also measure the photons 1 and 4 at very far distant places, and you can arrange these measurements to be space like separated from each other as well as from the Bell measurement at the photons (23). In this way, always arguing within relativistic local (!) QED, you entangle the pair (14) for the subensemble selected by the local Bell measurement of the pair (23) without bringing photons 1 and 4 ever in direct causal contact. Indeed this standard argument about the impossibility of causal contact between photons 1 and 4 but being still entangled is in fact not only compatible with but heavily relies on the validity of the microcausality constraint of the local relativistic QFT!

a) You of course agree that the 2 Bell test photons are not tested local to each other in the cited experiments, they are tested each outside the light cone of the other and would show perfect correlations.

Of course, photons 2 and 3 are brought together in polarizing beam splitters and are detected in a local setup. How else do you want to do a projection to a Bell state (the most simple one is to use the polarization-singulett state, because then you only have to make a coincidence measurement where both detectors register a photon).

I'm referring to the paper by Zeilinger et al:

http://www.physics.drexel.edu/~bob/Entanglement/entanglement_never_interacted.pdf

See Fig. 2: The Bell measurment on photons 2&3 is in the gray box at the upper part of the figure, i.e., indeed a local manipulation at a beam splitter, where indeed the trick using the polarization-singlet state of the pair (23) is used.

b) You of course agree that the projective BSA measurement can be performed at any time and any place, where the time and place can be suitably distant to both of the Bell test photons. So there can be no classically causal effect from photon 2 to photon 1 (or photon 3 to photon 4) which exceeds c.

I don't know, what you mean by "BSA", but indeed, as I said, you can do the experiment such that there's no causal connection between the three local measurements (Bell measurement on pair (23) and polarization measurements on the single photons 1 and 4). Then there's no temporal order at all, because space-like separated events have no temporal order!

c) And regardless of whether you think the projective BSA measurement is merely "post-selection" (as you do) or a necessary event which actually changes the distant Bell pair and is evidence of quantum nonlocality (as I do): You of course also agree that unless that projective measurement is performed, and due to monogamy of entanglement: the 1 & 4 photons cannot be entangled with each other when they are already maximally entangled (1 with 2, and 3 with 4).

So how can the measurements on 1, 2, 3, and 4 be considered local? Only the measurements on 2 & 3 are local, the 1 & 4 measurements are distant and 1 & 4 have never been in classical causal contact. In the reference above, they clearly refer to nonlocality in their abstract:

The measuremtn on (23) is local as well as the measurement on 1 as well as the measurement on 4, but 1 and 4 can be detected from each other as well as from the Bell-measurement place on (23). Of course you need some way to only use the photons from one pair of entangled photon states from the beginning: This can be achieved by taking accurate time stamps of the 3 measurements and then finally bring these 3 measuerments' protocols together and only after everything is long done postselect the events via the Bell-measurement on (23), and only these events define a 4-photon ensemble, where with photon pair (23) also photon pair (14) is entangled.

"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. "

I don't know, from where this quote is from, but for sure the authors mean something different when they use the word "non-locality". It cannot mean "violation of the microcausality principle" or that the results contradict the predictions of microcausal relativistic QFT.

5. Apparently, the members of this scientific team (Eisenberg et al) are completely unaware of the existence of your "local" QFT. Otherwise they would agree with you and not me.

That's then not my fault. Usually local relativistic QFT and the Standard Model of elementary particle physics is taught in the 5th or 6th semester of the BSc curriculum. Of course, it may well be that Eisenberg et al never attended such a lecture nor where interested in learning relativistic QFT, but that's not a feature, when you want to discuss about "locality" and "non-locality" in a relativistic context ;-)).

 

[PeterDonis]

I have a definition of local as used in my scientific community

Apparently, the members of this scientific team (Eisenberg et al) are completely unaware of the existence of your "local" QFT.

All, we've had this discussion before. It has nothing to do with physics; it's just about whether the word "local" is an appropriate word to use to describe the commutation relations that quantum fields satisfy. Some people, like @vanhees71, think it is; others, like @DrChinese, think it is not. Different parts of the scientific community might well take each side of this debate. But one thing is sure: we're not going to settle it here. Can we at least, then, not continue a pointless argument about it?

 

[PeterDonis]

for sure the authors mean something different when they use the word "non-locality".

We've had this discussion before too: "non-locality" means "violations of the Bell inequalities are observed". Some people, like @DrChinese, think "non-locality" is an appropriate word to describe that; others, like you, think it isn't. The disagreement here exactly parallels the disagreement I described in post #13 just now, about whether "local" is an appropriate word to describe what you are calling "microcausal relativistic QFT". Which means, again, that it's a disagreement about words, not about physics. The physics is clear: violations of the Bell inequalities are perfectly consistent with "microcausal relativistic QFT". So your "locality" and @DrChinese's "non-locality" are perfectly consistent with each other.

 

[DrChinese]

1. I have a definition of local as used in my scientific community, using relativistic QFT, where the Hamiltonian is build from a hamiltonian density which is expressed in terms of quantum-field operators that transform due to a "local" representation of the proper orthochronous Poincare group and fulfill the canonical equal-time (anti-)commutation relation, and this implies that the local operators that represent local observables commute at space-like separated arguments. This implies that there are no causal connections between space-like separated events.

You start with the photon pair (12), which is created, e.g., by parametric down-conversion, i.e., the interaction of a laser beam with a BBO at some place (described by local interactions) and the same for a photon pair (34) at some other (maybe far distant) place. The two pairs are by assumption uncorrelated and were in no causal connection between each other, which can be guaranteed (arguing exactly within local (!) QED) by ensuring that the "creation events" are space-like separated.

2. Then you let these pairs freely propagate and then you make an again local (!) projective Bell measurement at the two photons (23), and you also measure the photons 1 and 4 at very far distant places, and you can arrange these measurements to be space like separated from each other as well as from the Bell measurement at the photons (23).

3. In this way, always arguing within relativistic local (!) QED, you entangle the pair (14) for the subensemble selected by the local Bell measurement of the pair (23) without bringing photons 1 and 4 ever in direct causal contact.

4. ...as I said, you can do the experiment such that there's no causal connection between the three local measurements (Bell measurement on pair (23) and polarization measurements on the single photons 1 and 4).

5. Then there's no temporal order at all, because space-like separated events have no temporal order!

6. I don't know, from where this quote is from, but for sure the authors mean something different when they use the word "non-locality". It cannot mean "violation of the microcausality principle" or that the results contradict the predictions of microcausal relativistic QFT.

6. (cont.) I don't know, what you mean by "BSA",

7. That's then not my fault. Usually local relativistic QFT and the Standard Model of elementary particle physics is taught in the 5th or 6th semester of the BSc curriculum. Of course, it may well be that Eisenberg et al never attended such a lecture nor where interested in learning relativistic QFT, but that's not a feature, when you want to discuss about "locality" and "non-locality" in a relativistic context ;-)).

Where to start?

1. To comply with @PeterDonis' suggestion in the previous, I will not debate this. I do think that vanhees71's definition of locality (microcausality) in QFT somehow matches the common phrase "quantum nonlocality". 2. Yes, I agree with this exactly. You can also arrange so there is temporal separation, 1 and 4 are measured before 2 and 3 are. Or 1 is measured before 4, etc.3. Exactly! 1 and 4 are never in causal contact (within a common light cone). And since the BSM occurs distant from both 1 and 4 being subjected to a Bell test, how exactly do you propose that the entanglement swap occurs "locally"?

And in fact: There is no requirement that the partners of photons 1 and 4 (which we label 2 & 3) ever meet! You can place yet another entangled pair between pairs [1 & 2] and [3 & 4], let's call them [5 & 6], so that the swapping is daisy chained. This is of course a principle of extended quantum networking.

[1 & 2] [5 & 6] [3 & 4]

The sequence (which can be arranged in many other orders without changing the results.
a. Entangled pairs [1 & 2] and [3 & 4] are created far apart.
b. 1 and 4 are subjected to a Bell test, which shows perfect correlations.
c. Entangled pair [5 & 6] is created.
d. A BSM is performed on [2 & 5], and a BSM is performed on [3 & 6]. These swap entanglement such that already observed [1 & 4] are entangled.

Note that in this scenario, your concept that the 2 & 3 pair interact "locally" - which you claim explains somehow that 1 & 4 become entangled - does not apply. The middle pair is created AFTER 1 & 4 are measured, and no longer exist.4. Again agreed. There need not be the possibility causal contact between any elements between 1 & 4 that could lead to 1 & 4 being entangled. That trick occurs as a result of quantum nonlocality, and nothing else.5. Yes, and no. Your statement as written is fine. The issue is that you can have both 1 & 4 spacelike separated, AND have all observers agree that the BSM occurs AFTER 1 & 4 were measured. It really doesn't matter at all about reference frames, inertial or accelerated, because the quantum mechanical predictions don't change. Not sure why anyone brings up frames, when that changes nothing when you are discussing quantum nonlocality. 6. As I said, the quote is from the abstract of the reference. "...the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. "

BSA=Bell State Analyzer. BSM=Bell State Measurement. Same thing. Zeilinger uses both in papers.7. I was being humorous when I said they hadn't heard of QFT. We must assume the authors of leading edge papers are suitably familiar with QFT. More specifically, there is nothing about these experiments that QM doesn't provide for. There are no useful corrections to the quantum mechanical predictions provided by QFT, at least in swapping experiments.

 

[PeterDonis]

To comply with @PeterDonis' suggestion in the previous, I will not debate this.

Thanks! And a note to all participants, please follow the same policy and keep discussion focused on the physics and the question posed in the OP.

I do think that vanhees71's definition of locality (microcausality) in QFT somehow matches the common phrase "quantum nonlocality".

In the sense that QFT is perfectly consistent with violations of the Bell inequalities and with the entanglement swapping results, yes, certainly.

 

[lodbrok]

2. Yes, I agree with this exactly. You can also arrange so there is temporal separation, 1 and 4 are measured before 2 and 3 are. Or 1 is measured before 4, etc.3. Exactly! 1 and 4 are never in causal contact (within a common light cone). And since the BSM occurs distant from both 1 and 4 being subjected to a Bell test, how exactly do you propose that the entanglement swap occurs "locally"?

And in fact: There is no requirement that the partners of photons 1 and 4 (which we label 2 & 3) ever meet! You can place yet another entangled pair between pairs [1 & 2] and [3 & 4], let's call them [5 & 6], so that the swapping is daisy chained. This is of course a principle of extended quantum networking.

[1 & 2] [5 & 6] [3 & 4]

The sequence (which can be arranged in many other orders without changing the results.
a. Entangled pairs [1 & 2] and [3 & 4] are created far apart.
b. 1 and 4 are subjected to a Bell test, which shows perfect correlations.
c. Entangled pair [5 & 6] is created.
d. A BSM is performed on [2 & 5], and a BSM is performed on [3 & 6]. These swap entanglement such that already observed [1 & 4] are entangled.

I have a question about this, what precisely do you mean by the numbers 1, 2, 3, 4, 5, and 6 in the context of an entanglement-swapping experiment such as https://www.nature.com/articles/srep09333 or any similar published experiment of your choice?

 

[Nullstein]

DrChinese's mistake is to confuse the full ensemble with the post-selected subensembles. In the full ensemble, there is monogamous entanglement between 1&2 and 3&4, while in the post-selected subensembles, there is monogamous entanglement between 1&4. Now, in the entanglement community, the correlation in the subensembles is often referred to as "non-local", but that doesn't imply anything about the cause-and-effect relations in an entanglement swapping experiment. "Non-locality" here is just defined as the presence of correlations that exceed the bound of Bell's inequality. But correlation does not imply causation.

In order to analyze the causal structure of entanglement swapping, more care must be taken. If the entanglement between 1&4 were present in the full ensemble, like it would be the case for photons, which are generated by parametric down-conversion, this would be very mysterious, because the only way to explain it would be a spooky action at a distance. (A common cause is excluded by Bell's theorem.) However, in entanglement swapping, entanglement is present only in the post-selected subensembles. The result of the Bell state measurement at 2&3 is caused by both photon 2 and photon 3. Therefore, the measurement result is a common effect.

Now, everyone knows that conditioning on a common cause can make spurious correlations go away. What is less known is that conditioning on a common effect can make correlations appear that are not at all induced by a cause-and-effect relationship. This phenomenon is commonly known as Berkson's paradox. Regarding entanglement swapping as an example of this phenomenon is a perfectly valid explanation of the non-local correlations between 1&4.

So the subensembles at 1&4 really are entangled and they do violate Bell's inequality. Thus, they are often referred to as "non-local" by the entanglement community, because they trivially meet said definition. But it is important to understand that the cause-and-effect relationship that DrChineses believes is there, can not be inferred in this situation. The Bell state measurement does not cause the entanglement in the subensembles. On the contrary, the initial preparation of the state causes the result of the Bell state measurement. The appearance of this result is a common effect and inferring causal relationships from correlations that arise by conditioning on common effects is a well understood statistical fallacy.

It is important to note that nobody in the entanglement community makes any claims about cause-and-effect relationships based on the appearance of Bell-violating correlations, since this mostly a matter of interpretation. People are interested in researching experimental setups that produce Bell-violating ensembles and want to uncover results that are interpretation-independent. DrChinese reads way more into the word "non-locality" than the authors of the papers he cites want to imply.

 

[vanhees71]

Where to start?

1. To comply with @PeterDonis' suggestion in the previous, I will not debate this. I do think that vanhees71's definition of locality (microcausality) in QFT somehow matches the common phrase "quantum nonlocality".2. Yes, I agree with this exactly. You can also arrange so there is temporal separation, 1 and 4 are measured before 2 and 3 are. Or 1 is measured before 4, etc.3. Exactly! 1 and 4 are never in causal contact (within a common light cone). And since the BSM occurs distant from both 1 and 4 being subjected to a Bell test, how exactly do you propose that the entanglement swap occurs "locally"?

The entanglement swap is just done by selecting or post-selecting subenembles by the projection to a Bell state of pair (23) and the measurements on the single photons 1 and 4. Due to the entanglement of the independent pairs (12) and (34) the pair (14) in this subensemble are entangled. The possibility of this entanglement swap despite the fact that the photon in the pair (14) were never in causal contact is due to the entanglement of the original pairs (12) and (34), i.e., the entanglement of (14) for the subensemble which you get by projecting on a Bell state of (23) is already present in this entanglement of the original pairs.

And in fact: There is no requirement that the partners of photons 1 and 4 (which we label 2 & 3) ever meet! You can place yet another entangled pair between pairs [1 & 2] and [3 & 4], let's call them [5 & 6], so that the swapping is daisy chained. This is of course a principle of extended quantum networking.

[1 & 2] [5 & 6] [3 & 4]

The sequence (which can be arranged in many other orders without changing the results.
a. Entangled pairs [1 & 2] and [3 & 4] are created far apart.
b. 1 and 4 are subjected to a Bell test, which shows perfect correlations.

This you can again only do with a local measurement on the pair (14), i.e., in this case you must manipulate and detect this pair with some setup like the beam splitter + the two detectors in the here discussed experiment. The principle description within local relativistic QED is the same as with the original setup.

c. Entangled pair [5 & 6] is created.
d. A BSM is performed on [2 & 5], and a BSM is performed on [3 & 6]. These swap entanglement such that already observed [1 & 4] are entangled.

Sure, again you need local measurements to perform Bell tests on the pairs you want (I still don't know, what "BSM" means).

Note that in this scenario, your concept that the 2 & 3 pair interact "locally" - which you claim explains somehow that 1 & 4 become entangled - does not apply. The middle pair is created AFTER 1 & 4 are measured, and no longer exist.4. Again agreed. There need not be the possibility causal contact between any elements between 1 & 4 that could lead to 1 & 4 being entangled. That trick occurs as a result of quantum nonlocality, and nothing else.

Then please explain what you understand under non-locality! It cannot contradict standard local (!!!) QED!

5. Yes, and no. Your statement as written is fine. The issue is that you can have both 1 & 4 spacelike separated, AND have all observers agree that the BSM occurs AFTER 1 & 4 were measured. It really doesn't matter at all about reference frames, inertial or accelerated, because the quantum mechanical predictions don't change. Not sure why anyone brings up frames, when that changes nothing when you are discussing quantum nonlocality.

If you want to resolve the tensions between long-ranged correlations and inseparability and relativistic causality you have to argue within a relativistic theory, and relativistic QT, which describes the phenomena in our real world is formulated exclusively in terms of local relativistic QFTs. So if you call long-ranged correlations and inseparability of entangled parts of quantum systems "non-local" you must explain how this does not contradict the locality (microcausality) of relativistic QFTs.

6. As I said, the quote is from the abstract of the reference. "...the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. "

Sure, but it's obviously again long-range correlations and inseparability not a violation of locality=microcausality of relativistic QFTs.

BSA=Bell State Analyzer. BSM=Bell State Measurement. Same thing. Zeilinger uses both in papers.

Thanks. Then my arguments apply.

7. I was being humorous when I said they hadn't heard of QFT. We must assume the authors of leading edge papers are suitably familiar with QFT. More specifically, there is nothing about these experiments that QM doesn't provide for. There are no useful corrections to the quantum mechanical predictions provided by QFT, at least in swapping experiments.

In QM there's no tension whatsoever between actions at a distance (to the contrary it's the standard paradigm to describe interactions in non-relativistic physics). So to discuss claims on "non-locality" and tensions to "relativistic causality" you have to argue within relativistic theories/models.

 

[Demystifier]

A pair of identical twins are born, Alice and Berta, who have identical DNA. Another pair of identical twins are born, Charles and Dave, who also have identical DNA. Alice goes to the US where she perishes in an accident. Dave goes to Thailand, where he also perishes in an accident. Berta and Charles meet in a cafe in Paris and fall in love. They are shocked (after autopsies on their siblings) to discover that the deceased Alice and Dave have the same DNA.

That's the quantum analogy. Due to monogamy of entanglement, Alice cannot have the same DNA as both Berta and Dave. And yet, in the quantum world: Alice's DNA matches Berta's at one point in time, and later matches Dave's instead. The event (quantum interaction) which is responsible for that change in Alice's DNA is the distant meeting of Berta and Charles. That meeting, in Paris, can occur before or after (or nearly simultaneous with) the deaths of Alice and Dave.

Excellent explanation! I've changed my opinion now.

 

[Demystifier]

The Bell state measurement does not cause the entanglement in the subensembles. On the contrary, the initial preparation of the state causes the result of the Bell state measurement.

But if there was no Bell state measurement, there would be no entanglement in the subensembles, right? Now you will argue that the measurement only induced a post-selection, that measurement didn't do anything "physical". But that's wrong, the contextuality (Kochen-Specker etc) theorems show that quantum measurements do make a change of objective physical properties, if objective physical properties exist at all. Of course, as with other quantum non-localities, a local interpretation is possible, but the cost is very big.

 

[Nullstein]

But if there was no Bell state measurement, there would be no entanglement in the subensembles, right?

The state of 1&4 is uniformly distributed. A uniform distrubution can always be decomposed into entangled subensembles, so entangled subensembles do exist in principle. It is a valid interpretation to say that one such decomposition corresponds to the subensembles one would have arrived at by performing a Bell state measurement at 2&3 and then conditioning on the result. However, one can never prove it, as it is a counterfactual statement. Neither is it possible to disprove it. But the point is that the possibility is enough to allow for different interpretations, one being that the measurement at 2&3 does not influence the outcomes at 1&4.

Now you will argue that the measurement only induced a post-selection, that measurement didn't do anything "physical". But that's wrong, the contextuality (Kochen-Specker etc) theorems show that quantum measurements do make a change of objective physical properties, if objective physical properties exist at all.

No, I don't argue that the measurement didn't do anything physical. I argue that it does something physical only to the 2&3 photon pair, but does nothing physical to the 1&4 photon pair. In fact, one can show that the reduced density matrix of the 1&4 pair is the same before and after the measurement. So it is a valid interpretation that no non-local cause-and-effect relationship is established. Of course, there is an equally valid interpretation saying that there is a non-local cause-and-effect relationship, but the point is that there is no way to decide which statement is true without a deeper theory than QM. At the level of QM, both interpretations are possible.

Of course, as with other quantum non-localities, a local interpretation is possible, but the cost is very big.

I don't think the cost is very big in this case. There is no need for mysterious mechanisms such as superdeterminism or retrocausality. Entanglement swapping fits perfectly in the setting of Berkson's paradox and it is a perfectly reasonable explanation.

 

[PeterDonis]

if you call long-ranged correlations and inseparability of entangled parts of quantum systems "non-local" you must explain how this does not contradict the locality (microcausality) of relativistic QFTs.

That's already explained: as I've already said, "nonlocal" means "Bell inequality violations", and everybody already agrees that relativistic QFTs predict Bell inequality violations for these experiments.

 

[martinbn]

The state of 1&4 is uniformly distributed. A uniform distrubution can always be decomposed into entangled subensembles, so entangled subensembles do exist in principle. It is a valid interpretation to say that one such decomposition corresponds to the subensembles one would have arrived at by performing a Bell state measurement at 2&3 and then conditioning on the result. However, one can never prove it, as it is a counterfactual statement. Neither is it possible to disprove it. But the point is that the possibility is enough to allow for different interpretations, one being that the measurement at 2&3 does not influence the outcomes at 1&4.

No, I don't argue that the measurement didn't do anything physical. I argue that it does something physical only to the 2&3 photon pair, but does nothing physical to the 1&4 photon pair. In fact, one can show that the reduced density matrix of the 1&4 pair is the same before and after the measurement. So it is a valid interpretation that no non-local cause-and-effect relationship is established. Of course, there is an equally valid interpretation saying that there is a non-local cause-and-effect relationship, but the point is that there is no way to decide which statement is true without a deeper theory than QM. At the level of QM, both interpretations are possible.

In my opinion this is the same as the measument of one subsystem in an entangled pair does not do anything physical to the other subsystem. The swapping only muddles the issue and is irrelevent for this point.

 

[martinbn]

That's already explained: as I've already said, "nonlocal" means "Bell inequality violations", and everybody already agrees that relativistic QFTs predict Bell inequality violations for these experiments.

But @DrChinese never said what he means by nonlocal. My impression, might be wrong, is that he insists on something more than Bell inequality violations.

 

[DrChinese]

1. DrChinese's mistake is to confuse the full ensemble with the post-selected subensembles. In the full ensemble, there is monogamous entanglement between 1&2 and 3&4, while in the post-selected subensembles, there is monogamous entanglement between 1&4. Now, in the entanglement community, the correlation in the subensembles is often referred to as "non-local", but that doesn't imply anything about the cause-and-effect relations in an entanglement swapping experiment. "Non-locality" here is just defined as the presence of correlations that exceed the bound of Bell's inequality. But correlation does not imply causation.

2. If the entanglement between 1&4 were present in the full ensemble, like it would be the case for photons, which are generated by parametric down-conversion, this would be very mysterious, because the only way to explain it would be a spooky action at a distance. (A common cause is excluded by Bell's theorem.) However, in entanglement swapping, entanglement is present only in the post-selected subensembles. The result of the Bell state measurement at 2&3 is caused by both photon 2 and photon 3. Therefore, the measurement result is a common effect.

3. Now, everyone knows that conditioning on a common cause can make spurious correlations go away. What is less known is that conditioning on a common effect can make correlations appear that are not at all induced by a cause-and-effect relationship. This phenomenon is commonly known as Berkson's paradox. Regarding entanglement swapping as an example of this phenomenon is a perfectly valid explanation of the non-local correlations between 1&4.

4. So the subensembles at 1&4 really are entangled and they do violate Bell's inequality. Thus, they are often referred to as "non-local" by the entanglement community, because they trivially meet said definition.

As vanhees71 does, so do you. You are simply quoting yourself. How about an actual quote from an actual suitable reference. I am tired of quoting Zeilinger, Weinberg, and authors of well known experiments who all say the same thing in one way or another: ...the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation." This is the standard viewpoint of the scientists designing and performing the experiments, in complete opposition to your viewpoint.

There aren't any suitable papers on swapping where they say anything like you do: "of course, quantum teleportation across time and space always respects c". By definition (since it is called teleportation), it never respects c.

I remain confident no quote will be forthcoming.1. Correlation may not always assure us there is causation... but that is exactly what violations of Bell's Inequality (by photons 1 & 4) tells us! That's the whole point!! The "cause" of such a violation - keep in mind it is not a classical cause, but one that follows quantum mechanical rules (which transcend the usual spacetime restrictions) - is the overall context.

And the "cause" of the entanglement swap (again, not a classical cause as time order is NOT a factor) is the Bell State Measurement (BSM) on photons 2 & 3. In QM, a complete measurement context involves elements that defy normal past-to-future ordering (classical = cause must precede effect), and defy restrictions imposed by light cones (locality=respects c). There aren't any generally accepted papers being written by the community that say otherwise.2. You need to read what you wrote again. You say the post-selection on 2 & 3 places distant 1 & 4 into an entangled state, which would be an example of spooky action at a distance if true. And then you say a common cause is excluded by Bell. I quite agree! What you have actually done is demonstrate that without the 2 & 3 swap, 1 & 4 would not be entangled. That is correct sir!! In the quantum world, the swap "causes" the entanglement (where "cause" means cause in the quantum sense, which is not classical).

We all know the swap is a condition for 1 & 4 entanglement. What we don't know is how/why is the swap not a pre-condition for that entanglement. It need not occur in advance of the entanglement. And the best answer we have is that quantum mechanics looks at the full context - which as already discussed defies classical norms for causality - to provide us with expectation values.

You say: "Therefore, the measurement result is a common effect." Hand-waving at its best, sorry, but this is not a valid deduction.3. Berkson's paradox is a red herring. We are talking about actual experiments in which there are perfect correlations between photons 1 & 4, which have never interacted - and at the same time violate Bell inequalities. No classical example will match this scenario. And folks who quote this paradox are grasping at straws. Here's my counter-example, which better describes the quantum situation in a classical analogy.

A pair of identical twins are born, Alice (1) and Berta (2), who have identical DNA. Another pair of identical twins are born, Charles (3) and Dave (4), who also have identical DNA. Alice goes to the distant US where she perishes in a tragic accident. Dave goes to distant Thailand, where he also perishes in a tragic accident. Berta and Charles (2 & 3) meet in an outdoor cafe in distant Paris and fall in love. They are shocked (after autopsies on their respective siblings) to discover that the deceased Alice and deceased Dave (1 & 4) have the same DNA (same DNA=perfect correlations, and violations of Bell inequalities).

Due to monogamy of entanglement, Alice cannot have the same DNA as both Berta and Dave. And yet, in the quantum world: Alice's DNA matches Berta's at one point in time, and later matches Dave's instead. The event (quantum interaction) which is responsible for that change in Alice's DNA is the distant meeting of Berta and Charles [that's the swap in the analogy]. That meeting, in Paris, can occur before or after (or nearly simultaneous with) the deaths of Alice and Dave.

Of course, DNA is a substitute for the entangled (nonseparable) polarization state - which we know actually cannot be predetermined (per Bell's Theorem) as DNA at birth might imply. But it does give a general explanation for the observed perfect correlations. The quantum measurement context then is analogous to the countries where the accidents occur and the autopsies are performed.

When you can find a way to explain the swapping actions in terms like this - but as merely a post-selection phenomenon and not an action/event as I do - then we'll have something more to talk about.

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

And just to address your ridiculous assertion that the full 1 & 4 ensemble contains a uniform distribution ("...a uniform distrubution can always be decomposed into entangled subensembles...") which includes pairs that were entangled without the performance of a swap: Because 1 & 2 are maximally entangled, monogamy of entanglement prevents 1 & 4 from also being maximally entangled. You basically made this argument up on your own, and I thought we had previously dispelled you from this viewpoint in this forum - even considering the latitude allowed here.

 

[lodbrok]

A lot of confusion would be avoided if more precise language is used in describing 1, 2,3,4,5 and 6. These are not individual particles, these are streams of particles as per the experimental descriptions. Saying entanglement is transferred from one "pair" of particles to another "pair" is not an accurate description of these experiments, no such thing ever happens.

If anyone thinks otherwise, please explain why coincidence counting is used in entanglement-swapping experiments.

 

[DrChinese]

A lot of confusion would be avoided if more precise language is used in describing 1, 2,3,4,5 and 6. These are not individual particles, these are streams of particles as per the experimental descriptions. Saying entanglement is transferred from one "pair" of particles to another "pair" is not an accurate description of these experiments, no such thing ever happens.

If anyone thinks otherwise, please explain why coincidence counting is used in entanglement-swapping experiments.

Answer: The coincidence counting is used to identify (measure) individual members of the pairs, as they need to arrive within a narrow time window to qualify for a swap. Most photons won't qualify. It is a true statement that the entangled sources creates biphotons, which are in fact nonseparable systems of 2 particles (and therefore not 2 individual particles while prior to causing a detector click, just as you say).

However, the point you are making about streams is not correct. Entanglement IS transferred from [1 & 2] and [3 & 4] to [1 & 4] each and every time a successful swap is registered by a Bell State Measurement (BSM) on [2 & 3].

 

[Simple question]

@Nullstein, "No, I don't argue that the measurement didn't do anything physical. I argue that it does something physical only to the 2&3 photon pair, but does nothing physical to the 1&4 photon pair".

It seems to me that you do. I am quite sure you don't question that entanglement between two particles IS physical AND change "density matrix of all P1&P2" of such ensembles of monogamously entangled pairs (compared to "classical" entanglement)

Now are you saying that the full ensemble of pair 1&4 have the same "density matrix" of that of non-entangled pair ?
If yes, it means that what(or when)ever happens at 2&3, one would never be able to successfully entangled 100% (or really even more than the classical mechanic limit) of pairs, because it would select the whole (or above classical/ detectable=>FLT communication) sub-ensemble, an this is a contradiction.
If no, how is it possible ? By your own account 2&3 do nothing to 1&4. So how could they be anything but fully (or with classical limit) non entangled ?

I kind of agree with you (as per FLT communication impossibility), but I am quite sure many physicist do pretend that "swapping" IS a (even mildly useful in cryptography) physical thing. That is: what (whatever whenever) happens at 2&3 does create records, that will, whatever your preferred "interpretation", have physical consequence (let's not say "be the cause", but...) of what can be deduced at 1&4 once the records is transported there.

That "consequence" is impossible to explain, or even simulate BUT by doing some quantum physical thing with 2&3 (and with computable probabilities). That a-causal "physical 2&3 thing" will "reveal" (let's not say influence or change) classically impossible correlation between (possibly a sub set of) 1&4.

That's why I agree with DrChinese, because not only photons of 1 & 4 pair have NEVER been anywhere near one another, AND, per you own argumentation, the combined light-cones of 2&3 never-ever get in contact with the 1&4 measuring site. Still it "probes and reveal" things about it

This is the only sense in which this is fully non-local, and a-causal. And this is more dramatic than "first degree" entanglement, where the "probing" single pair photon DOES intersect with both measuring(s) site(s).

Funny thing: maybe if one put the source of original pairs far enough (let's say about the size of the observable universe, possibly less), and put 2&3 "swapper" in opposite direction that 1&2, I am under the impression that you will create those records (information) at 2&3, about some "sets of event" at 1&2, that maybe be completely disjoint, and NEVER reachable (because of universe expansion).

 

[lodbrok]

Answer: The coincidence counting is used to identify (measure) individual members of the pairs, as they need to arrive within a narrow time window to qualify for a swap. Most photons won't qualify. It is a true statement that the entangled sources creates biphotons, which are in fact nonseparable systems of 2 particles (and therefore not 2 individual particles while prior to causing a detector click, just as you say).

However, the point you are making about streams is not correct. Entanglement IS transferred from [1 & 2] and [3 & 4] to [1 & 4] each and every time a successful swap is registered by a Bell State Measurement (BSM) on [2 & 3].

Coincidence counting is a heralding mechanism. Particle pairs which are matched by coincidence counting are entangled in this case. A BSM does not transfer anything between particle pairs, it simply heralds that their properties are correlated.

In entanglement-swapping experiments, you have a stream of entangled pairs [1 & 2] and another stream of entangled particles [3 & 4]. You use the interaction between the pairs from the [2 & 3] to select subsets of [1 & 4] that would be correlated. The entanglement is transferred by the post-selection of the [1&4] stream using information from the [2 & 3] interaction and the reason it works is that 1 is already correlated with 2 and 3 with 4.

From: https://www.nature.com/articles/srep09333 (NOTE: in this paper, the BSM is done on 1 & 4 instead of 2 & 3)

The detection of an entangled state in ch1 and ch4 heralds the existence of entanglement in ch2 and ch3, which originally have no correlation.

Note that they are detecting an entangled state between ch1 & ch4. But why do that when the particles in ch1 and ch4 are not correlated originally? Because they want to identify the subset of particles in ch1 that are correlated with co-propagating particles in ch4. It follows that if a particle in ch4 is correlated with a particle in ch1, then its entangled sibling in ch3 will be correlated with the sibling of the other particle in ch2.

Therefore by simply doing a BSM measurement between particles in ch1 & ch4, you can detect the subset of particles in ch1 & ch4 that are correlated and use this information to post-select subsets of ch2 and ch3 which would show the same correlation.

This is the basis of entanglement swapping.

When you describe it as though an experiment was done on exactly 4 particles, two of which interacted with each other and the other two which never interacted gained entanglement, it is wrong and very misleading.

 

[Simple question]

But why do that when the particles in ch1 and ch4 are not correlated originally?

Can you explain what correlation you are talking about ? What is the quantum property that two unrelated particles are supposed to share/be-correlated before measurement ? Are you invoking super determinism, and that any random pair of particle in the universe are entangled (because of the BB), you just have to look at them the right way ?

Because they want to identify the subset of particles in ch1 that are correlated with co-propagating particles in ch4. It follows that if a particle in ch4 is correlated with a particle in ch1, then its entangled sibling in ch3 will be correlated with the sibling of the other particle in ch2.

Therefore by simply doing a BSM measurement between particles in ch1 & ch4, you can detect the subset of particles in ch1 & ch4 that are correlated and use this information to post-select subsets of ch2 and ch3 which would show the same correlation.

Indeed. And I haven't seen anybody describe this otherwise.

This is the basis of entanglement swapping.

Again, true. Some unrelated series of particle pairs that had no business to be untangled in the first place can be "assigned" an entanglement, by a process taking place in a completely disjoint (space-like) region.
I think we call it "swapped" because the other pair entanglement is destroyed (or the particle themselves) to preserve monogamy.

When you describe it as though an experiment was done on exactly 4 particles, two of which interacted with each other and the other two which never interacted gained entanglement, it is wrong and very misleading.

I don't think Dr Chinese did that... at all. There a many (but finite) pairs of pair that are processed.

What I fail to understand is that it is obvious that 100% of swapping can never been achieved, but I haven't found the lower bound in the paper, nor how to compute it.

 

[DrChinese]

Coincidence counting is a heralding mechanism. Particle pairs which are matched by coincidence counting are entangled in this case. A BSM does not transfer anything between particle pairs, it simply heralds that their properties are correlated.

In entanglement-swapping experiments, you have a stream of entangled pairs [1 & 2] and another stream of entangled particles [3 & 4]. You use the interaction between the pairs from the [2 & 3] to select subsets of [1 & 4] that would be correlated. The entanglement is transferred by the post-selection of the [1&4] stream using information from the [2 & 3] interaction and the reason it works is that 1 is already correlated with 2 and 3 with 4.

From: https://www.nature.com/articles/srep09333 (NOTE: in this paper, the BSM is done on 1 & 4 instead of 2 & 3)Note that they are detecting an entangled state between ch1 & ch4. But why do that when the particles in ch1 and ch4 are not correlated originally? Because they want to identify the subset of particles in ch1 that are correlated with co-propagating particles in ch4. It follows that if a particle in ch4 is correlated with a particle in ch1, then its entangled sibling in ch3 will be correlated with the sibling of the other particle in ch2.

Therefore by simply doing a BSM measurement between particles in ch1 & ch4, you can detect the subset of particles in ch1 & ch4 that are correlated and use this information to post-select subsets of ch2 and ch3 which would show the same correlation.

This is the basis of entanglement swapping.

When you describe it as though an experiment was done on exactly 4 particles, two of which interacted with each other and the other two which never interacted gained entanglement, it is wrong and very misleading.

There are no experimental references, and certainly not the one you presented, which treat swapping as post-selection rather than a quantum operation. From your reference (which is just another confirming swapping experiment with different labeling, no better or worse than those already cited, so I don't know why you are distracting us with its inclusion):

"The detection of an entangled state in ch1 and ch4 heralds the existence of entanglement in ch2 and ch3, which originally have no correlation." (All: note that in this reference, channels labeled [2 & 3] perform the same role as [1 & 4] in the other references. These are the photons that a Bell test are performed on.)

As I get tired of saying: the monogamy of entanglement (you can start another thread if you doubt this and want to debate it, but it is orthodox QM) prevents the kind of correlations you think exist between photons prior to a swap. There is no such thing, you have made this up to preserve your opinion. Swapping is a quantum operation, and if you can find an experiment that says otherwise, please... quote. And save us all some time by a verbatim quote, not a vague/useless reference requiring reading of an entire paper.

In conclusion: Swapping is an experiment done on [sets of] exactly 4 particles, two of which interacted with each other and the other [distant] two which never interacted [but still] gained [maximal] entanglement. This is orthodox science, and sorry: it is you who is misleading. I guess you are free to imagine your own interpretation, but please, even here is not the place to debate such a point. Even my esteemed colleague @vanhees71 - who views the situation quite differently than I - recognizes the need for a successful Bell State Measurement as a requirement for the swap.

 

[DrChinese]

What I fail to understand is that it is obvious that 100% of swapping can never been achieved, but I haven't found the lower bound in the paper, nor how to compute it.

Good question.

The rate of successful swaps compared to all entangled pairs generated is indeed very low. From source A, the rate might be 1 in 100 million; and the same in source B. So roughly, there might be 1 swap out of (100 million)^2 pairs. You might get 10 per seconds, to 1 in 10 minutes; obviously this varies widely based on laser strength, etc.

However: these experiments set a narrow time window for the successful Bell State Measurement (BSM). Any and all events that match the stated criteria are used. There is no scientific issue with this; as when the BSM is successful, there will be maximum entanglement for the other distant photons which have never been in a common light cone.

If a sufficient number of the included pairs are *not* actually entangled, then the CHSH S value might drop below 2. That doesn't happen, as is shown in many papers. Vice versa: if some of the entangled pairs are excluded, then the S value won't be high enough above 2 to violate a Bell inequality in a convincing manner. Either way, you can't "accidentally" violate a Bell inequality in this kind of test (assuming a reasonable sample size).

 

[PeterDonis]

the entanglement of (14) for the subensemble which you get by projecting on a Bell state of (23) is already present in this entanglement of the original pairs.

This doesn't make sense. The original pairs are (12) and (34). Each of those pairs are entangled, but the overall 4-photon state is a product state of the two pairs. So where in the original state is there any entanglement between (14)? There can't be. And if there isn't any entanglement between (14) in the original state--which there can't be--how can any entanglement between (14) in the final results be explained using the original state? It's no answer to say "subensemble" because there aren't even any subensembles of the original state that have entanglement between (14). You can't "project out" subensembles that don't exist in the first place.

 

[PeterDonis]

conditioning on a common effect can make correlations appear that are not at all induced by a cause-and-effect relationship. This phenomenon is commonly known as Berkson's paradox.

But here we're talking about perfect correlation or anti-correlation. Berkson's paradox can't account for that.

To take Berkson's original example as it is described in the Wikipedia page on Berkson's paradox [1], if we have two diseases that are uncorrelated in the general population, they can appear to be negatively correlated in a particular subpopulation, say hospitalized patients. So, for example, if Alice is in the hospital for disease A, she is less likely to have disease B than a member of the general population, and if Bob is in the hospital for disease B, he is less likely to have disease A than a member of the general population. So if we just sample Alices and Bobs from hospitals, we might be led to believe that disease A has some negative causal impact on the chance of getting disease B, and vice versa, when actually it doesn't if we look at the whole population. And we could similarly find subpopulations that showed a spurious positive correlation between diseases A and B.

But now, to paraphrase @DrChinese's description of what is going on in entanglement swapping experiments: suppose Alice and Charlie are "prepared" so that they both have disease A and not B, and Bob and Donna are "prepared" so that they both have disease B and not A. Alice and Bob each go off on their own and never meet each other. But Charlie and Donna meet and decide to get a disease test, and they find that they now both have disease B and not A; and Alice and Bob each decide at some point to get a disease test, and both find that they have disease A and not B. There's no way to account for that using Berkson's paradox. There's no way to somehow "pick subensembles" to accomplish it, because there are no subensembles of the starting ensemble in which Bob has disease A and not B, and Charlie has disease B and not A.

[1] https://en.wikipedia.org/wiki/Berkson's_paradox