I Realistic interpretation of QM

[Nullstein]

Assuming I am willing to learn, what would I have to read specifically?

You would have to read about how conditioning on colliders produces fake correlations. If you are bothered by the words "fake correlations", here's how Wikipedia puts it: "In the terminology of causal graphs, conditioning on the collider opens the path between X and Y. This will introduce bias when estimating the causal association between X and Y, potentially introducing associations where there are none." But again, all of this is explained in full detail in Pearls book.

I assume that Pearl won't explicitly mention entanglement, and even less entanglement swapping (or "fake correlations"). I see that he does mention quantum mechanics from time to time, like in:

or:
I guess I prefer saying that quantum-level locality and causality follows its own rules and intuitions (like Pearl effectively did in the quotes above), instead of talking of a coffin for those concepts.

I too, like Pearl, think that quantum-level causality follows its own rules. It's just that entanglement swapping adds nothing to the mystery, because particles A & D are actually not entangled. Only subensembles are entangled, but that's just a well understood statistical effect resulting from conditioning on a collider. What's left to explain is really just why A & B and C & D are entangled. This is indeed a mystery.

 

[kurt101]

When you measure A, this influences B. When you measure D, this influences C. Then when you do the swapping with B & C, they are already tainted by the respective polarizer you used when measuring A and B.

I meant to say "Then when you do the swapping with B & C, they are already tainted by the respective polarizer used when measuring A and D", but I must have edited the comment to many times already to change it.

 

[PeterDonis]

I am just pointing out the flaw in @DrChinese claim that these experiments says anything meaningful about reality or hidden variables.

If by this you mean that "reality" and "hidden variables" are things that vary from interpretation to interpretation, so no experiment can tell you things about them directly, because no experiment can distinguish between different QM interpretations (since they all make the same experimental predictions), that's fine.

But you appear to be saying more than that: you appear to be saying that some interpretation must exist that has all the properties you like. And you can't just claim that. You have to actually show us the interpretation--and not just as your personal theory but as something in the actual literature. So far, the main message of the discussion in this thread appears to me to be that there is no interpretation in the actual literature that has all the properties you like. For you to just keep insisting that there must be, in the absence of any support for that claim from the literature, is pointless and this thread will simply be closed if that is where we are.

 

[kurt101]

If by this you mean that "reality" and "hidden variables" are things that vary from interpretation to interpretation, so no experiment can tell you things about them directly, because no experiment can distinguish between different QM interpretations (since they all make the same experimental predictions), that's fine.

But you appear to be saying more than that: you appear to be saying that some interpretation must exist that has all the properties you like. And you can't just claim that. You have to actually show us the interpretation--and not just as your personal theory but as something in the actual literature. So far, the main message of the discussion in this thread appears to me to be that there is no interpretation in the actual literature that has all the properties you like. For you to just keep insisting that there must be, in the absence of any support for that claim from the literature, is pointless and this thread will simply be closed if that is where we are.

I don't want the thread closed. I found it useful to have the discussion with @DrChinese about entanglement swapping. Maybe it is too early to conclude this, but I have learned that the A & D photons in the entanglement swapping are not entangled but correlated. For a realist, this is an extremely important to know.

For me, the value of an interpretation is to aid in understanding of the math and the experimental results.

I see General Relativity, Quantum Mechanics, Bell non-locality, as improvements on understanding a Newtonian Universe, not as invalidating it. I think this is a very reasonable interpretation to hold to, especially since we know these improvements have issues and don't integrate well with each other. Also, these improvements rely heavily on classical logic in their formulation and so I don't see any reason to abandon the classical logic they were founded on.

I see Quantum Mechanics as a mathematical framework to make statistical predictions. Though, no doubt it also tells us a great deal about reality, but as a realist, I don't think all of its principles are true outside the context of the statistical mathematical framework.

I imagine I will be able to find some acceptable peer review papers that support different aspects of my form of a realist interpretation, but is there no actual name for such an interpretation? It seems to be used all through the history of formulating Quantum Mechanics in some form or another. Sometimes I see it referred to as hidden variable theory, but it is clearly there, even if it is not described in as much detail as say a Bohmian Mechanics interpretation is.

I like aspects of the Bohmian Mechanics interpretation, but I think it goes too far in making assumptions that don't fit well with reality.

I will try to find an interpretation I can use for discussions on realism that is acceptable to both myself and this forum. I appreciate any constructive suggestions.

 

[PeroK]

Given the experimental evidence of the 20th and 21st centuries, I'd say it's highly unrealistic to be a realist and interpret modern physics as a addendum to Newtonian mechanics!

 

[kurt101]

Given the experimental evidence of the 20th and 21st centuries, I'd say it's highly unrealistic to be a realist and interpret modern physics as a addendum to Newtonian mechanics!

Ok, why? What specific experiments? And obviously we have to be specific about what aspects of a Newtonian universe are kept and what are abandoned in such a discussion. I would like to be able to discuss this, but I am not sure how to do so and stay within the confines of the rules. I know in at least other forums mentioning terms such as absolute time and space are not allowed even if they were for the purpose of understanding why they are invalid or incompatible.

 

[PeterDonis]

I don't want the thread closed.

I understand that, but we still have to have some basis for discussion other than your personal opinion.

I like aspects of the Bohmian Mechanics interpretation, but I think it goes too far in making assumptions that don't fit well with reality.

I will try to find an interpretation I can use for discussions on realism that is acceptable to both myself and this forum.

Unfortunately, the most "realist" interpretation of QM we have is the Bohmian interpretation. If you don't like that one, you're going to like all the others even less.

 

[PeroK]

Ok, why? What specific experiments? And obviously we have to be specific about what aspects of a Newtonian universe are kept and what are abandoned in such a discussion.

Newton's laws don't extend to SR, GR or QM. In some cases they are good approximations, but only in special cases.

 

[PeterDonis]

I see General Relativity, Quantum Mechanics, Bell non-locality, as improvements on understanding a Newtonian Universe, not as invalidating it. I think this is a very reasonable interpretation to hold to

No, it isn't, it's an extremely unreasonable interpretation to hold to. See below.

Ok, why? What specific experiments?

The fact that you have to ask this question tells me that you need to spend some serious time becoming familiar with the vast body of experimental evidence that has forced physicists to abandon Newtonian mechanics and adopt relativity and QM. Richard Feynman once said that "quantum physics was not wished upon us by theorists". The same is true of relativity, although it's harder to see historically because Einstein was able to come up with a working theoretical framework for both special and general relativity based on a fairly small body of evidence. But pretty much every other physicist had to be dragged to relativity kicking and screaming, just as they all had to be dragged to QM. But now that that process has taken place, it is obvious that Newtonian mechanics, considered as a viewpoint on "how the universe works", is simply wrong. The only viable view of Newtonian mechanics now is that it is an approximation to relativity and QM that is valid under certain very restricted conditions. It just so happens that our everyday experience here on Earth, outside of scientific experiments, meets those very restricted conditions.

There is an excellent Living Reviews article on experimental tests of general relativity here:

https://link.springer.com/article/10.12942/lrr-2014-4

Unfortunately I don't know of a similar single source for experimental tests of QM. But some obvious pivotal experimental tests historically were:

Black body radiation spectrum

Photoelectric effect

Compton effect

Davisson-Germer experiment

Stern-Gerlach experiment

Lamb shift

 

[DrChinese]

This is the exactly the correct explanation for this phenomenon and it's well understood. It's just the effect of conditioning on a Collider. I tried to explain this to DrChinese in another thread already without success. His central misunderstanding is to believe that A & D are entangled when really they are in a perfectly uncorrelated product state. Only the conditional subensembles are entangled, but that doesn't entail any causal relationship, because conditioning on a collider generally generates fake correlations. Entanglement swapping indeed adds nothing new to the mystery of entanglement.

The experiment is performed on the entangled sub-ensemble, the other pairs are not of any interest. You never consider B & C pairs that do not arrive together within a suitably small time window. The other pairs appear equally often, separated into 4 combinations. For all intents and purposes, all of those are considered.

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

Obviously, the problem with your idea is that you want it both ways... the A & D pairs are in product states to begin with, but they become entangled by your purported distillation process. Were that true, then you would be agreeing with me and be inconsistent. But I will try to work through your reasoning as best possible anyway.

As I mention, your distillation process - "entanglement swapping" or "quantum teleportation" is what everyone else calls it - doesn't have enough outcome options to match up photons with leading to perfect correlations for ultimately entangled A & D pairs. There are essentially a large (or perhaps infinite) number of angle settings at which they would need to matched for your idea to work. Your idea being that A & D happen to have identical predetermined orientations (which are reflected in their respective twins, B & C).

So let's say we have A & B entangled, and C & D entangled. We ALREADY know from Bell that the A & B (or C & D) entanglement cannot itself be explained by any local hidden variables. So basically, your idea is already failed (as you are attempting to push a local realistic explanation for entanglement swapping in which Bell's Inequality is violated).

Regardless, and still going down your path: We compare B & C, considering only those pairs in which B & C arrive together at a single polarizing beam splitter within a small time window; and are therefore indistinguishable. There can be only 4 outcomes corresponding to the four maximally entangled Bell states |Φ+>, |Ψ+>, |Ψ−>, and |Φ −>. If your idea is correct, there is no "process" occurring - since there is nothing happening when B & C interact other than to "reveal" some pre-existing correlation. But what would that pre-existing correlation be IF there are only 4 possibilities? That implies that there exist exactly 2 and only 2 different streams possible from a PDC source (since combining those 2 types you'd get 2x2=4). That doesn't sound too crazy at first blush, but it begs the question: why do you need the compared streams to be *indistinguishable* to reveal their matching state? You could equally well run the B & C photons into *different* polarizing beam splitters such that their arrival times were within the coincidence window - just as they would be if they appeared in the same PBS. They would now be distinguishable (remember there are still only 4 outcome possibilities, as you need there to be only 2 types of PDC streams), but there would be no interaction and no swapping process. This shouldn't make any difference if your idea is correct. A & D do NOT end up entangled, unless B & C are indistinguishable. Which is the opposite of your idea.

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

The ideas you push are wrong, and it is more fully debunked in a generally accepted reference I gave in post #36. In their words:

https://arxiv.org/abs/0911.1314

"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."

"In our scenario, however, they are two separate sources S1 and S2. It it thus natural to assume that the local model assigns two different states λ1 and λ2, one to each source..." [Just as I describe above.]

"Even though the local variables λ1 and λ2 are initially independent, once conditioned on the joint measurement result of Bob they will bear enough correlations to reproduce 2 non-trivial correlations between Alice’s and Charles’s system. These correlations, however, are much weaker than those that can be established through joint measurements in quantum theory. We introduce below a (quadratic) Bell inequality that is satisfied by all bilocal correlations, but which is violated by quantum correlations." [I.e. you can't get perfect correlations from your assumptions.]

I could quote as many additional seminal papers on the subject as one would desire. None of them will agree with your analysis, and as of yet no one here has bothered to present anything remotely suitable to rebut the above references or anything I have said on the subject.

This is the Interpretations subforum and the rules are more relaxed here; but generally accepted science is still generally accepted science. The facts are: entanglement swapping is a quantum process, and it itself violates local realism. I say it is a physical process, and if you follow Bohmian Mechanics or MWI you should agree with me. I don't see how it can be viewed as OTHER than a physical process, but I would acknowledge there are plenty of other interpretations that might see things differently. But it is not a local realistic phenomena.

 

[kurt101]

@DrChinese here is a paper that refutes your claim. https://link.springer.com/article/10.1007/s10701-021-00511-3

 

[Nullstein]

The experiment is performed on the entangled sub-ensemble, the other pairs are not of any interest. You never consider B & C pairs that do not arrive together within a suitably small time window. The other pairs appear equally often, separated into 4 combinations. For all intents and purposes, all of those are considered.

Sure, that makes them subensembles, which are entangled. It's just that this kind of entanglement is entirely non-mysterious, since it is a statistical effect.

Obviously, the problem with your idea is that you want it both ways... the A & D pairs are in product states to begin with, but they become entangled by your purported distillation process. Were that true, then you would be agreeing with me and be inconsistent.

First of all, it's not my idea. It's well understood statistics, I provided a reference with thousands of citations. Also, A and D don't become entangled. The full system is in a product state, but the subensembles are entangled. It's just that this entanglement is entirely non-mysterious. What's mysterious still, is that A&B are entangled and that C&D are entangled.

As I mention, your distillation process - "entanglement swapping" or "quantum teleportation" is what everyone else calls it - doesn't have enough outcome options to match up photons with leading to perfect correlations for ultimately entangled A & D pairs. There are essentially a large (or perhaps infinite) number of angle settings at which they would need to matched for your idea to work. Your idea being that A & D happen to have identical predetermined orientations (which are reflected in their respective twins, B & C).

I never claim that A & D have identical predetermined orientations, so that's a non-starter and shows that you haven't understood the argument.

So let's say we have A & B entangled, and C & D entangled. We ALREADY know from Bell that the A & B (or C & D) entanglement cannot itself be explained by any local hidden variables. So basically, your idea is already failed (as you are attempting to push a local realistic explanation for entanglement swapping in which Bell's Inequality is violated).

Again, you misrepresent "my idea". I don't want to explain anything by local hidden variables. I don't believe in hidden variables to begin with. I totally agree that the entanglement between A & B (and C & D respectively) cannot be explained by a local realistic model. The entanglement between A & B is mysterious. It's just that the entanglement of a subensemble of A & D is not mysterious given that the initial pairs are entangled for whatever mysterious reason.

Regardless, and still going down your path: We compare B & C, considering only those pairs in which B & C arrive together at a single polarizing beam splitter within a small time window; and are therefore indistinguishable. There can be only 4 outcomes corresponding to the four maximally entangled Bell states |Φ+>, |Ψ+>, |Ψ−>, and |Φ −>. If your idea is correct, there is no "process" occurring - since there is nothing happening when B & C interact other than to "reveal" some pre-existing correlation.

Not true. There is no "pre-existing correlation" in A & B to begin with, so propagating this correlation by entanglement swapping won't suddenly make it "pre-existing." So you have completely misunderstood the argument.

But what would that pre-existing correlation be IF there are only 4 possibilities?

There is no pre-existing correlation and I didn't claim there was one.

The ideas you push are wrong, and it is more fully debunked in a generally accepted reference I gave in post #36. In their words:

https://arxiv.org/abs/0911.1314

"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."

I fully agree that the subensembles are fully entangled and violate Bell's inequality and that there is no local realistic explanation for this. I'm just saying that entanglement swapping does not add any additional mystery on top of the initial entanglement of the particle pairs A&B and C&D. The swapping "process" itself is just a statistical artifact.

This is the Interpretations subforum and the rules are more relaxed here; but generally accepted science is still generally accepted science. The facts are: entanglement swapping is a quantum process, and it itself violates local realism. I say it is a physical process, and if you follow Bohmian Mechanics or MWI you should agree with me. I don't see how it can be viewed as OTHER than a physical process, but I would acknowledge there are plenty of other interpretations that might see things differently. But it is not a local realistic phenomena.

I don't disagree with any accepted science. It's just that you don't understand the argument I'm making. It is in full agreement with generally accepted science.

 

[PeterDonis]

The full system is in a product state, but the subensembles are entangled.

This doesn't make sense. "Subensembles" don't even have states. In each individual run of the experiment, the full system, consisting of A, B, C, D, is entangled, because pairs of subsystems, A&B, C&D, are entangled.

 

[Nullstein]

This doesn't make sense. "Subensembles" don't even have states. In each individual run of the experiment, the full system, consisting of A, B, C, D, is entangled, because pairs of subsystems, A&B, C&D, are entangled.

Subensembles do have states in the sense that the statistics of the subensemble is perfectly well described by a density matrix. Of course there is entanglement between A&B and C&D, but what I meant to say was that the composite system A&B is not entangled with the composite system C&D and that the subsystem A&D is in a product state.

 

[DrChinese]

1. Sure, that makes them subensembles, which are entangled. It's just that this kind of entanglement is entirely non-mysterious, since it is a statistical effect.

2. First of all, it's not my idea. It's well understood statistics, I provided a reference with thousands of citations. Also, A and D don't become entangled. The full system is in a product state, but the subensembles are entangled. It's just that this entanglement is entirely non-mysterious. What's mysterious still, is that A&B are entangled and that C&D are entangled.

3. I never claim that A & D have identical predetermined orientations, so that's a non-starter and shows that you haven't understood the argument.

4, The entanglement between A & B is mysterious. It's just that the entanglement of a subensemble of A & D is not mysterious given that the initial pairs are entangled for whatever mysterious reason.

1. And how do those sub-ensembles become entangled into 1 of 4 Bell states? By the swapping process, of course! In principle, there are no sub-ensembles that do not cast entangled A & D into an entangled state. So the idea you have - that only the "correlated" sub-ensembles are being selected - is totally wrong. You completely skipped over my explanation about how A & D come to be entangled. Again, there are 4 Bell states that result from a Bell State Analyzer, and they are not entangled unless they are indistinguishable. This idea does not relate to anything you describe, and of course, it can't.

2. It IS your idea... try quoting a source. You place a URL here, and then you extract a relevant quote that directly refutes my argument or directly supports yours. It's easy for me to request, because this is a lop-sided exercise. And please, don't tell me to Google something. You have it, or you don't.

3. Well, you claimed that there is no interaction between B & C that affects A & D. So... how do A & D magically become perfectly correlated?

4. The entire point of entanglement swapping is that it is equally "mysterious". Gisin et al say: "entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests." Maybe you have Gisin (or Zeilinger, or Pan) saying something different?

 

[PeterDonis]

what I meant to say was that the composite system A&B is not entangled with the composite system C&D

Yes.

and that the subsystem A&D is in a product state.

No. Since the subsystems A&B are entangled and the subsystems C&D are entangled, you cannot factor out a product state for the subsystem A&D.

 

[Nullstein]

1. And how do those sub-ensembles become entangled into 1 of 4 Bell states? By the swapping process, of course!

It's not a physical process, it's an artificial selection. Nothing becomes entangled in a physical sense.

In principle, there are no sub-ensembles that do not cast entangled A & D into an entangled state. So the idea you have - that only the "correlated" sub-ensembles are being selected - is totally wrong.

That's not the idea that I have. You are just putting words in my mouth.

You completely skipped over my explanation about how A & D come to be entangled. Again, there are 4 Bell states that result from a Bell State Analyzer, and they are not entangled unless they are indistinguishable. This idea does not relate to anything you describe, and of course, it can't.

Your explanation is based on invalid premises as I have pointed out.

2. It IS your idea... try quoting a source. You place a URL here, and then you extract a relevant quote that directly refutes my argument or directly supports yours. It's easy for me to request, because this is a lop-sided exercise. And please, don't tell me to Google something. You have it, or you don't.

I gave you a reference, just scroll up.

3. Well, you claimed that there is no interaction between B & C that affects A & D. So... how do A & D magically become perfectly correlated?

They don't become perfectly correlated, they are completely uncorrelated. Only a subensemble is perfectly correlated much like a random ensemble of heads and tails becomes perfectly deterministic if you choose only the subensemble of events consisting of only heads.

4. The entire point of entanglement swapping is that it is equally "mysterious". Gisin et al say: "entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests." Maybe you have Gisin (or Zeilinger, or Pan) saying something different?

No, there is no "whole point of entanglement swapping" in the first place, it's just a phenomenon with many applications. Entanglement swapping is a classical statistical phenomenon that happens on top of a quantum mechanical description involving two pairs of entangled particles. I gave you a reference that explains it (with several thousand citations), you just need to read if you are willing to learn.

By the way, nonlocal in the foundations community is just a term that means "violates Bell's inequality." It doesn't entail anything about causality and some people only keep using it for historic reasons. The less interpretation-laden contemporary term would be inseparable.

 

[Nullstein]

No. Since the subsystems A&B are entangled and the subsystems C&D are entangled, you cannot factor out a product state for the subsystem A&D.

That's not correct. First of all, you don't factor anything out. You get the state of a subsystem by taking partial traces. If the full system is in the state $\rho_{AB}\otimes\rho_{CD}$, then the partial trace with respect to B and C will just be $\mathrm{Tr}_B(\rho_{AB})\otimes\mathrm{Tr}_C(\rho_{CD})$, which is a product state.

 

[DrChinese]

1. I gave you a reference, just scroll up.

2. No, there is no "whole point of entanglement swapping" in the first place, it's just a phenomenon with many applications. Entanglement swapping is a classical statistical phenomenon that happens on top of a quantum mechanical description involving two pairs of entangled particles. I gave you a reference that explains it (with several thousand citations), you just need to read if you are willing to learn.

3. By the way, nonlocal in the foundations community is just a term that means "violates Bell's inequality." It doesn't entail anything about causality and some people only keep using it for historic reasons. The less interpretation-laden contemporary term would be inseparable.

1. LOL. Not surprising you can't produce anything to counter:

"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."-Gisin et al.

If they are entangled, they are entangled. It is not "revealing a statistical coincidence". Please, maybe you have something different from Zeilinger, Tittel, Pan, Kwiat, Zurek, Weihs, Branciard, or any of the other pioneers in this area.2. The whole point is the whole point. That's why it's a thing. Otherwise, it wouldn't be a thing.3. I agree with this. Quantum nonlocality is what Bell's Theorem demonstrates. It doesn't require a rejection of locality, it could also be explained by a rejection of causal direction, by MWI, and any of a number of viable interpretations. Of course, swapping is a demonstration of a much deeper level of quantum nonlocality... see 2 above.

 

[johnsankey]

All I know is that when I was trapping single ions of barium or strontium, and playing Maxwell's daemon with one electron at a time, I saw quanta that were as clear and definite as golf balls. And when I use observations as the basis for inference with entangled states, I see an equally clear result; cf. [Link to personal website redacted by the Mentors]
Never forget the gap between mathematics based upon consistency, and physics based on observables.

 

[Nullstein]

1. LOL. Not surprising you can't produce anything to counter:

"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."-Gisin et al.

I don't have to counter that because I fully agree with it. You still don't seem to understand that. The subensemble paris are genuinely entangled pairs in every aspect. The fact that you don't even understand what my position is just shows that you are still very far away from being able to formulate a counterargument. First you need to put some effort into understanding the actual argument.

Just to explain it again in simpler terms: Both A&B, C&D and the subensembles of A&D are entangled. But the point is that while we have no good explanation for the entanglement of A&B and C&D, the entanglement of the subensembles of A&D can be understood using classical statistics as long as one doesn't ask how A&B and C&D came to be entangled in the first place. Entanglement swapping thus doesn't add to the mystery.

If they are entangled, they are entangled. It is not "revealing a statistical coincidence". Please, maybe you have something different from Zeilinger, Tittel, Pan, Kwiat, Zurek, Weihs, Branciard, or any of the other pioneers in this area.

I agree that I the subensembles are entangled, so I don't have to counter these people. None of what I'm saying is in contradiction to them.

2. The whole point is the whole point. That's why it's a thing. Otherwise, it wouldn't be a thing.

There is no point to a physical phenomenon. There is no point to entanglement swapping just like there is no point to gravity. Nature doesn't want to make a point.

 

[PeterDonis]

First of all, you don't factor anything out.

You do if you want to avoid throwing away information.

You get the state of a subsystem by taking partial traces.

No, you get something which in some respects you can call a "state" of a subsystem, but which throws away information about the entanglement. So of course it won't tell you about the entanglement information that you threw away in getting it. In an entangled system, no individual subsystem has a state in the strict sense; only the full joint system does. Taking partial traces can be useful for some computations, but that does not mean you can interpret it physically the way you are claiming, precisely because doing it throws away important physical information.

 

[Nullstein]

You do if you want to avoid throwing away information.

I don't want to avoid throwing away information. I want the state of the subsystem, which is the state that contains all information about the subsystem, but no information beyond that. Otherwise it would just be the state of a larger system and not the subsystem under consideration.

No, you get something which in some respects you can call a "state" of a subsystem, but which throws away information about the entanglement. So of course it won't tell you about the entanglement information that you threw away in getting it. In an entangled system, no individual subsystem has a state in the strict sense; only the full joint system does. Taking partial traces can be useful for some computations, but that does not mean you can interpret it physically the way you are claiming, precisely because doing it throws away important physical information.

Not true, there is a state of the full system, which contains all information about the subsystem and the rest of the system and additionally information about their entanglement. And there is the state of the subsystem, which contains all information about the subsystem and nothing beyond it. That's absolute standard terminology in quantum theory. See e.g. Breuer, Petruccione "The Theory of Open Quantum Systems":

 

[PeterDonis]

I don't want to avoid throwing away information. I want the state of the subsystem, which is the state that contains all information about the subsystem, but no information beyond that.

I understand what the "state" obtained by partial tracing is. I just don't think it justifies the claims you are making.

See e.g. Breuer, Petruccione "The Theory of Open Quantum Systems":

This reference supports what I just said above. It explicitly says that the partial trace is only relevant if all you are interested in is measurements restricted to the subsystem in question. But that is not the case in the experiments under discussion here.

 

[Nullstein]

I understand what the "state" obtained by partial tracing is. I just don't think it justifies the claims you are making.

What claims am I making? I said that the subsystem A&D is not entangled, which is absolutely true given standard terminology and there is good reason for this choice of terminology. If a subsystem is not entangled, this will be reflected in the data, i.e. there will be zero correlations in experiments pertaining only to the subsystem.

This reference supports what I just said above. It explicitly says that the partial trace is only relevant if all you are interested in is measurements restricted to the subsystem in question. But that is not the case in the experiments under discussion here.

If I'm talking about entanglement between A&D, I'm only interested in measurements restricted to this system. Particle A is not entangled with particle D. Sure, I have thrown away the information that particle A is entangled with particle B and that particle C is entangled with particle D, but that's not relevant for the statement that particle A is not entangled with particle D. All information about the entanglement between A and D is fully contained in the reduced density matrix of the subsystem A&D. The subsystem A&D is not entangled. One really shouldn't have to discuss these basics in an intermediate level thread.

Sure, one needs the state of the full system to discuss the experiment, but one just needs the state of the subsystem A&D to make the statement that A&D is not entangled. This is only an aspect of the discussion, so it's perfectly valid to talk about the subsystem regarding this specific aspect.

The fact that the subsystem A&D is not entangled is fully in accordance with the experimental facts. If you don't have information about B&C, you cannot perform the post-selection and you will get find completely uncorrelated measurement results. As I said multiple times, only the subensembles are entangled. In the full system, there are zero correlations between A and D. You will absolutely see this fact in the data. It's akin to rolling two dice. The full dataset will be perfectly uncorrelated, but if you post-select only those throws that, say, add up to 5, then this subensemble will be correlated. (And nothing is mysterious about that.)

 

[Nullstein]

Here's a different way to see that A cannot possibly be entangled with D: Since we know that A&B is in a maximally entangled state (the standard EPRB singlet state), then by the monogamy of entanglement, A cannot possibly be entangled with anything else and in particular not with D.

 

[Maarten Havinga]

1. LOL. Not surprising you can't produce anything to counter:

"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."-Gisin et al.

It is clear to me that also academia have different opinions on whether they are truly entangled and how to interpret it. It's simply a difficult subject and all of us can't know everything. I'm sure I don't, after googling around and reading your comments.

I'm afraid this discussion is not going to be constructive unless we allow for others disagreeing with ourselves - just leaving it like that. In any case, the best that can be achieved is an interpretation that matches observations and makes everything sort of understandable from our own beliefs. It seems to me like everyone already has that! And it's not like we need to convert others to those beliefs, I'd say.

Regardless of what is the truth, I'm myself intrigued by Mark v Raamsdonk's view: that entanglement is more fundamental to the geometry of spacetime and general relativity is the emergent description in a natural situation. It's not my goal to have you agree with me.

 

[vanhees71]

This doesn't make sense. "Subensembles" don't even have states. In each individual run of the experiment, the full system, consisting of A, B, C, D, is entangled, because pairs of subsystems, A&B, C&D, are entangled.

Of course "subensembles" have states. In this case the subensembles are operationally defined by doing coincidence measurements on photons B and C. The statistical operator of the subensembles is then given by the corresponding projections of the statistical operator describing the full ensemble (which is of course a bit idealized assuming ideal detectors).

The important point is that you can select the subensembles even after all measurements are done if you have a complete measurement protocol involving the coincidence measurements on photons B&C as well as on photons A&D. The entanglement between photons A&D in each of the subensembles is due to the initial state, i.e., the entanglement between A&B as well as C&D, while the initial state describing the full ensemble is of the form $\hat{\rho}=\hat{\rho}_{AB} \otimes \hat{\rho}_{CD}$, i.e., for the full ensemble photons A and D are indeed not entangled, and it's indeed all about correlations and statistics. In the subensembles A&D are entangled through selection (or even post-selection) due to measurements on B&C, i.e., you are able to prepare entangled states of photons A&D without A&D having ever been in direct "causal contact", but also without violating anywhere locality (in the usual sense of relativistic local QFT, which is used to describe this experiment).

 

[vanhees71]

It's not a physical process, it's an artificial selection. Nothing becomes entangled in a physical sense.

But for the (post-)selected subensembles, based on coincidence measurements on photons B&C, the photons A&D are indeed entangled. That's just what's called "entanglement swapping".

That's not the idea that I have. You are just putting words in my mouth.Your explanation is based on invalid premises as I have pointed out.

I gave you a reference, just scroll up.

They don't become perfectly correlated, they are completely uncorrelated. Only a subensemble is perfectly correlated much like a random ensemble of heads and tails becomes perfectly deterministic if you choose only the subensemble of events consisting of only heads.

That's correct, but it wouldn't work for any "classical ensembles". Entanglement swapping in this experiment only works because photons A&B as well as photons C&D are entangled. It's not explainable in terms of a "local realistic theory" in Bell's sense, and indeed for each subensemble photons A&D are entangled and thus can be used to demonstrate the violation of Bell's inequality.

No, there is no "whole point of entanglement swapping" in the first place, it's just a phenomenon with many applications. Entanglement swapping is a classical statistical phenomenon that happens on top of a quantum mechanical description involving two pairs of entangled particles. I gave you a reference that explains it (with several thousand citations), you just need to read if you are willing to learn.

It's NOT a "classical statistical phenomenon" but a generic "quantum statistical phenomenon".

By the way, nonlocal in the foundations community is just a term that means "violates Bell's inequality." It doesn't entail anything about causality and some people only keep using it for historic reasons. The less interpretation-laden contemporary term would be inseparable.

Indeed, but it's hopeless, because in this forum people insist on using these confusing "double meaning" of the words "local" and "non-local". When I say local I always mean it, of course, in the well-defined mathematical sense of relativistic local (sic!) QFT: the Hamilton density is built from field operators that transform locally (sic) under proper orthochronous Poincare transformations, and local (sic) observable-operators commute at space-like separation of their arguments (microcausality), leading to the well-established class of relativistic QTs with a unitary, Poincare covariant S-matrix, obeying the cluster-decomposition principle but of course are able to describe all the experiments with entangled states but at the same time fulfill the said constraints of relativistic causality by realizing them in terms of a local (sic!) relativistic QFT.

 

[akvadrako]

The interesting thing is that entanglement between sub-ensembles can be created via post-selection, even in the past. We know it's real entanglement, since they can be used to violate Bell inequalities. Obviously it's just a statistical phenomenon, not time travel, strongly implying all entanglement is just a statistical phenomenon.

 

[vanhees71]

Of course, it's a "statistical phenomenon", but it's a generic "quantum phenomenon", i.e., it cannot be modeled with "local realistic HV theories", exactly because Bell's inequalities are violated. It's all about correlations, not about a violation of locality in the sense of local relativistic QFTs, which by construction cannot imply any "spooky actions at a distance".

 

[Nullstein]

But for the (post-)selected subensembles, based on coincidence measurements on photons B&C, the photons A&D are indeed entangled. That's just what's called "entanglement swapping".

I never objected to that. I said from the very beginning that the subensembles are entangled. My only point is that the swapping itself is just a well understood statistical phenomenon and it adds nothing to the mystery of entanglement. All the mystery is contained in the initial entanglement of the A&B and C&D pairs.

That's correct, but it wouldn't work for any "classical ensembles". Entanglement swapping in this experiment only works because photons A&B as well as photons C&D are entangled. It's not explainable in terms of a "local realistic theory" in Bell's sense, and indeed for each subensemble photons A&D are entangled and thus can be used to demonstrate the violation of Bell's inequality.

Again, I fully agree with that. One needs initial pairs of entangled particles to find entanglement in the post-selected ensembles, so this is a genuine quantum situation. I'm just saying that the swapping process alone is a fully understood classical statistical phenomenon. The A&D subensembles just inherit the original entanglement of A&B, C&D by this well understood process. Hence, entanglement swapping is not a more severe version of entanglement, as DrChinese wants to imply. Instead, it's fully understood classical statistics and adds nothing to the mystery. The only mystery in an entanglement swapping scenario is the initial entanglement of A&B and C&D, precisely, because we can not just explain it by invoking classical statistics.

It's NOT a "classical statistical phenomenon" but a generic "quantum statistical phenomenon".

The swapping itself is a classical statistical phenomenon. The resulting entangled subensembles of A&D particles is a quantum statistical phenomenon, but not because of the swapping. The quantum aspecct is fully contained in the initial entanglement of the initial pairs.

 

[Nullstein]

Of course, it's a "statistical phenomenon", but it's a generic "quantum phenomenon", i.e., it cannot be modeled with "local realistic HV theories", exactly because Bell's inequalities are violated. It's all about correlations, not about a violation of locality in the sense of local relativistic QFTs, which by construction cannot imply any "spooky actions at a distance".

I fully agree and I never objected to that. All I'm saying is that the swapping itself is classical. All of the quantum is contained in the entanglement of the initial pairs. The swapping adds nothing peculiar on top of the entanglement of the initial pairs. The A&D subensembles are fully entangled and violate Bell's inequality, but this is just the result of post-selection and it's entirely non-surprising to someone who knows classical statistics. All the mystery is in the entanglement of the initial pairs. (If they weren't entangled in the first place, one could not post-select an entangled subensemble.)

 

[vanhees71]

I never objected to that. I said from the very beginning that the subensembles are entangled. My only point is that the swapping itself is just a well understood statistical phenomenon and it adds nothing to the mystery of entanglement. All the mystery is contained in the initial entanglement of the A&B and C&D pairs.

Well, there is no mystery to begin with. Entanglement is a pretty straight-forward consequence of the mathematical basic structure of QT. There is nothing mystical in why you can prepare two photons in various ways in an entangled state. In the very beginning of these investigations it done with a atomic cascade (Alan Aspect) et al. Nowadays one rather uses parametric downconversion or quantum dots for higher efficiency. The entanglement of the two photons in polarization and/or momentum is not at all mysterious.

Again, I fully agree with that. One needs initial pairs of entangled particles to find entanglement in the post-selected ensembles, so this is a genuine quantum situation. I'm just saying that the swapping process alone is a fully understood classical statistical phenomenon. The A&D subensembles just inherit the original entanglement of A&B, C&D by this well understood process. Hence, entanglement swapping is not a more severe version of entanglement, as DrChinese wants to imply. Instead, it's fully understood classical statistics and adds nothing to the mystery. The only mystery in an entanglement swapping scenario is the initial entanglement of A&B and C&D, precisely, because we can not just explain it by invoking classical statistics.

It's NOT classical, it's QUANTUM. Otherwise we seem to fully agree.

The swapping itself is a classical statistical phenomenon. The resulting entangled subensembles of A&D particles is a quantum statistical phenomenon, but not because of the swapping. The quantum aspecct is fully contained in the initial entanglement of the initial pairs.

Sure, all these quantum correlations are due to the preparation of the two photon pairs, and indeed there's no need to assume any "spooky actions at a distance" to understand these very correlations within a local relativistic QFT, which excludes any "spooky actions at a distance" by construction.

 

[CoolMint]

But those quantum correlations arise due to inseparability. Which is quite the mystery given that everything 'classical' appears completely separable.

 

[Nullstein]

Well, there is no mystery to begin with. Entanglement is a pretty straight-forward consequence of the mathematical basic structure of QT. There is nothing mystical in why you can prepare two photons in various ways in an entangled state. In the very beginning of these investigations it done with a atomic cascade (Alan Aspect) et al. Nowadays one rather uses parametric downconversion or quantum dots for higher efficiency. The entanglement of the two photons in polarization and/or momentum is not at all mysterious.

I agree that it is fully described my quantum mechanics, but for me and many people, the entanglement of the initial pairs is still mysterious, because the classical notion of causality seems to be inadequate in quantum mechanics and we don't have a well motivated quantum mechanical replacement. The entanglement can't be caused by any classical mechanism unless one accepts superdeterministic explanations (that's the content of Bell's theorem), so how did it came to be then if it wasn't caused? Personally, I do feel that a generalized notion of causality that is compatible with quantum mechanics will eventually be discovered, but until then, it remains a mystery, at least for me.

It's NOT classical, it's QUANTUM. Otherwise we seem to fully agree.

What is quantum about the mere act of selecting a subensemble out of an already recorded list of measurement results?

Sure, all these quantum correlations are due to the preparation of the two photon pairs, and indeed there's no need to assume any "spooky actions at a distance" to understand these very correlations within a local relativistic QFT, which excludes any "spooky actions at a distance" by construction.

I agree with that.

 

[vanhees71]

But those quantum correlations arise due to inseparability. Which is quite the mystery given that everything 'classical' appears completely separable.

Exactly, quantum correlations are inseparable, but there's no need for "spooky actions at a distance" to describe them. Einstein himself did not like the EPR paper, because the inseparability was his real concern, and it's Bell's merit to have found a way to empirically test whether nature is describable with a local, deterministic hidden-variable theory or whether the inseparability of QT is correct, and as is very well demonstrated in all experiments, the latter is the case.

 

[DrChinese]

1. I don't have to counter that because I fully agree with it. You still don't seem to understand that. The subensemble paris are genuinely entangled pairs in every aspect.

2, Just to explain it again in simpler terms: Both A&B, C&D and the subensembles of A&D are entangled. But the point is that while we have no good explanation for the entanglement of A&B and C&D, the entanglement of the subensembles of A&D can be understood using classical statistics as long as one doesn't ask how A&B and C&D came to be entangled in the first place. Entanglement swapping thus doesn't add to the mystery.

1. Great... except that in post #76, you say:

"Here's a different way to see that A cannot possibly be entangled with D: Since we know that A&B is in a maximally entangled state (the standard EPRB singlet state), then by the monogamy of entanglement, A cannot possibly be entangled with anything else and in particular not with D."

Your above statement of course is completely wrong. The reason it is called "entanglement swapping" is because A's monogamous entanglement is swapped from B to D.2. There are no "statistical sub-ensembles" of pairs A & B and C & D that have any properties that will re-produce the quantum mechanical results (at least not without knowing how A & D are to be measured first).
I have presented an example to explain this, and I have presented a paper by a top team which provides the formal theoretical no-go argument. Please, feel free to provide a counter-example. So far, you have failed to provide a single quote by someone in the field with suitable credentials. If you were representing the mainstream, you'd be able to reel that off with ease. In the hundreds of papers I have read on teleportation, none of them say anything OTHER than the Bell State Analyzer is responsible for the process whereby the A & D photons become entangled. (I didn't use the word "causes" in that sentence, for the reason that temporal order of the process can be ambiguous.)

"This procedure is also known as ”Entanglement Swapping” because one starts with two pairs of entangled photons A–B and C–D, subjects photons B and C to a Bell-state measurement by which photons A and D also become entangled."-Zeilinger et al

Try to explain what (heretofor unknown) properties an entangled PDC pair (A & B) must have such that it can be "selected" (by a measurement on B & C) into some subset so that photon A is now matched to photon D; yielding the usual quantum relationship. You will quickly see this is not possible, there are no subsets with these attributes. It requires the creation of a direct relationship between A & D to yield the statistical results, even though A & D have never existed within a common spacetime region.

Ask yourself: why exactly does the Bell State Measurement need to be done such that the B & C photons are indistinguishable? That seems an odd requirement, if all we are doing is selecting a subset.

--------------------------------
In all fairness, I have clearly demonstrated that Kurt101's premise below is false, and that entanglement of A & D (which are not local to each other) occurs by executing a process on distant B & C. For this thread, that should be enough. I will start a separate thread if necessary to demonstrate why there are no subsets of B & C that condition an entangled relationship between A & D (without of course there being changes to A & D on bringing bringing B & C together).

"3. Entanglement is a non-local behavior between particles that is created through local preparation."

 

[vanhees71]

I agree that it is fully described my quantum mechanics, but for me and many people, the entanglement of the initial pairs is still mysterious, because the classical notion of causality seems to be inadequate in quantum mechanics and we don't have a well motivated quantum mechanical replacement. The entanglement can't be caused by any classical mechanism unless one accepts superdeterministic explanations (that's the content of Bell's theorem), so how did it came to be then if it wasn't caused? Personally, I do feel that a generalized notion of causality that is compatible with quantum mechanics will eventually be discovered, but until then, it remains a mystery, at least for me.

Why should, in your opinion, nature behave classically? It's the other way round: Classical behavior is an effective, approximate description of properties of macroscopic systems. On a more fundamental level, it's however a many-body quantum system.

Also quantum theory is completely causal, i.e., given the state at an initial time and the Hamiltonian of the system the state is known at any later time. It's, however, indeterministic, because there's no state, where all observables take determined values, and thus the knowledge of the state only implies the probabilities for the outcomes of measurements on any observable of this system, i.e., nature is inherently probabilistic rather than deterministic. Imho there's no way out of this result of physical research over the centuries, and as soon as you accept this, there's no more mystery in entanglement. To the contrary, QT delivers an amazingly accurate description of these phenomena.

What is quantum about the mere act of selecting a subensemble out of an already recorded list of measurement results?

Well, this selection is of course entirely "classical". What's quantum is the entanglement of photons A&D in these subensembles. This cannot be explained in any classical way but only by the entanglement of photons A&B and C&D in the initial state.

 

[vanhees71]

1. Great... except that in post #76, you say:

"Here's a different way to see that A cannot possibly be entangled with D: Since we know that A&B is in a maximally entangled state (the standard EPRB singlet state), then by the monogamy of entanglement, A cannot possibly be entangled with anything else and in particular not with D."

Your above statement of course is completely wrong. The reason it is called "entanglement swapping" is because A's monogamous entanglement is swapped from B to D.2. There are no "statistical sub-ensembles" of pairs A & B and C & D that have any properties that will re-produce the quantum mechanical results (at least not without knowing how A & D are to be measured first).
I have presented an example to explain this, and I have presented a paper by a top team which provides the formal theoretical no-go argument. Please, feel free to provide a counter-example. So far, you have failed to provide a single quote by someone in the field with suitable credentials. If you were representing the mainstream, you'd be able to reel that off with ease. In the hundreds of papers I have read on teleportation, none of them say anything OTHER than the Bell State Analyzer is responsible for the process whereby the A & D photons become entangled. (I didn't use the word "causes" in that sentence, for the reason that temporal order of the process can be ambiguous.)

That's of course true. The point here is to use measurements on photons B&C (uncorrelated in the initial state!) to select (or even post-select) subensembles where A&D are entangled (but uncorrelated in the initial state, and this is also not changed by the measurements on B&C, i.e., the total ensemble of A&D is just described by the product state of two completely unpolarized photons). It's the statistics of different ensembles: For the full ensemble A&D are just uncorrelated photons. For each of the four subensembles, chosen by projection measurements on B&C, A&D are entangled, i.e., in the corresponding Bell state, and thus (in a sense maximally) correlated.

"This procedure is also known as ”Entanglement Swapping” because one starts with two pairs of entangled photons A–B and C–D, subjects photons B and C to a Bell-state measurement by which photons A and D also become entangled."-Zeilinger et al

Try to explain what (heretofor unknown) properties an entangled PDC pair (A & B) must have such that it can be "selected" (by a measurement on B & C) into some subset so that photon A is now matched to photon D; yielding the usual quantum relationship. You will quickly see this is not possible, there are no subsets with these attributes. It requires the creation of a direct relationship between A & D to yield the statistical results, even though A & D have never existed within a common spacetime region.

Indeed, the only properties the four photons must have is that A&B as well as C&D are prepared as entangled photon pairs. The initial state, describing the four photons is $\hat{\rho}=\hat{\rho}_{AB} \otimes \hat{\rho}_{CD}$, where $\hat{\rho}_{AB}=|\Psi_{AB} \rangle \langle |\Psi_{AB} \rangle$ with $\Psi_{AB}$ being a Bell state (and analogously of the pair C&D). Within Q(F)T there are no other properties (aka "hidden variables"), and there are also no other properties needed to describe the outcome of the experiment.

Ask yourself: why exactly does the Bell State Measurement need to be done such that the B & C photons are indistinguishable? That seems an odd requirement, if all we are doing is selecting a subset.

That's indeed not and odd requirement, but the prerequisite to really realize the "entanglement-swapping protocol".

 

[Nullstein]

1. Great... except that in post #76, you say:

"Here's a different way to see that A cannot possibly be entangled with D: Since we know that A&B is in a maximally entangled state (the standard EPRB singlet state), then by the monogamy of entanglement, A cannot possibly be entangled with anything else and in particular not with D."

Your above statement of course is completely wrong. The reason it is called "entanglement swapping" is because A's monogamous entanglement is swapped from B to D.

You fail to understand the difference between the full ensemble and the subensembles. The full ensemble is not entangled. The subensembles are entangled. Nothing is actively swapped, the subensemble arises purely due to selection. The local measurement at B&C has no influence on the state of the A&D subsystem. The no communication theorem clearly proves that $\mathrm{Tr}_{BC}(P\rho) = \mathrm{Tr}_{BC}(\rho)$ if $P$ only acts on the B&C subsystem.

2. There are no "statistical sub-ensembles" of pairs A & B and C & D that have any properties that will re-produce the quantum mechanical results (at least not without knowing how A & D are to be measured first).

That's not correct. Since the state of the A&D subsystem is not changed by the local measurement at B&C, it must already contain all the entangled subensembles that are post-selected later. You may just not know how to select them without the data from B&C. The full, non-entangled state of A&D will yield the entangled subensembles upon conditioning on the data from B&C.

I have presented an example to explain this, and I have presented a paper by a top team which provides the formal theoretical no-go argument. Please, feel free to provide a counter-example. So far, you have failed to provide a single quote by someone in the field with suitable credentials. If you were representing the mainstream, you'd be able to reel that off with ease. In the hundreds of papers I have read on teleportation, none of them say anything OTHER than the Bell State Analyzer is responsible for the process whereby the A & D photons become entangled. (I didn't use the word "causes" in that sentence, for the reason that temporal order of the process can be ambiguous.)

"This procedure is also known as ”Entanglement Swapping” because one starts with two pairs of entangled photons A–B and C–D, subjects photons B and C to a Bell-state measurement by which photons A and D also become entangled."-Zeilinger et al

Try to explain what (heretofor unknown) properties an entangled PDC pair (A & B) must have such that it can be "selected" (by a measurement on B & C) into some subset so that photon A is now matched to photon D; yielding the usual quantum relationship. You will quickly see this is not possible, there are no subsets with these attributes. It requires the creation of a direct relationship between A & D to yield the statistical results, even though A & D have never existed within a common spacetime region.

Ask yourself: why exactly does the Bell State Measurement need to be done such that the B & C photons are indistinguishable? That seems an odd requirement, if all we are doing is selecting a subset.

There is nothing odd about that. It just happens to be the procedure that leads to the correct post-selection rule. That just follows from the math.

 

[Nullstein]

Why should, in your opinion, nature behave classically?

It shouldn't in my opinion. It's just that we don't have any accepted notion of causality in quantum theory yet, so people, who want to understand the causal mechanism behind all of this, can't be satisfied quite yet. Sure, we have a theory that describes everything precisely, but it doesn't come with a causal mechanism. The situation was better in the classical theory.

Also quantum theory is completely causal, i.e., given the state at an initial time and the Hamiltonian of the system the state is known at any later time. It's, however, indeterministic, because there's no state, where all observables take determined values, and thus the knowledge of the state only implies the probabilities for the outcomes of measurements on any observable of this system, i.e., nature is inherently probabilistic rather than deterministic. Imho there's no way out of this result of physical research over the centuries, and as soon as you accept this, there's no more mystery in entanglement. To the contrary, QT delivers an amazingly accurate description of these phenomena.

I agree that QT delivers an accurate description of the phenomena, but as you said, you have to accept the formalism and not ask any deeper questions in order to be happy. Not everyone is satisfied with that.

Well, this selection is of course entirely "classical". What's quantum is the entanglement of photons A&D in these subensembles. This cannot be explained in any classical way but only by the entanglement of photons A&B and C&D in the initial state.

I agree. When I'm saying that entanglement swapping is understood classically, I'm referring to the fact that the act of post-selection and thereby introducing correlation into the subensembles is a purely classical process. Of course, there are still quantum phenomena involved.

 

[vanhees71]

You fail to understand the difference between the full ensemble and the subensembles. The full ensemble is not entangled. The subensembles are entangled. Nothing is actively swapped, the subensemble arises purely due to selection. The local measurement at B&C has no influence on the state of the A&D subsystem. The no communication theorem clearly proves that $\mathrm{Tr}_{BC}(P\rho) = \mathrm{Tr}_{BC}(\rho)$ if $P$ only acts on the B&C subsystem.

No, in this case in the subensembles A&D are indeed entangled, and the two traces are not the same. For the rather simple calculation (working with the corresponding state vectors), see, e.g.,

https://doi.org/10.1103/PhysRevLett.80.3891

That's not correct. Since the state of the A&D subsystem is not changed by the local measurement at B&C, it must already contain all the entangled subensembles that are post-selected later. You may just not know how to select them without the data from B&C. The full, non-entangled state of A&D will yield the entangled subensembles upon conditioning on the data from B&C.

Of course you cannot select them without the data from B&C. It's important to always look at real experiments and not discuss about measurements that haven't been really done or are even physically impossible.

There is nothing odd about that. It just happens to be the procedure that leads to the correct post-selection rule. That just follows from the math.

That's true, but you must do the correct math ;-).

 

[gentzen]

I will start a separate thread if necessary to demonstrate why there are no subsets of B & C that condition an entangled relationship between A & D (without of course there being changes to A & D on bringing bringing B & C together).

Yes, please do. But not for "convincing" Nullstein. It would have been "his" task to bring forward a convincing argument, including references to back it up.

Are you saying that the difficult Bell-state measurements on B & C change the relationship between A & D in other ways than by partitioning it into 4 subensembles? I sort of get your argument that the mystery of the entanglement between A & B and C & D alone cannot be enough to explain the mystery of entanglement swapping, because if "the rest" could just be explained classically, then the required measurement on B & C should be less difficult than it actually is. But if you would claim that this difficult measurement on B & C could change the state of A & D by some instantaneous action at a distance, then it would be "your" task to bring forward a convincing argument, including references to back it up.

In the hundreds of papers I have read on teleportation, none of them say anything OTHER than the Bell State Analyzer is responsible for the process whereby the A & D photons become entangled. (I didn't use the word "causes" in that sentence, for the reason that temporal order of the process can be ambiguous.)

That's of course true. The point here is to use measurements on photons B&C (uncorrelated in the initial state!) to select (or even post-select) subensembles where A&D are entangled (but uncorrelated in the initial state, and this is also not changed by the measurements on B&C, i.e., the total ensemble of A&D is just described by the product state of two completely unpolarized photons). It's the statistics of different ensembles: For the full ensemble A&D are just uncorrelated photons. For each of the four subensembles, chosen by projection measurements on B&C, A&D are entangled, i.e., in the corresponding Bell state, and thus (in a sense maximally) correlated.

Despite starting with "That's of course true," vanhess71 makes it pretty clear that what is entangled are the "selected" the subensembles of A & D, but not the total ensemble of A & D.

 

[Nullstein]

No, in this case in the subensembles A&D are indeed entangled, and the two traces are not the same. For the rather simple calculation (working with the corresponding state vectors), see, e.g.,

https://doi.org/10.1103/PhysRevLett.80.3891

The subensembles are of course entangled, as I said multiple times. I don't deny that. But the full ensemble has no entanglement (between A&D) even after the measurement at B&C. There is no contradiction. In that paper, they project onto a Bell state to go from the full ensemble to a subensemble. But if you just perform the measurement and still describe everything using the full ensemble (which you have to do if you're interested in the statistics of the unconditioned A&D subsystem after measurement at B&C), then $P(\rho)$ is really given by
$$P(\rho) = \sum_i (\mathbb 1_A\otimes P_{i,BC}\otimes\mathbb 1_D)\rho(\mathbb 1_A\otimes P_{i,BC}\otimes\mathbb 1_D)$$ where the $P_{i,BC}$ are the four projectors onto the Bell basis and then by the no communication theorem, you get
$$\rho_{AD,after} = \mathrm{Tr}_{BC}(P(\rho_{AB}\otimes\rho_{CD})) =\mathrm{Tr}_{BC}(\rho_{AB}\otimes\rho_{CD}) =\rho_{AD,before}$$
The full ensemble of the subsystem A&D is the same as before. If you take $P$ to be a projection onto only one of the Bell states, say $P_{3,BC}$, then of course you will find an entangled state, but you also aren't talking about the full ensemble anymore.

(Just in case anyone asks for a citation for this simple computation, here it is: https://arxiv.org/pdf/quant-ph/0212023.pdf, sec. II.E)

Of course you cannot select them without the data from B&C. It's important to always look at real experiments and not discuss about measurements that haven't been really done or are even physically impossible.

Well, I said from the beginning that you need the data from B&C for this post-selection, so I don't see what your point is here.

That's true, but you must do the correct math ;-).

I did the correct math. I'm just talking about the transition from the full ensemble to the full ensemble, while the paper talks about the transition from the full ensemble to a subensemble. I'm in full agreement with the paper. As I always said, the subensembles are entangled. But it is also true that the full ensemble of the A&D subsystem is still in a product state.

Yes, please do. But not for "convincing" Nullstein. It would have been "his" task to bring forward a convincing argument, including references to back it up.

Which claim do you want me to provide references for that I haven't already provided? If DrChinese claims that the full ensemble of the A&D subsystem is entangled (before or after the Bell state projection at B&C, it doesn't matter), then its him who is in contradiction with accepted mainstream science and he should provide a reference.

 

[Nullstein]

Let me explain this in more detail:
If we perform a measurement on a state $\rho$ in a basis $\left|\Psi_i\right>$, then the state of the subensemble corresponding to the result $\left|\Psi_{i_0}\right>$ (where $i_0$ is fixed) is given by $$\rho_{i_0}=\frac{P_{i_0}\rho P_{i_0}}{\mathrm{Tr}(P_{i_0}\rho P_{i_0})}$$ where $P_{i_0}=\left|\Psi_{i_0}\right>\left<\Psi_{i_0}\right|$. We end up in this subensemble with probability $p_{i_0} = \mathrm{Tr}(P_{i_0}\rho P_{i_0})$.

The full ensemble after measurement is the mixed state given by $$\rho^\prime = \sum_i p_i \rho_i = \mathrm{Tr}(P_i\rho P_i) \frac{P_i\rho P_i}{\mathrm{Tr}(P_i\rho P_i)} = \sum_i P_i\rho P_i$$
In the case of a composite system, the density matrix is defined on a product Hilbert space $\mathcal H=\mathcal H_X\otimes H_Y$ and if we perform only local measurements, then the $P_i$ will have the form $P_i = \tilde P_i\otimes\mathbb 1$, where the $\tilde P_i$ act only on $\mathcal H_X$. In this situation, the formula for $\rho^\prime$ becomes $$\rho^\prime = \sum_i (\tilde P_i\otimes\mathbb 1)\rho (\tilde P_i\otimes\mathbb 1)$$
The state of the subsystem Y (before and after) is given by $\rho_Y = \mathrm{Tr}_X\rho$ and $\rho_Y^\prime = \mathrm{Tr}_X\rho^\prime$ respectively.

By the no communication theorem it then follows that $$\rho_Y^\prime = \mathrm{Tr}_X\rho^\prime = \mathrm{Tr}_X\rho = \rho_Y$$
That means that the full ensemble of subsystem Y is not changed by the local operation at subsystem X. All of this is absolute mainstream physics.

In our case, system Y is given by A&D and system X is given by B&C. Hence, the full ensemble of A&D is not entangled even after the measurement at B&C.

 

[vanhees71]

Are you saying that the difficult Bell-state measurements on B & C change the relationship between A & D in other ways than by partitioning it into 4 subensembles? I sort of get your argument that the mystery of the entanglement between A & B and C & D alone cannot be enough to explain the mystery of entanglement swapping, because if "the rest" could just be explained classically, then the required measurement on B & C should be less difficult than it actually is. But if you would claim that this difficult measurement on B & C could change the state of A & D by some instantaneous action at a distance, then it would be "your" task to bring forward a convincing argument, including references to back it up.

In each of the four subensembles, selected by (projective) measurements on photons B&D, photons A&D are entangled. They are not entangled in the full ensemble. There's nothing else needed to ensure this than the preparation of the original photons in the initial state. There is nothing mysterious. To the contrary it's well understood by quite simple application of the rules of QT.

 

[gentzen]

Which claim do you want me to provide references for that I haven't already provided?

Your initial claim at the end of your first post in this thread:

Entanglement swapping indeed adds nothing new to the mystery of entanglement. Those willing to learn can read more about this e.g. in Pearl's famous book titled "Causality."

If DrChinese claims that the full ensemble of the A&D subsystem is entangled

Then you should first ask him to confirm that he really wants to claim that. And if he insists, then try at least to untangle that discussion from the discussion about your initial claim. And if he neither explicitly confirms, nor denies that he wants to claim that, then I would accept that too, and not put words into his mouth, or guess at his intentions.

 

[Nullstein]

Your initial claim at the end of your first post in this thread:

Well, the sentence you quoted already contains the reference explicitely, so I don't understand what you are asking for.

Then you should first ask him to confirm that he really wants to claim that. And if he insists, then try at least to untangle that discussion from the discussion about your initial claim. And if he neither explicitly confirms, nor denies that he wants to claim that, then I would accept that too, and not put words into his mouth, or guess at his intentions.

Point 1 in his post #88 makes it very clear that he either does claim exactly that or that he doesn't understand the difference between the full ensemble and the subensemble. In the first case, he is contradicting accepted mainstream science. In the second case, it shows that he hasn't understood the argument and is therefore unable to meaningfully argue against it in the first place.

I can't untangle these discussions, because it is essential to the argument that the measurement at B&C does not change the full ensemble at A&D. The whole point is that the entanglement in the subensembles can be understood as mere conditioning of the full subensemble of A&D on results from B&C. If the full subensemble of A&D was changed by the measurement, the argument would no longer go through.

Moreover, he is the one who permanently claims that I contradict mainstream science and puts words in my mouth in the whole discussion even though I said numerous times that I fully agree with the contents of the papers he cited. So you might direct this criticism to him as well.

 

[gentzen]

Well, the sentence you quoted already contains the reference explicitely, so I don't understand what you are asking for.

Honestly, I guess that entanglement swapping adds something to the mystery of entanglement. I have read your reference, and it didn't convince me otherwise. But as I said, it doesn't even mention entanglement, so this is no real surprise.

So if DrChinese wants to open a new thread where he discusses why entanglement swapping adds something, I welcome this, especially since I believe that it is possible to do. But if all he wants is to "convince you," then I would not welcome it.

Point 1 in his post #88 makes it very clear that he either does claim exactly that or that he doesn't understand the difference between the full ensemble and the subensemble.

Maybe. What about the difference between an individual pair, and an ensemble of pairs? If he just takes one individual pair from anyone of the subensembles, couldn't he rightfully claim that this "resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities"? Or maybe the language used by Gisin et al here is misleading, and only ensembles of pairs can violate Bell inequalities?