Entanglement swapping, monogamy, and realism

[kurt101]

If you assume Causality (as @vanhees71 does, for example), then naturally your explanation will center on what happens first. It does lead to awkward explanations (as the before/after scenarios will not be consistent).

When you refer to awkward explanations you are referring to how to describe relativistically versus absolutely?

 

[PeterDonis]

When you refer to awkward explanations you are referring to how to describe relativistically versus absolutely?

He's referring to the fact that the actual math is the same regardless of the time ordering of the measurements--as has already been repeatedly pointed out. That means that any purported "explanation" in words that changes depending on the time ordering of the measurements has a problem in explaining how it can be consistent with the math, which doesn't depend on the time ordering of the measurements.

 

[DrChinese]

When you refer to awkward explanations you are referring to how to describe relativistically versus absolutely?

What @PeterDonis said, which as usual he states better and more succinctly than I can.

 

[kurt101]

He's referring to the fact that the actual math is the same regardless of the time ordering of the measurements--as has already been repeatedly pointed out. That means that any purported "explanation" in words that changes depending on the time ordering of the measurements has a problem in explaining how it can be consistent with the math, which doesn't depend on the time ordering of the measurements.

Ok, I don't really think that is a blocker to my perspective, but I can at least understand the push back on my perspective.

My argument to support how can it be consistent is this:

The entanglement swapping experiment where BSM test is done last, run in reverse is essentially an EPR experiment. Photons 2 & 3 start out in the same state. The reverse non-local action happens between 1 & 2. The reverse non-local action happens between 3 & 4. And the 4 ends up in a state that is entangled with 1. So intuitively this explanation should not be surprising at all.

 

[vanhees71]

Nobody disagrees with the math, but I think there is considerable disagreement on how to interpret it.But how does this work? The math doesn't say. If you are satisfied with just pointing at the math and leaving any question the math doesn't answer unanswered, that's fine. But many people aren't; that's why this thread exists. And it doesn't seem like that's the position you're taking anyway: you're asserting what I quoted above as an explanation; you're not saying that no explanation is required at all.

On its face, it seems like you are describing a local hidden variable model of the kind that is ruled out by Bell's Theorem.

But what else do you need as "explanation"? Of course, the quantum formalism is pretty abstract, but we don't have anything more intuitive to express this quantum behavior. Nature doesn't care about what we find intuitive!

There is no hidden variable in what I've written above. It's just QFT, and indeed there's not the slightest hint to any hidden variables from any experiment. The important point is that QFT is "local" due to the microcausality constraint, but is not "realistic", i.e., observables don't need to take determined values

 

[PeterDonis]

The reverse non-local action happens between 1 & 2. The reverse non-local action happens between 3 & 4.

But 1 & 4 don't even exist when the BSM is done in this scenario. In the "forward" version they were measured and destroyed before the BSM was done. In the "reverse" version they would have to be created somehow (and I don't know how you would do that).

 

[vanhees71]

1. Agreed by me.

2. What does this even mean? What correlations? You agree that (14) are NOT entangled in the initial state (good, we agree). And all of them (in the ideal case) are entangled in one of the 4 Bell states in the final state (even if that particular state is unknown).

I have said this before: Certainly there is nothing that connects the successful swap to any change in the statistical relationship of the (14) pairs in *your* reading of the experiment. But we are talking about perfect correlations and violation of Bell inequalities here. According to your reading, EVERY entangled pair anywhere in the universe at any time could be shown to have the same Bell correlations with (12) or (34) - and each other. Because in your mind, those correlations are present (pre-existing) in any 2 entangled pairs - they are just waiting to be uncovered. (Since of course, nothing actual happens/changes with a BSM - in your worldview).

I guess the problem is that it's hard to say what I want to say, and English is not my mother tong. The point is that (12) is max. entangled as well as (34). Now you take 2 from one of these entangled pairs and 3 from the other and entangle them by project them to a Bell state, which necessarily also implies entanglement of (14). The entanglement swapping is possible, because of the entanglement (i.e. the stronger-than-classical correlations described by them) of (12) and of (34). In the so selected subensemble neither (12) nor (34) are entangled (that's why it's called "swapping").

How do you make any physical sense of that? Any 2 entangled pairs anywhere have these hidden correlations, waiting to be revealed? Are you really saying that?

In a sense yes. Of course for each single system it's random, whether I'm succesful or not in swapping. It's as in the somewhat simpler case of teleportation.

 

[vanhees71]

This is "realist", but it isn't local, because 1 & 2 are spatially separated when photon 1 is measured, and 3 & 4 are spatially separated when photon 4 is measured. So this is a nonlocal "action at a distance" model. You might be satisfied with that, but the others that have been objecting to the interpretation @DrChinese has been using won't be; they have been trying to defend a local interpretation, where there is no "action at a distance" even when particles are entangled, so measuring photon 1 can't change anything about photon 2, and measuring photon 4 can't change anything about photon 3.

The projection of pair (23) to a Bell state is a local measurement, i.e., the involved photons interact locally with the PBS.

 

[PeterDonis]

The projection of pair (23) to a Bell state is a local measurement, i.e., the involved photons interact locally with the PBS.

Yes. But @kurt101 is saying that this measurement also changes photons 1 and 4. That is not local. (I'm not saying you claim this, only that @kurt101 does.)

 

[DrChinese]

1. I guess the problem is that it's hard to say what I want to say, and English is not my mother tong.

2. The point is that (12) is max. entangled as well as (34). Now you take 2 from one of these entangled pairs and 3 from the other and entangle them by project them to a Bell state, which necessarily also implies entanglement of (14). The entanglement swapping is possible, because of the entanglement (i.e. the stronger-than-classical correlations described by them) of (12) and of (34). In the so selected subensemble neither (12) nor (34) are entangled (that's why it's called "swapping").

3. In a sense yes. Of course for each single system it's random, whether I'm successful or not in swapping. It's as in the somewhat simpler case of teleportation.

1. I have always thought your English is excellent, and in fact superior to most native English speakers. I have always assumed your mother tongue is German, but I guess I should ask.

2. It not that it "implies entanglement of (14)"... it is the cause of it.

3. This is the point I keep making: in the ideal case they are ALL successful swaps. If there are matched 1 & 4 clicks, a swap occurs (assuming the BSM setup is operating). You don't know the resulting state, but they are entangled. So there really is no subensemble in the sense you imagine. Once you realize that ALL of the matched 1 & 4 pairs are entangled and that there are no rejects, you realize that the "out" you are relying upon doesn't work. You could send the (23) pair into outer space (after the BS where they are made indistinguishable, never detecting them) and 1 & 4 would still be entangled - again you wouldn't know which Bell state they are in.

All of the (14) matched pairs are... entangled. So since they didn't start that way, as we agree, something changed. There is only one candidate cause: the BSM. Without that, none of the (14) matched pairs are entangled. None.

 

[kurt101]

But 1 & 4 don't even exist when the BSM is done in this scenario. In the "forward" version they were measured and destroyed before the BSM was done. In the "reverse" version they would have to be created somehow (and I don't know how you would do that).

I don't really think that you can run the entanglement swapping experiment backwards, but if you could it looks like an EPR experiment. I mean the case where the BSM test is done after the measurement of 1 & 4. Anyways this is what made me think that my explanation might actually work.

Yes. But @kurt101 is saying that this measurement also changes photons 1 and 4. That is not local. (I'm not saying you claim this, only that @kurt101 does.)

And just to be clear I am only saying that the 2 & 3 measurement changes photons 1 & 4 in the case where the BSM test on 2 & 3 is done before measuring 1 & 4. I thought this was @DrChinese position as well.

In the case where the BSM test is done after 1 & 4, I am saying that the measurement of 1 & 4 changes the photons prior to the BSM test of 2 & 3.

 

[PeterDonis]

I don't really think that you can run the entanglement swapping experiment backwards

It's not even a matter of not being able to do it in practice: you can't even build a working theoretical model of it in principle.

but if you could it looks like an EPR experiment.

No, it doesn't, because in the reversed version, photons 2 & 3 would not be entangled when they "emerge" from the "BSM" (since in the forward version they are not entangled going into the BSM). This is not even considering the fact that it is impossible to create photons 1 & 4 (which do not even exist at the time 2 & 3 "emerge" from the "BSM" in the backward versions) in just the right states to match up wtih 2 & 3.

I am only saying that the 2 & 3 measurement changes photons 1 & 4 in the case where the BSM test on 2 & 3 is done before measuring 1 & 4. I thought this was @DrChinese position as well.

@DrChinese is taking the position that the 2 & 3 BSM has the same effect (it swaps entanglements) regardless of the time ordering of the 2 & 3 vs. 1 & 4 measurement. You are not taking that position; you are saying that the BSM only has this effect if it happens first.

In the case where the BSM test is done after 1 & 4, I am saying that the measurement of 1 & 4 changes the photons prior to the BSM test of 2 & 3.

Yes, and that is not the position @DrChinese is taking. See above.

 

[kurt101]

It's not even a matter of not being able to do it in practice: you can't even build a working theoretical model of it in principle.No, it doesn't, because in the reversed version, photons 2 & 3 would not be entangled when they "emerge" from the "BSM" (since in the forward version they are not entangled going into the BSM). This is not even considering the fact that it is impossible to create photons 1 & 4 (which do not even exist at the time 2 & 3 "emerge" from the "BSM" in the backward versions) in just the right states to match up wtih 2 & 3.

Yes, you are strictly correct, but I still think there is symmetry in running the experiment backwards that looks a lot like the EPR experiment which guides intuition on why my explanation works. If you run one side in reverse, photon 2 would leave the BSM. Then when photon 1 reaches the detector (also going backwards) the spooky action in reverse would happen. Then eventually 1 & 2 would meet having the same state. So the last part if is out of order for the EPR experiment and that is a flaw in my analogy. And to make the analogy work you have to think as 1 & 2 acting together as a single photon. It is far from perfect, but it is what made me think it should work.

@DrChinese is taking the position that the 2 & 3 BSM has the same effect (it swaps entanglements) regardless of the time ordering of the 2 & 3 vs. 1 & 4 measurement. You are not taking that position; you are saying that the BSM only has this effect if it happens first.Yes, and that is not the position @DrChinese is taking. See above.

Agreed.

 

[PeterDonis]

I still think there is symmetry in running the experiment backwards that looks a lot like the EPR experiment

Unless you can justify this claim with math (which you can't), it's personal speculation and is off limits here.

 

[kurt101]

Unless you can justify this claim with math (which you can't), it's personal speculation and is off limits here.

I can write a program which I tend to think of the program as being the math, but it is not the language of math that you are looking for. Correct?

And even if I was able to translate the program to math that was acceptable, I imagine it would still fall under the grounds of speculative theory.

So unless I get something published and peer reviewed, I think I have gone as far as I can here.

I feel as if I have gotten my question answered and understand @DrChinese position.

 

[PeterDonis]

I can write a program

That's not the math of QM, that's just some program you wrote. I am talking about the standard math of QM.

even if I was able to translate the program to math that was acceptable

Or you could just use the standard math of QM. That's what it's for.

 

[Morbert]

Regarding precisely "when" (14) pairs become entanglemed in the BSM experiment according to the minimalist* interpretation: The point where the minimalist interpretation makes contact with reality is in macroscopic preparations and macroscopic outcomes. Quantum states, Hermitian operators etc do not characterise the microscopic system. They instead characterise macroscopic interventions on the microscopic system. In statistical language, projectors mentioned previously in this thread like $\{\mathbb 1_1 \otimes P_{23,i} \otimes \mathbb 1_4\}$ that project to the BSM basis, select for subensembles according to BSM outcome. No other element of reality beyond the macroscopic BSM events is considered by the theory. If the experiment is modified to include a BSM on (14) as well, then projectors like $\{\mathbb 1_2 \otimes P_{14,i} \otimes \mathbb 1_3\}$ will select for subensebles according to this BSM outcome. Reality is not characterised by some time-evolution process whereby (14) entanglement is induced at some moment at or after preparation. Reality is instead *only* characterised by a collection of experimental outcomes that followed from identical preparations, with computable frequencies and correlations. Locality is readily preserved.

*By minimalist I am referring to the account of QM presented by Fuchs and Peres in articles like this one https://physicstoday.scitation.org/doi/pdf/10.1063/1.883004

 

[Morbert]

PS re/ realism and locality - For posterity I will repost the obligatory video by Gell-Mann that talks about the recovery of a local realist interpretation of measurement as revealing pre-existing properties, without recourse to hidden variables. https://www.webofstories.com/play/murray.gell-mann/165

 

[PeterDonis]

the minimalist* interpretation

This seems to be more or less the interpretation that @vanhees71 is using.

 

[Morbert]

This seems to be more or less the interpretation that @vanhees71 is using.

I think so too. The only possible difference is that Fuchs and Peres are also willing to talk about the likelihood of single events as well as frequencies of events in ensembles, which I am not sure vanhees is willing to do.

"When we are told that the probability of precipitation tomorrow is 35%, there is only one tomorrow." -- Fuchs and Peres

 

[PeterDonis]

The only possible difference is that Fuchs and Peres are also willing to talk about the likelihood of single events

I believe their approach to probabilities is Bayesian, which treats probabilities as states of epistemic belief and so has no problem assigning probabilities to single events.

 

[gentzen]

*By minimalist I am referring to the account of QM presented by Fuchs and Peres in articles like this one https://physicstoday.scitation.org/doi/pdf/10.1063/1.883004

This seems to be more or less the interpretation that @vanhees71 is using.

I think so too. The only possible difference is ...

No, just no. This is NOT the minimal statistical interpretation. And this is not close to vanhees71's usage of the minimal statistical interpretation either.

 

[DrChinese]

... Locality is readily preserved.

*By minimalist I am referring to the account of QM presented by Fuchs and Peres in articles like this one https://physicstoday.scitation.org/doi/pdf/10.1063/1.883004

Quantum theory is inherently nonlocal, although signal locality is respected. You - as many - have formulated requirements for some definition of nonlocality that cannot be met. Specifically, you basically reject experimental nonlocality proofs which some central observer does not experience until all of the information arrives - which is limited by signal. Circular reasoning - you have proved what you assume.

What is clearly nonlocal, as we have discussed here: An experimentalist here can create - or not - a distant biphoton from components that have never existed in a common light cone. There really is no disputing this experimental fact as I have characterized it. If you choose to reject this because it does not demonstrate signal nonlocality, that's... circular.

Logically, if there is something called "quantum nonlocality" (as I say there is) and it can be demonstrated (as it can be), but it does not feature FTL signaling: then it cannot be judged by a "macroscopic" experiment where component results must be brought together before you accept the nonlocality. Macroscopic Alice can write her results down and compare them with the measurement results of Macroscopic Bob and Victor anytime. Obviously, their combined story indicates that there is quantum nonlocality. You can't wave your hands and ignore the obvious.

Well, I guess you can...

 

[Morbert]

No, just no. This is NOT the minimal statistical interpretation. And this is not close to vanhees71's usage of the minimal statistical interpretation either.

Dreischner calls the account of Peres + Fuchs a minimal instrumentalist interpretation and cites Friebe (though I do not have access to the cited text). By minimal statistical interpretation, do you mean a minimal ensemble interpretation? I don't know if they are as different as you imply, but the minimal interpretation as described in this thread and others has an instrumentalist character (for example, the association of a quantum state with a preparation procedure). If there is some important distinction or misrepresentation then please be explicit.

 

[Morbert]

Quantum theory is inherently nonlocal, although signal locality is respected.

Here you are making a stronger claim that can't be categorised as a difference in interpretation. And it's one I disagree with. E.g. According to decoherent histories interpretations and minimal instrumentalist interpretations, quantum theory is no more nonlocal than classical theory.

 

[Fra]

What is clearly nonlocal, as we have discussed here: An experimentalist here can create - or not - a distant biphoton from components that have never existed in a common light cone.

Sure, but we can also agree the experimenter can not "create this" without information about measurements on other entangled parts of both the components. Ie. The experimebter cant create this without this information. Do we agree?

There really is no disputing this experimental fact as I have characterized it. If you choose to reject this because it does not demonstrate signal nonlocality, that's... circular.

As we use different notions of locality, I'm fine with agreeing with you with that disclaimer.

But that form of nonlocality you refer to is not a problem per see (At least not for me). The notion of locality that is part of the often constructing principles of physics isnt the kind of locality that you speak of. The only problem is that its almost the same word for different things.

/Fredrik

 

[Nullstein]

This is wrong. The "event ready" signal is generated by a combination of things: the 2 & 3 photons arriving at the BSM device within the same narrow time window, and the output of the BSM indicating the particular Bell state that the BSM is set up to distinguish. This happens at the BSM, not at the initial preparation. @DrChinese is more familiar than I am with the specific papers describing the experiments, and I'm sure can give specific references to the descriptions in those papers that match the above.

I don't think the specific details are relevant. The point of the event ready signal is to select those events which can safely be assumed to be successful measurements. This doesn't add anything conceptually new to the analysis of the idealized experiment. You still have a full ensemble of events which constitue successful measurements and you decompose this full ensemble into subensembles according to the measurement result of the BSM.

For our purposes, let's assume that the 1 & 4 measurement systems (PBS plus 2 detectors for each) are positioned such that when we have a successful BSM, the 1 & 4 detectors go off at the same time (within our designated time window). We add fiber cable to make that work out, and we place them at the same spot. Additionally, we do the same with the BSM detector array. We use fiber to adjust the travel time, and route them to the same location as the 1 & 4 detectors. All 4 photons will arrive at location where all of the detectors are, and the photons will all arrive within the same time window. I am adding this little twist so you can see exactly what should be discussed when we talk about an ensemble or subset or subensemble. So what we expect, with a successful BSM, is that 4 detectors will click at almost precisely the same time. For the 1 & 4 photons, each will generate one click indicating their polarization relative to their respective PBS. The BSM detector array will register 2 clicks, one for the 2 photon and one for the 3 photon - but we won't know which is which. So 4 "simultaneous" clicks means we have a successful BSM in this setup.

These events taken together, i.e. prior to post-selection, constitute the full ensemble.

In theory: for every single case where the 1 & 4 photons are detected within the time window: they are entangled.

This sentence makes no sense without saying with respect to which data set you make it. If you consider a dataset consisting of only a single data point, it makes no sense, because the unbiased estimator of covariance is not well defined for a single data point. If you consider the full ensemble, then the statement is false. The photons 1&4 will be uncorrelated in the full ensemble. The statement is true for the post-selected subensembles only.

We may not know which of the 4 Bell states they are in - and therefore we can't perform a Bell test on them - but they ARE entangled. [...] But assuming we are good scientists, there is no subensemble yet.

No. If you don't look at a subensemble, there will not be entanglement in the data. The correlation will be zero. This follows strictly from the math.

 

[Nullstein]

Quantum theory is inherently nonlocal, although signal locality is respected.

You are being imprecise on purpose here. Quantum non-locality means nothing more than the fact that Bell's inequality is violated. What you want to imply is that there are non-local cause and effect relationships. The broad consensus among physicists is that no non-local cause and effect relationship can be inferred from the data. QM can be interpreted either way.

 

[PeterDonis]

I don't think the specific details are relevant.

They most certainly are. Basing the signal on what happens at the BSM is very different from basing it on something from the initial preparation, which is what you said before.

The point of the event ready signal is to select those events which can safely be assumed to be successful measurements.

Not quite. The point of the event ready signal in these experiments is to select those events in which photons 2 & 3 are projected into the particular Bell state that the BSM is set up to uniquely detect. That doesn't mean the other events aren't successful measurements; they're just measurements whose results can't be distinguished by the humans reading the output of the apparatus. But they still involve projecting photons 2 & 3 into a Bell state and everything associated with that (for example, that photons 1 & 4 are also projected into a Bell state).

You still have a full ensemble of events which constitue successful measurements and you decompose this full ensemble into subensembles according to the measurement result of the BSM.

That's not correct for these particular experiments. The "event ready" signal runs are the only runs for which the measurement result of the BSM can be determined. The other runs involve BSM results that the humans reading the apparatus can't distinguish from each other. So the other subensembles can't be picked out. Only the "event ready" subensemble can.

It would be possible in principle to design a more sophisticated BSM that could distinguish all 4 Bell states, so that 4 subensembles could be picked out; but my understanding is that the technical difficulties in doing that in practice have not yet been figured out. In such an experiment, the "event ready" signal would be the arrival of photons 2 & 3 at the BSM within a narrow enough time window for the BSM to act on them at all (if they don't arrive within a narrow enough time window, the BSM does nothing).

 

[Nullstein]

Let me try once more to explain the relationship between correlation and causation and how it applies to entanglement swapping:

Experimentally, we find that certain sets of data show correlation between spacelike separated variables $A$ and $B$. In general though, correlation does not imply a cause and effect relationship between those variables, i.e. we may not conclude that $A$ caused $B$ or the other way around. Why is that?

1. The correlation may be mediated by a third variable $C$, i.e. $C$ caused $A$ and $C$ caused $B$. In that case, the correlation will go away if we condition on the variable $C$. This is called a common cause explanation. Bell's theorem proves that a common cause explanation for the EPR correlations is excluded.
2. The correlation may arise, because we are only looking at a specific subset of the data. In particular, if we look at data which was obtained by conditioning on a common effect, then inferring causality is forbidden if the correlation goes away after summing over the common effect variable. This is the case in entanglement swapping. Here, the correlation in the subensembles will go away if we sum over the possible measurement outcomes of the BSM, i.e. if we pass to the full ensemble.

If there was still correlation between $A$ and $B$ after we have taken care of these issues, we may indeed infer causality from the fact that $A$ and $B$ are correlated. But in the case of entanglement swapping, it is just a fact that the correlation goes away after taking care of these issues, so we may not infer causality.

All of this is well understood applied statistics. It's not something I made up. This is how causal inference is taught and done in every empirical field of science. The paper https://arxiv.org/abs/1606.04523 shows that this is also well understood in the case of entanglement swapping. Robert Spekkens, one of the authors, is one of the leading researchers in quantum foundation and the application of causal inference to quantum mechanics, so this should certainly be taken seriously.