Entanglement swapping and Bohmian mechanics

[DrChinese]

1. Well the paper from Norsen I quoted is from 2013. Do you mean you specifically want a BM treatment of a modern (delayed) entanglement swap experiment? I am not aware of any, but if I come across one I'll post it here.

2. I have a feeling, and please tell me if I'm wrong, that when you say "observable" and you are referring to e.g. spin as viewed through the lens of Bohmian Mechanics, you are thinking of "a thing which has a definite value at all times" and for which a subsequent measurement will reveal this value. Is that so? Only talking Bohmian mechanics here.

1. That is precisely my point. Norsen's 2013 example explains successfully the example used in Bell's 1964 paper: entangled spin 1/2 particles. In the 60+ years since then, we've seen literally thousands of experiments and theory papers on entanglement following oQM. There has never (that I know of anyway) been a new result regarding entanglement that traced its origin to BM. BM is always playing catch up*. Currently, 30+ years behind by my reckoning.

However: I absolutely am interested in understanding the Bohmian perspectives on what I call "modern" entanglement. That would be things like swapping, delayed choice, and several other areas I follow. Anything you can share, I will check out. Thanks in advance.


2. To me, an observable is something that can distinguished in a laboratory experiment. Spin and polarization fit that definition. Whether it is an instrinsic or derived property isn't really important to me for our discussion. I am perfectly willing to accept that a Bohmian rejects spin as a fundamental property as long as that view does not conflict with experiment. Swapping experiments demonstrate entanglement using established protocols that are generally accepted science. BM must be able to explain how properties it rejects as non-existent fulfill these protocols.

As to "a thing which has a definite value at all times": I am pointing to the descriptions of spin by Norsen, Goldstein and others. Again, I'm asking members here, not telling anyone. If spin changes midflight in Bohmian terms, contrary to what the quotes say, I don't have a stake either way. Yes, I am trying my best to look at things through the Bohmian lens and reconcile that with modern experiments.


*And I reject all general statements to the effect that BM as a theory yields automatically the same predictions as oQM. As an Interpretation, maybe. But as a Theory different from oQM, certainly not. Theories earn their stripes.

 

[DrChinese]

Yes, I am testing your understanding of the concept of entanglement. More precisely, of the entanglement of apparatus with something else. This is extremely important for this thread because I (and others) emphasized a million times that it is the apparatus which is entangled with something, which you denied. And now, you didn't give me a straight answer, is it entangled or not? Yes or no? Without a straight answer to that question, I claim, it is impossible to understand BM in general, and BM explanation of entanglement swapping in particular.

A measurement apparatus - including related recording equipment - for photon A (post measurement) does not evidence any ongoing entanglement whatsoever with photon B. There is absolutely no test whatsoever that refutes this statement. Now, you or anyone can claim it does and that is your right. I will again point out that monogamy of entanglement (MoE) places severe theoretical limits on claims of this type. And in fact photon B need not ever even co-exist with photon A.

 

[DrChinese]

Roughly, this whole thread can be summarized as follows.
1) BM explains entanglement swapping by emphasizing the role of entanglement with the measuring apparatuses.
2) @DrChinese cannot accept that entanglement with the apparatus is a meaningful concept.
3) Therefore DrChinese thinks that BM cannot explain entanglement swapping.

1./2. I reject that concept as absurd, but it's totally fine if you rely on it. I already said I'll accept the Bohmian premises. But they still must fit with established experiment. I don't think that is asking too much.


3. Your previous "proof" is mostly what I would call a red herring. Adding an apparatus into the equation does not answer swapping questions, it just creates new ones in which more and more behind the scenes "magic" is required. For instance, you'll want to explain these two little details:

a) if the entire universe participates in the Pilot Wave, what singles out the photon A measurement apparatus for being entangled with midflight photon B as you assert?
b) If the measurement apparatus is entangled with photon B, how is it that the apparatus itself - containing many maximally entangled electrons in atomic orbitals - is able to maintain so many entangled relationships?

I mean, these are obvious questions that should have already been dispensed with without me needing to point them out.

---

Instead, our current stumbling block is that the only person in the entire internet universe that seems to be able to present a description of swapping is you. While I indeed consider you an authority (and have for many years), I am surprised that I can find no one else to tell your story in published works. Norsen hasn't. Goldstein hasn't. All the works I have read so far are basically just claims for BM equivalency without any meaningful supporting description. As I don't seem to understand what you say, if you find something more detailed written elsewhere, that would always be welcome.

 

[DrChinese]

He does not accept the expansion of pure states. E.g. He rejects equation (2) as an expression of the initial preparation in Ma's entanglement swapping experiment. https://arxiv.org/pdf/1203.4834

You are correct as to my position. As a matter of generally accepted science, Ma's (2) refers to a post-BSM expression. It has no connection otherwise to the initial state presented as (1). That's what the authors say in plain English.

...if Victor subjects his photons 2 and 3 to a Bell-state measurement, they become entangled. Consequently photons 1 (Alice) and 4(Bob) also become entangled and entanglement swapping is achieved. This can be seen by rewriting Eq. (1) in the basis of Bell states of photons 2 and 3:

|Ψ〉1234 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23) (2)

Your expansion has no physical meaning absent the BSM. So if that makes me reject accepted science in your mind, so be it. I stand with the authors of the paper, with their clear words exactly as written.

---

Now, a little thought will explain why I vehemently reject Morbert's expansion as meaningless - even if it appears to be sound from an algebraic point of view. There is initially no connection between the 1&2 pair and the 3&4 pair. So they cannot be in a combined Bell state. And in fact, they are no more in a Bell state with each other than any other entangled photon pairs in the entire universe. We could just as easily start with another pair, photons 5&6. Then we get (all unquestionable true):

|Ψ〉1234 = |Ψ−〉12⨂|Ψ−〉34
|Ψ〉1256 = |Ψ−〉12⨂|Ψ−〉56
|Ψ〉5634 = |Ψ−〉56⨂|Ψ−〉34

and end up with the following using Morbert's expansion:

|Ψ〉1234 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23)
|Ψ〉1256 = 1/2(|Ψ+〉16⨂|Ψ+〉25 − |Ψ−〉16⨂|Ψ−〉25 − |Φ+〉16⨂|Φ+〉25 + |Φ−〉16⨂|Φ−〉25)
|Ψ〉5634 = 1/2(|Ψ+〉54⨂|Ψ+〉63 − |Ψ−〉54⨂|Ψ−〉63 − |Φ+〉54⨂|Φ+〉63 + |Φ−〉54⨂|Φ−〉63)

None of these last 3 have any physical significance. And they cannot be simultaneously true. Hopefully that is obvious and needs no further explanation. You need to first overlap photons in a BSM apparatus to give it physical significance.

Note for new readers: This actually portion of the discussion has absolutely nothing to do with this thread's focus on Bohmian theory and Entanglement Swapping. It was more just an ad hominem side attack on me.

 

[Matterwave]

That would be things like swapping, delayed choice, and several other areas I follow. Anything you can share, I will check out. Thanks in advance.

What about Huggett's paper that @Motore linked in post #383? It's entanglement swapping, though it is not delayed choice.

2. To me, an observable is something that can distinguished in a laboratory experiment. Spin and polarization fit that definition.

I am perfectly willing to accept that a Bohmian rejects spin as a fundamental property as long as that view does not conflict with experiment.

BM must be able to explain how properties it rejects as non-existent fulfill these protocols.

From your statements here I am unable to glean an answer to my question in post #382.

This question:

when you say "observable" ... you are thinking of "a thing which has a definite value at all times" and for which a subsequent measurement will reveal this value. Is that so?

As to "a thing which has a definite value at all times": I am pointing to the descriptions of spin by Norsen, Goldstein and others.

Could you be specific about which statements exactly you are pointing too? For example, do you point to the quotes of Norsen, Durr, Goldstein and Zhanghi in my post #368?

I ask these questions for a specific reason. As Norsen points out in ("The pilot-wave perspective on spin," Am. J. Phys. 82, 337 (2014)), a common attack on Bohmian Mechanics is to assume that because it is a hidden variable theory, it assigns definite, pre-existing, values to "all observables" which are then simply revealed by measurement.

This view would make Bohmian Mechanics non-contextual. Such non-contextual hidden variable theories are (at least for Hilbert space dim >=3) ruled out by Kochen Specker ("The Problem of Hidden Variables in Quantum Mechanics," Journal of Mathematics and Mechanics 17, 59–87 (1967)) and by a nice argument from John Bell in ("On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447 (1966)).

I wonder if you also hold this view of Bohmian Mechanics and that is your core objection.

 

[Demystifier]

@DrChinese, here is one paper very much in spirit with my views of BM, by emphasizing the role of the apparatus, including the entanglement with the apparatus: https://arxiv.org/abs/2102.02519

One of the authors (F. Laloe) is a well-known expert on quantum foundations, being the author of the book "Do We Really Understand Quantum Mechanics?".

Some quotes from the paper:
"As expected with an entangled quantum state, the weights depend, not only of the position Q of the particle, but also on the positions Zp and Zn of all pointer particles."
"Now assume that the pointers have a finite velocity (V0= v0), so that the pointers are entangled with the spin particle."
"In practice, fast pointers occur in many experiments, namely each time a big and fast amplification process takes place within the measurement apparatus, which quickly entangles many particles of M with S."
"Slow pointers occur in the opposite situation: when the wave packets of S separate before S gets entangled with many particles in M."
"Needless to say, the model of the measurement apparatus we have used is oversimplified, assuming for instance the same Gaussian wave function for all the particles inside the measurement apparatuses that are entangled with the spin particle. This simplification does not change the structure of the entangled quantum state of the spin particle and the measurement apparatus. Since this structure is the origin of our results, we believe that they are generic. Moreover, for simplicity, we have focussed our discussion on the particles inside the pointers, but it is clear that other parts of the measurement apparatuses also play a role. The number of particles N should not be seen as referring only to the physical content of the pointers themselves. It should be understood as the number of particles that get entangled with the spin particle during the amplification process that takes place in any measurement apparatus and results in the physical displacement of the pointers."
"During the initial stage of a measurement process, S becomes entangled with some variables of M, so that the velocity of the Bohmian position variables attached to S depend on those of M. Our analysis takes into account this entanglement and studies in detail how it changes the way the wave function of the whole system drives every position."

Of course, the quotes are not a substitute for reading the whole paper. I would suggest you to read it as a whole. My own conclusion would be: The measuring apparatus in BM is not just a passive recorder of the measurement outcomes, but also an active creator of them. That's, after all, what contextuality of QM is telling us that should be the case, while BM offers an explicit model describing how exactly that happens.

 

[DrChinese]

I think you are completely wrong here. From this paper:
https://arxiv.org/html/0905.4036v1

Yes, I had seen this paper previously. I will look at it again. Thanks.

 

[DrChinese]

@DrChinese, here is one paper very much in spirit with my views of BM, by emphasizing the role of the apparatus, including the entanglement with the apparatus: https://arxiv.org/abs/2102.02519

One of the authors (F. Laloe) is a well-known expert on quantum foundations, being the author of the book "Do We Really Understand Quantum Mechanics?".

Good stuff. More homework!

 

[DrChinese]

1. What about Huggett's paper that @Motore linked in post #383? It's entanglement swapping, though it is not delayed choice.

2. I ask these questions for a specific reason. As Norsen points out in ("The pilot-wave perspective on spin," Am. J. Phys. 82, 337 (2014)), a common attack on Bohmian Mechanics is to assume that because it is a hidden variable theory, it assigns definite, pre-existing, values to "all observables" which are then simply revealed by measurement.

This view would make Bohmian Mechanics non-contextual. Such non-contextual hidden variable theories are (at least for Hilbert space dim >=3) ruled out by Kochen Specker ("The Problem of Hidden Variables in Quantum Mechanics," Journal of Mathematics and Mechanics 17, 59–87 (1967)) and by a nice argument from John Bell in ("On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447 (1966)).

1. Good! I had seen it before. It seemed dated (2009) when I first looked at it (his "Bell-ometer" versus the usual "Bell State Measurement"). But I will look at it deeper this time.

2. Well, some authors - I think @Demystifier holds this view - say that all system evolution in the universe is essentially predestined in something of a clockwork fashion. I may not be using the correct lingo, not sure. If so, that implies all derived observables have definite values. The ones I am most interested in are spin types. Demystifier has previously indicated that BM is contextual, something that most writers seem to agree with. So navigating between these views can be confusing.

---

And while I am not a Bohmian, I'm not sure I exactly object to it. I just think it makes an important assertion that is subject to challenge. And for me, I don't have a problem with the nonlocality particularly. I accept there is quantum nonlocality already, whatever that is. The issue for me is the forward in time only (FITO) evolution. Most popular interpretations feature this as well. But Bohmians push this as an adjunct to Bohmian theory, often implied more than made explicit.

But Delayed Choice experiments - where Nonlocality is already present by design - makes a good place to investigate the FITO assumption. In other words: BM already solves the nonlocality issue that many Interpretations struggle with. But there are a couple of reasons I have come here with questions about BM:

i) Swapping experiments demonstrate nonlocality in space (which BM neatly answers!) but also nonlocality in time (temporal nonlocality - the Megidish experiment). That's a different animal, not as neatly answered by BM.
ii) No existing swapping experiments demonstrate nonlocality outside the range of a specific pattern. Price and Wharton refer to it as "W" or Zigzag shape. The speed of "entanglement collapse" (if there is such a thing) can be made to appear to be any value, and in any causal direction. That doesn't seem like a good fit for BM.

I'm not saying BM can't answer these issues. I'm just trying to see where it might. But the literature is quite thin. Hence, me asking. While there are a number of Bohmians out there attempting to "sell" people on the Bohmian perspective, I consider it essential that Bohmians stay at the forefront of modern experiments. I don't think they are, on the whole, doing that. Obviously it's a smaller group of scientists, and everyone must parcel their efforts wisely.

 

[Demystifier]

2. Well, some authors - I think @Demystifier holds this view - say that all system evolution in the universe is essentially predestined in something of a clockwork fashion. I may not be using the correct lingo, not sure. If so, that implies all derived observables have definite values. The ones I am most interested in are spin types. Demystifier has previously indicated that BM is contextual, something that most writers seem to agree with. So navigating between these views can be confusing.

Predestination does not imply that observables have definite values. Predestination means that, in principle, it is possible to compute what will be the value of the observable in the future, but it does not imply the observable has a value now. Contextuality means that this value will be created by the measurement in the future, while now there is no value because it is not yet measured.

A simple analogy: If someone tells that a prince is predestined to become the king, it does not mean that he already is the king. The prince will become the king in the future because his father, the present king, will die. This means that becoming the king is contextual, because it depends on death of his father. And yet, it is predestined that his father will die, and consequently, that the prince will become a new king. I don't see why is that so difficult for some people to understand.

Another thing, that I often emphasize but people don't get it, is that determinism, i.e. predestination, is not at all important for BM. There are modifications of BM which postulate some truly random forces in dynamics of particles, without changing much the mechanism how observables attain definite values during measurements. (Likewise, one could include random forces which decide the death of the prince's father, without changing much the mechanism by which the prince becomes the king.) The essence of BM is not determinism. It is not even the particle trajectories, because there are versions of BM without particle trajectories. The essence of BM is the ontology. But most physicists don't understand what this o-word even mean, so they distort BM by over-emphasizing some notions that they do understand, but which are not that important.

 

[Matterwave]

Demystifier has previously indicated that BM is contextual, something that most writers seem to agree with.

As they must, or else BM would run afoul of the no-go theorems from Kochen-Specker and John Bell that I pointed out in post #395.

And while I am not a Bohmian, I'm not sure I exactly object to it.

You don't object to BM being contextual or you don't object to BM being non-contextual? You should object to the latter, as the latter statement, that BM is non-contextual, would rule out BM as a valid interpretation of QM.

For an experimental paper showing conflict with non-contextual hidden variable theories, see: https://arxiv.org/pdf/0904.1655

I agree that it is perhaps unintuitive for a realist interpretation to not assign definite values to all observables. Indeed, my original knee-jerk reaction to spin in BM was to think that it would be, just like position, something with a definite value at all times (a "hidden" variable). But the arguments from @Demystifier (in the slides he shared a while ago) and Norsen around what a spin measurement is -- specifically that all you see is ultimately a position measurement -- and that in BM the spin only ever appears in the guiding wave function and never in the "hidden variables" was convincing for me.

 

[Morbert]

You are correct as to my position. As a matter of generally accepted science, Ma's (2) refers to a post-BSM expression. It has no connection otherwise to the initial state presented as (1). That's what the authors say in plain English.

...if Victor subjects his photons 2 and 3 to a Bell-state measurement, they become entangled. Consequently photons 1 (Alice) and 4(Bob) also become entangled and entanglement swapping is achieved. This can be seen by rewriting Eq. (1) in the basis of Bell states of photons 2 and 3:

|Ψ〉1234 = 1/2(|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23) (2)

i) Nothing you have quoted marks (2) as a post-BSM expression. It is equation (1), rewritten. Ma explicitly says so "This can be seen by rewriting Eq. (1) in the basis of Bell states of photons 2 and 3".
ii) It's not meaningless as it reveals anticipated correlations whether we apply Ma's analysis or a forward-in-time analysis.
iii) You should be familiar enough with basic quantum theory to know your reading of Ma can't possibly be correct.

 

[javisot]

Of course, the quotes are not a substitute for reading the whole paper. I would suggest you to read it as a whole. My own conclusion would be: The measuring apparatus in BM is not just a passive recorder of the measurement outcomes, but also an active creator of them. That's, after all, what contextuality of QM is telling us that should be the case, while BM offers an explicit model describing how exactly that happens.

I once heard it put this way: "a measurement value does not exist until it is constructed using a measuring device."

But is this exclusive to BM, or is it true in general?

 

[Morbert]

I once heard it put this way: "a measurement value does not exist until it is constructed using a measuring device."

But is this exclusive to BM, or is it true in general?

Asher Peres preferred the term "test" over "measurement" because measurement implies the recording of some value of the measured system whereas a test implies the recording of a response to some probe.

 

[Demystifier]

I once heard it put this way: "a measurement value does not exist until it is constructed using a measuring device."

But is this exclusive to BM, or is it true in general?

I think it is even more true in Copenhagen interpretation, but there it is much more vague. For me, BM is a way to make some claims of "Copenhagen" interpretation, or more precisely the instrumental interpretation, more precise. See also the paper in my signature.

 

[martinbn]

May be it would be better if instead of entaglmnet swapping the discussion focuses on quantum teleportation. It has the same idea, it is experementaly verified, and it is a little bit easier to follow.

 

[Demystifier]

May be it would be better if instead of entaglmnet swapping the discussion focuses on quantum teleportation. It has the same idea, it is experementaly verified, and it is a little bit easier to follow.

Does anyone think that BM can't explain quantum teleportation? Or that it is not clear how does BM explain it? If so, what part of quantum teleportation one finds problematic from the BM point of view?

 

[martinbn]

Does anyone think that BM can't explain quantum teleportation? Or that it is not clear how does BM explain it? If so, what part of quantum teleportation one finds problematic from the BM point of view?

No, It was a suggestion to @DrChinese, because he i the one who gets lost in the details of entnglement swappig.

 

[Demystifier]

No, It was a suggestion to @DrChinese, because he i the one who gets lost in the details of entnglement swappig.

I think no phenomenon in QM interests him more than entanglement swapping.

 

[javisot]

I once heard it put this way: "a measurement value does not exist until it is constructed using a measuring device."

But is this exclusive to BM, or is it true in general?

I think it is even more true in Copenhagen interpretation, but there it is much more vague. For me, BM is a way to make some claims of "Copenhagen" interpretation, or more precisely the instrumental interpretation, more precise. See also the paper in my signature.

What interpretation corresponds to the opposing idea, the idea that quantum objects interact only with other quantum objects, rather than with macroscopic objects like measuring devices?

From the perspective of the tiniest scales, it also makes sense to think that a particle interacts with one of the particles making up the measuring device, rather than with the device itself as a macroscopic entity.

 

[Demystifier]

What interpretation corresponds to the opposing idea, the idea that quantum objects interact only with other quantum objects, rather than with macroscopic objects like measuring devices?

From the perspective of the tiniest scales, it also makes sense to think that a particle interacts with one of the particles making up the measuring device, rather than with the device itself as a macroscopic entity.

I don't think that there is such interpretation, but some interpretations don't emphasize the role of the macro apparatus. For example in consistent histories interpretation, the notion of apparatus dependent contextuality is replaced by framework dependence which does not rest on the existence of the apparatus.

 

[gentzen]

Note for new readers: This actually portion of the discussion has absolutely nothing to do with this thread's focus on Bohmian theory and Entanglement Swapping. It was more just an ad hominem side attack on me.

No, it was not an ad hominem attack on you. It was a technical correction of what you had written.

Nobody likes to be corrected, at least not in the specific momemt where you get corrected. But the purpose of such corrections are normally not the specific moment anyway. This is why you perceive it as a "side attack".

The reason why people like me (or Morbert) sometimes feel forced to issue such technical corrections is to prevent worse consequences later, in case such stuff remains uncontradicted, and gets assumed to be true.

See here for an instance where I corrected an expert you know about some "apparently irrelevant" aspect of entanglement:
https://www.astronews.com/community...etation-der-quantenmechanik.12314/post-151739
His reaction was to focus on that it is "irrelevant" for him, instead of trying to prove me wrong.

 

[gentzen]

I think this is the first thing you need the clear up, because in BM there is no such thing as the spin of the particle! Particles do not have spin. Spin is not a property of the particle alone.

Well, I think what would be more important to clear up are the "definitions" of entanglement, and how they depend on subdivisions of the system into subsystems via tensor products.

Suppose we have small quantum systems A and B, and a larger system C. One reason why DrChinese disagrees with Demystifier is that it never got clarified whether we are talking about tripartite entanglement of A, B, and C (for the state of system $H_A \otimes H_B \otimes H_C$), or about bipartite entanglement of A and (B,C) (for the state of system $H_A \otimes (H_B \otimes H_C)$).

The confusion is amplified by talking about particles instead of systems:
https://en.wikipedia.org/wiki/Multipartite_entanglement
https://en.wikipedia.org/wiki/Quantum_entanglement#Mathematical_details

A single particle cannot be maximally entangled with more than a particle at a time, a property called monogamy.

So when "particles" A and B are maximally entangled, DrChinese cannot understand why Demystifier claims that "particle" A would be maximally entangled with "system" (B,C). He believes that this would contradict monogamy of entanglement. It it doesn't, because Demystifier is talking about bipartite entanglement, whereas monogamy of entanglement is talking about multipartite entanglement.

 

[Demystifier]

So when "particles" A and B are maximally entangled, DrChinese cannot understand why Demystifier claims that "particle" A would be maximally entangled with "system" (B,C). He believes that this would contradict monogamy of entanglement. It it doesn't, because Demystifier is talking about bipartite entanglement, whereas monogamy of entanglement is talking about multipartite entanglement.

Good points! In addition, it seems to me that @DrChinese thinks that bipartite entanglement is the same as biparticle entanglement.

 

[DrChinese]

I think no phenomenon in QM interests him more than entanglement swapping.

I’d agree with that almost any day!!!

 

[DrChinese]

See here for an instance where I corrected an expert you know about some "apparently irrelevant" aspect of entanglement:
https://www.astronews.com/community...etation-der-quantenmechanik.12314/post-151739
His reaction was to focus on that it is "irrelevant" for him, instead of trying to prove me wrong.

What’s your handle there? I was looking, maybe post #401 was a bad place to start?

 

[DrChinese]

Well, I think what would be more important to clear up are the "definitions" of entanglement, and how they depend on subdivisions of the system into subsystems via tensor products.

Suppose we have small quantum systems A and B, and a larger system C. One reason why DrChinese disagrees with Demystifier is that it never got clarified whether we are talking about tripartite entanglement of A, B, and C (for the state of system $H_A \otimes H_B \otimes H_C$), or about bipartite entanglement of A and (B,C) (for the state of system $H_A \otimes (H_B \otimes H_C)$).

The confusion is amplified by talking about particles instead of systems:
https://en.wikipedia.org/wiki/Multipartite_entanglement
https://en.wikipedia.org/wiki/Quantum_entanglement#Mathematical_details

So when "particles" A and B are maximally entangled, DrChinese cannot understand why Demystifier claims that "particle" A would be maximally entangled with "system" (B,C). He believes that this would contradict monogamy of entanglement. It it doesn't, because Demystifier is talking about bipartite entanglement, whereas monogamy of entanglement is talking about multipartite entanglement.

Umm, never thought that nor said that. Particle A can be maximally entangled with system BC. But C cannot be maximally entangled with D at the same time on the same basis.

There’s a huge difference between a quantum system and a macroscopic object. And when it comes to entanglement, trying to talk about them on equal terms is virtually nonsensical.

I) For example, let’s talk about entangled photons and measurement apparati. I send entangled photon A to a polarization measurement apparatus. Some (Bohmians) seem to claim that apparatus is now entangled with photon B. Now, exactly what part of the apparatus is entangled to B? It first goes through a polarizing beam splitter. Is that what becomes entangled? Then later photon A continues on to a detector and is absorbed. Is that when it becomes entangled? Is the polarizer entangled with the detector and photon B?

II) And whatever apparatus is entangled with photon B: does this new entanglement have any impact on entangled electrons in atoms, composing the apparatus? Exactly what is entangled with what?

III) And suppose I send another entangled photon E (its partner is F) into the measurement apparatus while it is still entangled with B. Are B and F now entangled as well? Is the measurement apparatus entangled with both B and F simultaneously? By the way, this experiment is easily performed.

Hey, if that’s your hypothesis, just let me know! This is basically what I’m asking in the first place !! We take an initial assumption and direct one self towards reasonabledeductions.

 

[DrChinese]

Good points! In addition, it seems to me that @DrChinese thinks that bipartite entanglement is the same as biparticle entanglement.

You’re good, true dat! But you really can’t read my mind. I’m the one reminding you about monogamy of entanglement. It is not you that is reminding me.

There are all kinds of relationships possible between quantum systems. Entanglement is but one of them. For example: I can add energy to a system without creating entanglement. We simply have a new Product State. So the obvious question is, according to BM, what interactions create or destroy entanglement? Because I’ve been hearing a lot about entanglement in situations in which I would not expect in entanglement.

Are there any experiments that demonstrate and entanglement between a measurement apparatus and a photon? That would certainly settle a lot of questions.

 

[Demystifier]

Umm, never thought that nor said that. Particle A can be maximally entangled with system BC. But C cannot be maximally entangled with D at the same time on the same basis.

There’s a huge difference between a quantum system and a macroscopic object. And when it comes to entanglement, trying to talk about them on equal terms is virtually nonsensical.

I) For example, let’s talk about entangled photons and measurement apparati. I send entangled photon A to a polarization measurement apparatus. Some (Bohmians) seem to claim that apparatus is now entangled with photon B. Now, exactly what part of the apparatus is entangled to B? It first goes through a polarizing beam splitter. Is that what becomes entangled? Then later photon A continues on to a detector and is absorbed. Is that when it becomes entangled? Is the polarizer entangled with the detector and photon B?

II) And whatever apparatus is entangled with photon B: does this new entanglement have any impact on entangled electrons in atoms, composing the apparatus? Exactly what is entangled with what?

III) And suppose I send another entangled photon E (its partner is F) into the measurement apparatus while it is still entangled with B. Are B and F now entangled as well? Is the measurement apparatus entangled with both B and F simultaneously? By the way, this experiment is easily performed.

Hey, if that’s your hypothesis, just let me know! This is basically what I’m asking in the first place !! We take an initial assumption and direct one self towards reasonabledeductions.

First, BM (and most other interpretations) assume that there is no fundamental difference between a micro and a macro system. The differences are only practical. So in the macro case a talk about entanglement may be more difficult, but in principle should not be impossible. Conversely, if it was strictly impossible, then BM, and most other interpretations, would be wrong. If you are convinced that it is impossible, then you should reject BM, as well as most other interpretations, and consider only those which claim that there is a fundamental cut between the micro and the macro. Do you really believe that there is such a cut? If you do, then you should say it clearly, so that we don't have to waste time on futile discussions in which we try to convince you that QM, in principle, is valid also for the macro stuff.

Now answers to your questions. Initially photons A and B are entangled. Then the apparatus measures A. The part of the apparatus that absorbs A becomes entangled with B. But the thing that absorbs it is just one electron, so this entanglement cannot last for long. Instead, the apparatus performs an amplification of the signal, so after the amplification it is this more macroscopic stuff that carries the amplified signal that is entangled with B. But even that does not last for very long. Instead, the signal is is transmitted to the computer memory which permanently records the measurement outcome. So in the long run the thing which is entangled with B is the bits in the computer.

Note that the entanglement monogamy is never broken. Initially, B is maximally is entangled with A. Then, it is maximally entangled with the electron, no longer with A. Then, it is maximally entangled with the amplified signal, no longer with the electron. Then, it is maximally entangled with the bits in the computer, no longer with the amplified signal.

Of course, this could be explained in even more detail, but for that purpose I would need to spend some more time to study in more detail how the detector works, what exactly is the amplified signal, etc. Maybe you already know this stuff better than me, so you can fill the gaps in my explanation by yourself. But I don't think that these details are crucial for understanding the principles.

 

[DrChinese]

1. … in the macro case a talk about entanglement may be more difficult, but in principle should not be impossible.
2.Conversely, if it was strictly impossible, then BM, and most other interpretations, would be wrong. If you are convinced that it is impossible, then you should reject BM…

3.Now answers to your questions. Initially photons A and B are entangled… in the long run the thing which is entangled with B is the bits in the computer.

1. The very definition of hand-waving. I am not trying to talk about a micro macro difference. Just stating the obvious that a single photon is not going to be entangled with each and every atom and molecule in a large apparatus.

2. I am not trying to reject anything. Any scientist should feel comfortable asking questions, or answering questions regarding their views. In a sense, interpretations are like religions. If you accept one as primary, you reject all others. So to the extent I accept one – which I don’t really – I reject all others already.

3. Thanks for a straight answer. This was exactly what I was trying to understand if you believed.