I Entanglement swapping, monogamy, and realism

[martinbn]

Just to point out the the wikipedia article (although not an acceptable source) on teleportation has a good subsection on swapping.

 

[DrChinese]

1. Just once more for clarity in the notation you seem to prefer to the QFT-notation with creation operators: ...

That means that the subsystem consisting of photons 1 and 4 are in the reduced state
$$\hat{\rho}_{14} = \mathrm{Tr}_{23} \hat{\rho}_{1234}=\frac{1}{4} \hat{1}_{14},$$
i.e., the photons (14) are both unpolarized and uncorrelated.

2. Indeed if 2&3 are projected to the state $|\Psi_{23}^- \rangle$, which is what you call BSM (Bell-state measurment), then for the so selected subensemble 1&4 are also in the state $|\Psi_{14}^- \rangle$. In math it's completely clear that you do something to photons 2&3 but nothing (!!) to photons 1 and 4, i.e., when projecting 2&3 to $|\Psi_{23}^- \rangle$, then there's nothing interacting with photons 1 and 4:
$$\mathcal{N} |\Psi' \rangle = |\Psi_{23}^{-} \rangle \langle \Psi_{23}^{-} \rangle \otimes \hat{1}_{14} |\Psi \rangle=\frac{1}{2} |\Psi_{23}^{-} \rangle \otimes |\Psi_{14}^{-1} \rangle.$$
Thus the projection to this specific Bell state occurs with probability $(1/2)^2=1/4$, and the (renormalized) state of the subensemble is
$$|\Psi' \rangle=|\Psi_{23}^{-} \rangle \otimes |\Psi_{14}^{-} \rangle,$$
i.e., now (23) and (14) are in Bell states, but the pairs are completely uncorrelated.

The state $|\Psi_{23}^{-} \rangle$ is chosen by the experimenters, because with a polarizing beam splitter it's simply identified by the fact that only in this state both output channels register a photon (since photons are bosons and the two photons are in an odd polarization state, the momentum state must be also odd, i.e., the photons cannot exit the beam splitter in the same momentum state).

I think about these facts we agree, and I hope we also agree on the math.

3. If we agree on the math and the meaning of a projection measurement, then nothing has be done to photons 1 or 4 when projecting photons 2 and 3 to a Bell state, which is indeed a local measurement, because you have to bring these two photons together at the polarizing beam splitter and the detectors in the two exit channels of this splitter, i.e., this is something where the two photons interact with equipment in the pretty small space-time region.

4. ...if you accept the microcausality principle.

1. We are agreed as to this: 1 and 4 are initially completely uncorrelated and unentangled. There is no subset in which they are initially entangled with each other. We know this because of... Monogamy of Entanglement.

2. We disagree here. If we happen to project 2 & 3 into the $\psi-$ state, then it is true that 1 & 4 are changed into the entangled $\psi-$ state as well. They were previously in a completely uncorrelated and unentangled state, as we just agreed. That's the math!

And in the experiment we are discussing, the team is also able to discern the $\psi+$ state as well as the $\psi-$ state. The $\phi+/-$ states cannot be distinguished with APDs because they cannot reset fast enough using current technology to be able to count 2 photons going to the same detector in such close succession.

3. I don't know why you call the BSM a "local" measurement. It's not local to 1 or 4, and they are the ones affected because they have been projected into a Bell state that there were NOT previously in.

My assertion, which is supported by the math (which we just agreed upon):
Initial state (all cases): $|\Psi \rangle=|\Psi_{12}^{-} \rangle \otimes |\Psi_{34}^{-} \rangle$ [depending on Source type]
a. Final state (occurs 25%): $|\Psi' \rangle=|\Psi_{14}^{-} \rangle \otimes |\Psi_{23}^{-} \rangle$
b. Final state (occurs 25%): $|\Psi' \rangle=|\Psi_{14}^{+} \rangle \otimes |\Psi_{23}^{+} \rangle$
c. Final state (occurs 25%): $|\Psi' \rangle=|\Phi_{14}^{-} \rangle \otimes |\Phi_{23}^{-} \rangle$
d. Final state (occurs 25%): $|\Psi' \rangle=|\Phi_{14}^{+} \rangle \otimes |\Phi_{23}^{+} \rangle$

4. I don't, at least not as you apply it. It is contradicted by experiment, that is why we are having this debate. An action here objectively changes a state there. As we agree on the math, this should be easy... if you just ignore your wrong assumptions. So far, you haven't been able to explain how remotely created photons can violate a CHSH inequality without appealing to the (wrong) assumption that they were somehow already in that state previously. None of the 1 & 4 pairs were entangled to begin with, and there was no subset in which they were. Any more than you could take any 2 streams of photons from different sources and try to claim they are entangled.

5. Yes, we are. You deny that the full ensemble of 1&4 after the BSM is given by 𝟙𝟙141⊗1. Everyone accepts that other than you.

5. And just to dismiss @Nullstein's ridiculous argument: In all cases, the BSM leaves 1 & 4 in one of the entangled states per a, b c, or d above. That is NOT the same state by any means as you give (a random outcome).

Or what, you won't accept and use the available data? I guess when you do a typical Bell test, you only look at Alice's results... and throw away Bob's?

Here's a shocker: if you look at ANY stream of entangled particles, which are an equal mixture of $\psi-$ and $\psi+$ pairs, they will statistically show no correlation IF you discard the available information as to their state. But guess what: They are still entangled! It doesn't matter whether you know it or not. I don't know what kind of scientist you are that you require information to be discarded when running an experiment. While you are busy discarding useful information, the remainder of the scientific world is working on identifying all 4 Bell states after a BSM. And I expect someone will figure that out "soon", since there have already been proofs of concept.

 

[Nullstein]

5. And just to dismiss @Nullstein's ridiculous argument: In all cases, the BSM leaves 1 & 4 in one of the entangled states per a, b c, or d above. That is NOT the same state by any means as you give (a random outcome).

It speaks for itself that you find standard science "ridiculous." There is no evidence that the BSM has any effect on 1&4. The correlation in the post-selected ensembles is spurious, as any statistician will tell you. The conditioning on a common effect (the BSM result) introduces non-causal correlation. This is not controversial at all. It's the bread and butter of any statistician and a perfectly well-understood phenomenon.

Or what, you won't accept and use the available data? I guess when you do a typical Bell test, you only look at Alice's results... and throw away Bob's?

Nobody throws data away. All information is contained in the full ensemble. But you just haven't understood the difference between correlation and causation. You cannot infer causality from the existence of correlations. It is perfectly well-understood under what circumstances this is allowed. If there is conditioning on a common effect, then one must sum over the conditional variable. Otherwise, the correlation is meaningless for causal inference.

Here's a shocker: if you look at ANY stream of entangled particles, which are an equal mixture of $\psi-$ and $\psi+$ pairs, they will statistically show no correlation IF you discard the available information as to their state. But guess what: They are still entangled! It doesn't matter whether you know it or not.

No, the full data set is not entangled. The full ensemble is product state, as we have established multiple times now. One does not discard information. It's a necessary step in causal inference to sum over the common effect variables. It's not optional. It's the only correct way to perform causal inference. Only the subensembles are entangled, but no causal relationships can be inferred from this.

I don't know what kind of scientist you are that you require information to be discarded when running an experiment.

The information is not discarded. But if you don't sum over the common effect variable when performing causal inference, you are a bad scientist, because you are not taking into account that correlation doesn't imply causation.

While you are busy discarding useful information, the remainder of the scientific world is working on identifying all 4 Bell states after a BSM. And I expect someone will figure that out "soon", since there have already been proofs of concept.

Since we are discussing the idealized setting without any experimental complications, we have already taken care of that. As good theoretical physicists, we have already done the calculations and are waiting for the experimentalists to confirm them.--
And just so there are no misunderstandings: The fact that there is no evidence for non-local causal relationships doesn't imply that there can not be a non-local causal model. It just means that we are not forced to adopt one. This is also what the recent Nobel laureate Anton Zeilinger has chosen to do. If you think that that there is evidence for non-local causal relationships, then you are in direct contradiction with a recent Nobel laureate.

 

[martinbn]

5. And just to dismiss @Nullstein's ridiculous argument: In all cases, the BSM leaves 1 & 4 in one of the entangled states per a, b c, or d above. That is NOT the same state by any means as you give (a random outcome).

This is interpretation dependent. It may be how it is in some, say collapse, interpretations.

The interpretation independent statment is that it is a mixture of those four. The density matrix of 14 is the same before and after the measurement of 23. It is the partial trace that has been written many times in these theards.

 

[Fra]

They are still entangled! It doesn't matter whether you know it or not.

I assume that by "you", you mean the observer.

Are you actually saying that two quantum states can be entangled without the observers knowledge?? What does that even mean?

/Fredrik

 

[DrChinese]

1. This is interpretation dependent. It may be how it is in some, say collapse, interpretations.

2. The interpretation independent statement is that it is a mixture of those four. The density matrix of 14 is the same before and after the measurement of 23. It is the partial trace that has been written many times in these threads.

1. If each and every final 1 & 4 pair is identified as to its Bell state, and a Bell test is performed, and a CHSH inequality is violated: they are entangled. There is no interpretation I know of that denies this.

2. Why on earth you think they are not entangled if you throw away the information on the Bell state, I don't know. That is anti-science. There is absolutely no requirement that all entangled pairs after a swap be a single Bell state to consider them entangled.

3. The full ensemble is product state, as we have established multiple times now.

From Nullstein post #40:
I agree that the subensembles are entangled [into 1 of the 4 Bell states].

We have established many times that the initial 1 & 4 state is uncorrelated and unentangled, and that there is no relationship between them - hidden or otherwise. From the paper: "A successful entanglement swapping procedure will result in photons 1 and 4 being entangled, although they never interacted with each other." From @vanhees71: "the [initial] photons (14) are both unpolarized and uncorrelated."

Yes, it is trivially true that if you look at the 1 & 4 pairs and don't know their Bell state, no pattern pops out. I guess we need to tell this team that they are wasting their time when they run the experiment and announce: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4. Violation of a CHSH inequality is not only of fundamental interest because it rules out local-hidden variable theories. It also proves that the swapped states are strongly entangled and, as a result, distillable."

All I can say is "wow". Hundreds of teams out there are working to create quantum networks using swapping from point to point to point. They all seem to think there is entanglement, and they all seem to think the 2 & 3 BSM had something to do with it.

4. So you admit that there are 4 different Bell states, but still insist to write ρ^14 for all of them? If they are 4 different states (even so all are maximally entangled), then you should also use 4 different symbols for them, for example ρ^141, ρ^142, ρ^143, and ρ^144.

5. And then, wouldn't ρ′^1234=∑iρ^14i⊗ρ^23i be a more appropriate formula for the state, as long as no conditioning with respect to the 4 different states is done?

4. I am not "admitting" anything, since I have been saying there are 4 Bell states all along. I can spell them out (as I already did in later post #202), if it makes a difference to your understanding. But I think you know the answer already and don't need this:

Initial state (all cases): |Ψ⟩=|Ψ12−⟩ ⊗ |Ψ34−⟩ [depending on Source type]
a. Final state (occurs about 25%): |Ψ′⟩ = |Ψ14−⟩ ⊗ |Ψ23−⟩ [detected in the experiment]
b. Final state (occurs about 25%): |Ψ′⟩ = |Ψ14+⟩ ⊗ |Ψ23+⟩ [detected in the experiment]
c. Final state (occurs about 25%): |Ψ′⟩ = |Φ14−⟩ ⊗ |Φ23−⟩
d. Final state (occurs about 25%): |Ψ′⟩ = |Φ14+⟩ ⊗ |Φ23+⟩

Yes, all the 1 & 4 pairs are still entangled... exactly as I said since we started. Which is exactly as QM predicts for this experiment. Only 2 of 4 states are identified in this experiment, but it is only a matter of time before a version is run in which all 4 Bell states are identified. (They have already done this for remote teleportation.)

5. And why would we want to fail to condition? That would lead us to a completely useless formula. The authors of the paper do the exact opposite, they USE the conditioning to demonstrate entanglement: "Expectation values for the CHSH inequality depending on the outcome, ψ− or ψ+, of the BSM. Each of these values is calculated from four measurements of four photon coincidences integrated over 15000 seconds."

The scientists in this room use all the information they have to make their conclusions. I would everyone would. And one of those conclusions is that the BSM "causes" the projection of the random Bell State outcome onto the 1 & 4 pairs that were previously unentangled. The issue with the word "causes" is that time ordering doesn't matter. @vanhees71 is technically correct when he cites the "microcausality" condition to say there are no nonlocal causes. That's merely because quantum causality operates much differently than Einsteinian causality, and therefore cannot be applied like Einsteinian causality.

Any way you look at it: a BSM here creates an entangled biphoton there. Pretty hard to wave hands and make that result go away. 1 & 4 pairs: Not at all entangled before the BSM (as we all agree), 100% entangled after the BSM (in 1 of 4 Bell States) - which QM predicts.

 

[Morbert]

Everyone agrees that there is entanglement in the subensembles marked by the outcomes of the BSM. Where people disagree is the implication of this. There are three broad positions.

i) Under all established interpretations, it implies FTL influences
ii) Under all established interpretations, it doesn't imply FTL influences
iii) Under some established interpretations, it implies FTL influences, and under other established interpretations, it doesn't.

At the very least, there have been well-established interpretations presented here, consistent with experiment, that don't imply FTL. So at the very least, the right position is either ii) or iii)

 

[mattt]

The state of a Quantum System is a mathematical object that gives you a set of relative frequencies of possible results, for each of a set of measuring procedures, that can only be tested on a huge set of identically prepared copies of the system.

Dr Chinese seems to have problems understanding that a photon-pair can belong to a set (of identically prepared copies) collectively described as a Product State, and at the same time this photon-pair may also belong to a different set (for example, any of the four subensembles) collectively described (each of the four subsets) as a Maximally Entangled State (which are four different states by the way), without necessarily anything "changing" for that photon-pair.

The monogamy of Entanglement apply when you consider a given ensemble (of identically prepared copies), but it ceases to apply if you change the ensemble for a subensemble (if you change the state, that now describes a different collection).

Only if you consider the "state" as a "property" of each pair (regardless of the collection, the ensemble to which it may be considered to belong) you'll see a "non-local causation" (a "change of a property") in this experiment.

 

[DrChinese]

1. Everyone agrees that there is entanglement in the subensembles marked by the outcomes of the BSM.

2. Where people disagree is the implication of this. There are three broad positions.

i) It implies FTL
ii) It doesn't imply FTL
iii) The FTL implication is interpretation dependent

3. At the very least, there have been well-established interpretations presented here, consistent with experiment, that don't imply FTL. So at the very least, the right position is either ii) or iii)

1. I hope we have reached this point.

2. I agree with these basic positions as being represented here.

3. I don't see the range of interpretations as you do. Some continue to assert pre-Bell locality in the face of Bell, without stating exactly what they are giving up in the way of realism. Stated a different way: they present no mechanism as to how locality can be preserved in experiments such as Entanglement Swapping. Certainly the math of QM predicts without regard to spacetime distance.

Most interpretations attempt to maintain Einsteinian causality in all quantum contexts, when the evidence goes against it. That isn't a winning position. I don't know how nature pulls off its tricks, but I know that it displays quantum non-local/non-causal effects.

 

[DrChinese]

Dr Chinese seems to have problems understanding that a photon-pair can belong to a set (of identically prepared copies) collectively described as a Product State, and at the same time this photon-pair may also belong to a different set (for example, any of the four subensembles) collectively described (each of the four subsets) as a Maximally Entangled State (which are four different states by the way), without necessarily anything "changing" for that photon-pair.

The monogamy of Entanglement apply when you consider a given ensemble (of identically prepared copies), but it ceases to apply if you change the ensemble for a subensemble (if you change the state, that now describes a different collection).

I have quoted extensively on Monogamy and referenced papers. Where are your references disputing these quotes? According to QM: MoE applies to any and every single entangled pair. There is no requirement that there be a large set.

Further: of course you can model a system where you discuss an entangled pair (say 1 & 4) and other particles (let's say 5 & 6, which are not entangled). We would have a Product state with: (1 & 4) and (5) and (6). Unless there is some purpose to such a description, it isn't useful. And certainly has no relevance to our discussion. In our discussion, MoE applies exactly as follows:

If (1 & 2) are maximally entangled in any Bell state, then (1 & 4) are not at all entangled.
If (1 & 4) are maximally entangled in any Bell state, then (1 & 2) are not at all entangled.
If (3 & 4) are maximally entangled in any Bell state, then (1 & 4) are not at all entangled.
If (1 & 4) are maximally entangled in any Bell state, then (3 & 4) are not at all entangled.

Any other application is wrong. This is what is useful to our discussion.

 

[Morbert]

I don't see the range of interpretations as you do. Some continue to assert pre-Bell locality in the face of Bell, without stating exactly what they are giving up in the way of realism. Stated a different way: they present no mechanism as to how locality can be preserved in experiments such as Entanglement Swapping. Certainly the math of QM predicts without regard to spacetime distance.

Most interpretations attempt to maintain Einsteinian causality in all quantum contexts, when the evidence goes against it. That isn't a winning position. I don't know how nature pulls off its tricks, but I know that it displays quantum non-local/non-causal effects.

Three interpretations that preserve locality (not merely local signalling) that have been touched on in this thread:

i) The instrumentalist interpretation: Under this interpretation, quantum theories concern macroscopic preparations and measurements. Whether or not the BSM occurs, the source $\rho_{14,\mathrm{after}}$ will induce the same macroscopic detector responses. It is true that the physicist that performed the BSM can travel to the source and further prepare four new sources, or bin the detector responses into four groups based on their BSM data, but they must do so at sublight speed

ii) The minimalist ensemble interpretation: Under this interpretation, quantum states refer to structureless ensembles of microscopic systems instead of preparation procedures per se. Here, whether or not the BSM occurs, the same ensemble $\rho_{14,\mathrm{after}}$ is produced. You have elsewhere asserted that the ensemble prepared is actually different if the BSM occurs, due to all pairs being entangled. This might be true for some ensemble interpretations (e.g. "PIV" and hidden variable ensemble interpretations) but the minimal ensemble interpretation says nothing about the structure of the ensemble, and so we cannot say the all particles are entangled in the full ensemble. We have to explicitly produce 4 distinct subensembles to recover (14) entanglement (also limited to sublight speeds)

iii) Consistent histories: Consistent histories lets us construct the subensembles of entangled (14) pairs even if the BSM is not carried out. It's just that these subensembles are not accessible to any physicist unless the BSM is performed. Note that this is not a hidden variable interpretation, but the reasons why might take us too far from the topic at hand.

 

[kurt101]

When the BSM test is done before measuring 1 & 4, and the BSM test shows maximum entanglement, you can change the polarization angle used in the measurement at 1 and 4 at the very last moment, right before performing the measurement of 1 & 4 and you will still get the maximal entangled correlation between 1 & 4, right? So entanglement between 1 & 4 in this case is just as real as the entanglement in an EPR experiment correct? Does everyone on this thread agree on this?

 

[DrChinese]

Dr Chinese seems to have problems understanding that a photon-pair can belong to a set (of identically prepared copies) collectively described as a Product State, and at the same time this photon-pair may also belong to a different set (for example, any of the four subensembles) collectively described (each of the four subsets) as a Maximally Entangled State (which are four different states by the way), without necessarily anything "changing" for that photon-pair.

The monogamy of Entanglement apply when you consider a given ensemble (of identically prepared copies), but it ceases to apply if you change the ensemble for a subensemble (if you change the state, that now describes a different collection).

This is completely incorrect. I have quoted extensively on Monogamy and quoted papers. Where are your references?

According to QM: MoE applies to any and every single entangled pair. There is no requirement that there be a large set.

Further: of course you can model a system where you discuss an entangled pair (say 1 & 4) and other particles (let's say 5 & 6, which are not entangled). We would have a Product state with: (1 & 4) and (5) and (6). Unless there is some purpose to such a description, it isn't useful. And certainly has no relevance to our discussion. In our discussion, MoE applies exactly as follows:

If (1 & 2) are maximally entangled in a Bell state, then (1 & 4) are not at all entangled.

Any other application is wrong. And this is what is useful to our discussion.

 

[PeterDonis]

I think your view is contradicted by this post-selection swapping experiment

I think you need to look at the actual math, since that's all I was talking about. The results of that experiment, like all experiments done to date to test QM, are perfectly in accordance with the actual math of QM.

Are you trying to say that I must accept FTL influences?

Not at all. That's why I said "open to interpretation".

the idea that entanglement is statistical correlation instead of an objective property is a self-consistent position to hold.

Statistical correlation is an objective property; you can measure it just like you can measure any other objective property.

If you are referring to an ensemble interpretation of the quantum state vs. an interpretation that says the quantum state describes individual systems, I already referred to that.

how can entanglement be objective when it's frame dependent?

Entanglement is not frame dependent. As I have already said, whether a particular quantum state is entangled is an objective property that has a straightforward mathematical test.

I really think you need to look at the math before making any further claims.

From https://www.nature.com/articles/s41467-018-08155-0:

This paper appears to be highly speculative, and the claim about entanglement being frame dependent contradicts every QM textbook I have ever read.

 

[PeterDonis]

it's not convincing in the application of probability theory to physics.

Many Bayesian physicists (the canonical example would be E. T. Jaynes, but he is hardly the only one) would disagree with you. I suggest reading Jaynes' Probability Theory: The Logic of Science.

In this sense quantum states describe ensembles rather than single realizations of measurements.

Jaynes' viewpoint was that this just means QM is an incomplete theory: there are physical degrees of freedom that are simply missing from its model, which accounts for its inability to make predictions that aren't probabilistic. It's unfortunate that he never (AFAIK) studied the Bohmian interpretation, since that is a famous example of an underlying model that adds degrees of freedom.

 

[PeterDonis]

There are 3 systems, B, C and D in the paper. It discusses a general setting. System B corresponds to the 2&3 system in our case and systems C and D correspond to systems 1 and 4 respectively.

That's not what I see in the paper. What I see is two systems, with different letters labeling the systems at different times or after different operations are performed on them. I don't see more than two systems anywhere in the paper. Nor do I see anywhere in the paper where it claims to be talking about more than two systems: I only see section headings and figure captions that say "two systems".

 

[PeterDonis]

When the BSM test is done before measuring 1 & 4, and the BSM test shows maximum entanglement, you can change the polarization angle used in the measurement at 1 and 4 at the very last moment, right before performing the measurement of 1 & 4 and you will still get the maximal entangled correlation between 1 & 4, right? So entanglement between 1 & 4 in this case is just as real as the entanglement in an EPR experiment correct?

Yes, all of this is correct. You could also vary the relative angles of the 1 & 4 measurements to verify that the correlations between them violate the Bell inequalities and match the QM predictions. (In fact, you can do this regardless of the time ordering of the BSM and the 1 & 4 measurements.)

 

[PeterDonis]

According to QM: MoE applies to any and every single entangled pair. There is no requirement that there be a large set.

This is assuming a non-ensemble interpretation, i.e., an interpretation in which the quantum state describes individual quantum systems.

On an ensemble interpretation, the quantum state only describes ensembles, not individual systems. I have not seen a good discussion of how an ensemble interpretation deals with the theorems on monogamy of entanglement, but if anyone knows of such a discussion in the literature, I think it would be of interest in this thread.

It also might be of interest to see how proponents of ensemble interpretations (e.g., Ballentine) deal with recent experiments in quantum computing and quantum optics, in which quantum states are routinely treated as applying to individual systems when analyzing, for example, the effects of the various quantum gates.

 

[Fra]

Stated a different way: they present no mechanism as to how locality can be preserved in experiments such as Entanglement Swapping. Certainly the math of QM predicts without regard to spacetime distance.

Most interpretations attempt to maintain Einsteinian causality in all quantum contexts, when the evidence goes against it. That isn't a winning position. I don't know how nature pulls off its tricks, but I know that it displays quantum non-local/non-causal effects.

If this is your main drive, you have my symphaty. Indeed some focus on the math and avoid seeking a deeper mechanism.

This is however exactly what brought me to a qbism derivative stance. This is why I asked before about your interpretation. It is easier to speak to a different thinker if you understand each others positions.

/Fredrik

 

[vanhees71]

Many Bayesian physicists (the canonical example would be E. T. Jaynes, but he is hardly the only one) would disagree with you. I suggest reading Jaynes' Probability Theory: The Logic of Science.Jaynes' viewpoint was that this just means QM is an incomplete theory: there are physical degrees of freedom that are simply missing from its model, which accounts for its inability to make predictions that aren't probabilistic. It's unfortunate that he never (AFAIK) studied the Bohmian interpretation, since that is a famous example of an underlying model that adds degrees of freedom.

Although I like Jaynes's pioneering work in the application of information-theoretical methods in statistical physics, I don't think that he is right here. There are no hints at any hidden variables, and QT describes all observations correctly. For me it's incomplete, because there's no consistent description of the gravitational interaction (or, in your favorite interpretation, space-time geometry), but I don't see, where there should be any hidden variables to come for a rescue. Of course, that's speculation.

de Broglie Bohm may be appealing for non-relativistic QM, but I don't see a convincing extension to relativistic QFT. In addition it doesn't add anything that's not also described by the minimal interpretation. It's a nice example for a truely non-local HV theory in the non-relativistic realm, but there "non-locality" anyway is no problem to begin with.

 

[vanhees71]

The scientists in this room use all the information they have to make their conclusions. I would everyone would. And one of those conclusions is that the BSM "causes" the projection of the random Bell State outcome onto the 1 & 4 pairs that were previously unentangled. The issue with the word "causes" is that time ordering doesn't matter. @vanhees71 is technically correct when he cites the "microcausality" condition to say there are no nonlocal causes. That's merely because quantum causality operates much differently than Einsteinian causality, and therefore cannot be applied like Einsteinian causality.

I agree with everything else you said above, and we seem to very slowly converge now on microcausality. The last step is to understand that this in fact IS Einstein causality, i.e., to accept that relativistic local QFT is satisfying relativistic causality by construction due to the fulfilling of the microcausality constraint. "Nonlocality" refers to correlation of far-distantly observed parts of entangled quantum systems but not to an "action at a distance" or any violation of Einstein causality, which simply says that space-like separated events cannot be in a causal relation to each other.

Any way you look at it: a BSM here creates an entangled biphoton there. Pretty hard to wave hands and make that result go away. 1 & 4 pairs: Not at all entangled before the BSM (as we all agree), 100% entangled after the BSM (in 1 of 4 Bell States) - which QM predicts.

Of course, that's what all these experiments demonstrate, and it's not only predicted by QM (where we wouldn't have any problem with causality because in Newtonian physics, including QM, time is absolute) but also by local, relativistic QFT!

 

[vanhees71]

Three interpretations that preserve locality (not merely local signalling) that have been touched on in this thread:

ii) The minimalist ensemble interpretation: Under this interpretation, quantum states refer to structureless ensembles of microscopic systems instead of preparation procedures per se. Here, whether or not the BSM occurs, the same ensemble $\rho_{14,\mathrm{after}}$ is produced. You have elsewhere asserted that the ensemble prepared is actually different if the BSM occurs, due to all pairs being entangled. This might be true for some ensemble interpretations (e.g. "PIV" and hidden variable ensemble interpretations) but the minimal ensemble interpretation says nothing about the structure of the ensemble, and so we cannot say the all particles are entangled in the full ensemble. We have to explicitly produce 4 distinct subensembles to recover (14) entanglement (also limited to sublight speeds)

In the minimal interpretation, of course the state also refers to preparation procedures on single quantum states. Otherwise you couldn't even build the ensembles within this interpretation. The randomness, predicted by QT, and the corresponding probabilities refer to the outcome of measurements but not to the preparation procedure, which is a well-defined procedure in the lab for each experiment.

iii) Consistent histories: Consistent histories lets us construct the subensembles of entangled (14) pairs even if the BSM is not carried out. It's just that these subensembles are not accessible to any physicist unless the BSM is performed. Note that this is not a hidden variable interpretation, but the reasons why might take us too far from the topic at hand.

Then "consistent histories" is very misleading. QT refers to experiments that are really done, not to fictitious experiments which may not even be possible to be done from first principles.

 

[martinbn]

I think you are not paying attention to what I write. If you have a composite system in an entangled state. Each subsystem (this is already imprecise) is descirebed by its density matrix. If you perform measurement (or not) on one of the subsystems, the density matrix of the other does not change. Denying this is anti-science. The density matrix gives you the satatistics of the results of any measurment you do on the subsystem. Anything more you say about this is usuing implicitlely some interpretation. For example you say that the measurment on one subsystem (in this discussion 2&3) changes the state of the other (the 1&4). This automatically exludes ensemble interpretations, so it is not as you believe interepretation independent.

1. If each and every final 1 & 4 pair is identified as to its Bell state, and a Bell test is performed, and a CHSH inequality is violated: they are entangled. There is no interpretation I know of that denies this.

2. Why on earth you think they are not entangled if you throw away the information on the Bell state, I don't know. That is anti-science. There is absolutely no requirement that all entangled pairs after a swap be a single Bell state to consider them entangled.

1. See, you phrased it in a way that excludes ensemble interpretations. If you think of the whole ensemble of 1&4 it is simply not true. What you mean to say then is that the full ensemble consists of four subansembles, which are in their Bell states.

2. Because if you look only at the 1&4 and do whatever measurments you want, you will not see anything to suggest entanglemnt. You need to partition your results into four groups and then look only at each group. But you cannot do that if you don't have the information of the results of 2&3.

 

[vanhees71]

That's of course true. A nice example, where this is demonstrated is the "quantum eraser experiment", e.g., by Walborn et al. Here's the English translation of my Habilitation Colloquium slides:

https://itp.uni-frankfurt.de/~hees/publ/habil-coll-talk-en.pdf

 

[mattt]

@Demystifier: given that the state of the whole (1,4) ensemble is also a sum of four different (1,4) Bell-states (before and after, whether we do something to (2,3) or not), I guess that for Bohmian Mechanics you could say that, for the set of millions of (1,4) pairs created in the whole ensemble, there exists a partition in four subsets X, Y, W, Z (25% of the total (1,4) pairs, in each subset), such that if you run a Bell Test exclusively for the (1,4) pairs in X, the Bell inequality will be violated (whether something is done to (2,3) or not).

The same holds for Y, W, and Z.

(We are not able to identify that partition without the help from the (2,3) measurements).

Is this correct?

 

[martinbn]

@Demystifier: given that the state of the whole (1,4) ensemble is also a sum of four different (1,4) Bell-states (before and after, whether we do something to (2,3) or not), I guess that for Bohmian Mechanics you could say that, for the set of millions of (1,4) pairs created in the whole ensemble, there exists a partition in four subsets X, Y, W, Z (25% of the total (1,4) pairs, in each subset), such that if you run a Bell Test exclusively for the (1,4) pairs in X, the Bell inequality will be violated (whether something is done to (2,3) or not).

The same holds for Y, W, and Z.

(We are not able to identify that partition without the help from the (2,3) measurements).

Is this correct?

My guess is that BM doesn't concern itself with ensembles. My guess is that according to BM in the absolute frame one of the measurements (on 23 or 14) happens first and that instantaneously (according to the absolute time) changes something where the other pair is (or will be).

 

[mattt]

My guess is that BM doesn't concern itself with ensembles. My guess is that according to BM in the absolute frame one of the measurements (on 23 or 14) happens first and that instantaneously (according to the absolute time) changes something where the other pair is (or will be).

Ah, I'm not very cultured in Bohmian Mechanics yet.

I thought that, because the reduced wave function for (1,4) pairs (the state of the whole (1,4) pairs ensemble) is the same (before and after, whether something is done to (2,3) pairs or not) and this is expressible as a sum of its four Bell states, I thought that Bohmian Mechanics (even though it is non-local) would agree with the ensemble interpretation in the existence of that partition (even if we need "external help" to find it).

 

[Demystifier]

@Demystifier: given that the state of the whole (1,4) ensemble is also a sum of four different (1,4) Bell-states (before and after, whether we do something to (2,3) or not), I guess that for Bohmian Mechanics you could say that, for the set of millions of (1,4) pairs created in the whole ensemble, there exists a partition in four subsets X, Y, W, Z (25% of the total (1,4) pairs, in each subset), such that if you run a Bell Test exclusively for the (1,4) pairs in X, the Bell inequality will be violated (whether something is done to (2,3) or not).

The same holds for Y, W, and Z.

(We are not able to identify that partition without the help from the (2,3) measurements).

Is this correct?

I think this is correct. But as @martinbn nicely explained, this is not essential for understanding all this from the Bohmian point of view. Even in classical physics there are subensembles with correlations without a cause. But the point is that in classical physics, as well as in Bohmian mechanics without doing anything to (2,3), you cannot extract such subensembles without cherry-picking. On the other hand, when you do something to (2,3), this creates a correlation without cherry-picking, so it seems natural to believe that doing it was the actual cause of correlation. Bohmian mechanics provides an explicit model for this cause.

https://en.wikipedia.org/wiki/Cherry_picking

 

[gentzen]

4. I am not "admitting" anything, since I have been saying there are 4 Bell states all along. I can spell them out (as I already did in later post #202), if it makes a difference to your understanding. But I think you know the answer already and don't need this:

Yes, you are right that I don't need this, and explicitly knowing this makes things easier for me. Indeed, I wasn't sure how much you would protest about my "lazy" notation:

... And then, wouldn't $\hat{\rho'}_{1234}= \frac{1}{4} \sum_{i=1}^4 \hat{\rho}_{14}^i \otimes \hat{\rho}_{23}^i$ be a more appropriate formula for the state, as long as no conditioning with respect to the 4 different states is done?

Let me now slightly extend my formula to include the actual "classically recorded" measurement result:
$\hat{\rho'}_{1234,M}= \frac{1}{4} \sum_{i=1}^4 \hat{\rho}_{14}^i \otimes \hat{\rho}_{23}^i \otimes \hat{\rho}_{M}^i$, where M marks the "classical" part of the information. This allows me to give a better formula for the state $\hat{\rho}_{1234,M}$ before the BSM measurement:
$\hat{\rho}_{1234,M}= (\frac{1}{4} \sum_{i=1}^4 \hat{\rho}_{14}^i \otimes \hat{\rho}_{23}^i) \otimes \hat{\rho}_{M}^0$
The only difference to the state after the measurement is that $\hat{\rho}_{M}^i$ has been replaced by $\hat{\rho}_{M}^0$.

5. And why would we want to fail to condition? That would lead us to a completely useless formula. The authors of the paper do the exact opposite, they USE the conditioning to demonstrate entanglement: "Expectation values for the CHSH inequality depending on the outcome, ψ− or ψ+, of the BSM. Each of these values is calculated from four measurements of four photon coincidences integrated over 15000 seconds."

This is actually a good question. The reason why I "wanted to fail to condition" was that I wanted to have a correct formula. Your question caused me to realize that I can also write down an equation which still contains the "classically recorded" measurement result. Then I have at least the choice, whether I want to trace-out that measurement result and thereby "fail to condition", or whether I "want to condition," and then continue with 4 different formulas for the 4 different cases.

The scientists in this room use all the information they have to make their conclusions. I would everyone would.

Using the information I have is fine for me, even as an instrumentalist. What I object to as an instrumentalist is giving up a local description, just because of some information which is potentially there, but which I personally don't have.

 

[DrChinese]

1. This is actually a good question.

2. Using the information I have is fine for me, even as an instrumentalist. What I object to as an instrumentalist is giving up a local description, just because of some information which is potentially there, but which I personally don't have.

1. So I think we're on the same page at this point.

2. This is the position held by yourself and others here. I totally get the desire to preserve locality. But...

a. It does not seem reasonable that you require all of the information about an experiment (with spatial extent) to be available simultaneously (your "because of some information which is potentially there, but which I personally don't have.") Your requirement could never be met when the full context is nonlocal.

b. You must then fully reject the realist position that there are well-defined outcomes independent of the act of observation. So you fully accept subjective (observer created) reality. A lot of interpretations (not saying yours does) that preserve locality try to "sneak by" on this point; "revealing pre-existing correlations" and the like. They can't be pre-existing (if you preserve locality) unless you reject Bell.

c. I don't get why, in experiments like the one we are discussing: The most obvious thing to conclude is that there IS action at a distance - so why not start from that position? I mean, I get that there is the desire to preserve Einsteinian causality. And actually, in the sense that QM predicts action at a distance, there is preservation of Einsteinian ideas in that there is still signal locality. It seems to me there are 2 different spacetime metrics at work. (I am not proposing an interpretation, just attempting to describe what I see.)

i) One limits signals and determinate actions to forward in time cause/effects, which cannot exceed c in any frame. Everyone pretty well agrees on this, regardless of interpretation.

ii) The other allows the full quantum context to be identified in a manner that does defy the apparent limits of relativity, but limits action at a distance to random outcomes. My observation regarding this: Interestingly, the full quantum context itself (which may consist of many elements in spacetime) only includes individual points that can be connected by determinate action limited to c. I will explain this statement in terms of our example.

In our example of entanglement swapping, we have the following basic experimental points in spacetime:

a) The 2 initial PDC sources A (for 1 & 2) and B (for 3 & 4), distant from each other.
b) The 2 Bell test setups for the Bell test on 1 & 4, distant from each other.
c) The BSM setup for determining the Bell state on 2 & 3, distant from the Bell test setups.

Despite the distances between the 2 sources (individually not in a common light cone) and the 3 Bell/BSM test setups (individually not in a common light cone): Each source is connected to one Bell test setup and the BSM by a path that respects c. And that is always the case, regardless of how large the quantum swapping network is (N nodes). There are always paths between the initial elements and the final elements that respect c even though there are other paths that may not - there is no element of the full context that only connected to the rest of the context by a path that does respect c.

Although I believe that our swapping experiment objectively demonstrates action at a distance (the BSM here changes the state of a remote quantum system there): I also see that the nonlocal context is constructed from component paths that individually respect c.

 

[vanhees71]

1. So I think we're on the same page at this point.

2. This is the position held by yourself and others here. I totally get the desire to preserve locality. But...

a. You must then fully reject the realist position that there are well-defined outcomes independent of the act of observation. (Otherwise you run afoul of Bell, of course.) So you fully accept subjective (observer created) reality. A lot of interpretations (not saying yours does) that preserve locality try to "sneak by" on this point; "revealing pre-existing correlations" and the like. They can't be pre-existing (if you preserve locality) unless you reject Bell.

There is no subjectivity in the ensemble representation. The quantum state tells you the probabilities for the outcome of measurements given the state (preparation) of the system. The non-local correlations, described by entangled states are indeed "pre-existing" due to the preparation of the entangled state, and they are objective. What's strictly local within relativistic QFT are interactions due to the microcausality constraint.

b. I don't get why, in experiments like the one we are discussing: The most obvious thing to conclude is that there IS action at a distance - so why not start from that position? I mean, I get that there is the desire to preserve Einsteinian causality. And actually, in the sense that QM predicts action at a distance, there is preservation of Einsteinian ideas in there is still signal locality. It seems to me there are 2 different spacetime metrics at work. (I am not proposing an interpretation, just attempting to describe what I see.)

It's not obvious that there's action at a distance at all. You can obviously use standard QED to account for all observed effects on entangled states, and standard QED by construction has no actions at a distance but it's fully compatible with Einstein causality due to the microcausality constraint implemented in its construction. I don't know what you mean by "signal locality", but if you mean that there are no causal connections between any space-like separated events, then this indeed implies that there are no FTL signals and thus also no actions at a distance. There are no two different spactime metrics at work. We are completely within the realm of special relativity, and there the spacetime geometry is fixed to be a Minkowski space.

i) One limits signals and determinate actions to forward in time cause/effects, which cannot exceed c in any frame. Everyone pretty well agrees on this, regardless of interpretation.

But you don't respect it above in saying that it was obvious that there are actions at a distance. This morning I thought, we'd agreed, but now you deny again the mathematical properties of relativistic local QFT.

ii) The other allows the full quantum context to be identified in a manner that does defy the apparent limits of relativity, but limits action at a distance to random outcomes. My observation regarding this: Interestingly, the quantum context itself (which may consist of many elements in spacetime) only includes individual points that can be connected by determinate action limited to c. I will explain this statement in terms of our example.

I don't understand, what this is meant to say. There's a concise mathematical frame work, i.e., local relativistic QFT. I think to make this point clear, you have finally use concrete math rather than "many words"!

In our example of entanglement swapping, we have the following basic experimental points in spacetime:

a) The 2 initial PDC sources A (for 1 & 2) and B (for 3 & 4), distant from each other.
b) The 2 Bell test setups for the Bell test on 1 & 4, distant from each other.
c) The BSM setup for determining the Bell state on 2 & 3, distant from the Bell test setups.

Yes, and all what's done here is well-described by local interactions between the photons and the equipment used in all these steps of preparation (a), the measurements of polarizations on photons 1 and 4 needed to perform a Bell test later by exchanging the information about the results of these polarization measurements for the subensemble chosen due to the Bell-State Measurement on photons 2&3.

Despite the distances between the 2 sources (individually not in a common light cone) and the 3 Bell/BSM test setups (individually not in a common light cone): Each source is connected to one Bell test setup and the BSM by a path that respects c. And that is always the case, regardless of how large the quantum swapping network is (N nodes). There are always paths between the initial elements and the final elements that respect c even though there are other paths that may not - there is no element of the full context that only connected to the rest of the context by a path that does respect c.

Not again paths! There are no paths of photons. It's confusing and misleading language, as we have discussed several times before.

Although I believe that our experiment demonstrates action at a distance (the BSM here changes the state of a remote quantum system there): I also see that the nonlocal context is constructed from component paths that individually respect c.

Once more, you are contradicting yourself in on the one hand acknowledging that everything is described by QED but on the other hand denying that the interactions are local. The only thing that's "non-local" are the correlations between far distantly observed parts of entangled quantum systems, i.e., there are "non-local correlations" but there are NO "non-local interactions" (and thus no FTL signaling and no actions at a distance) thanks to the microcausality condition fulfilled by QED.

 

[Lord Jestocost]

Franck Laloë in chapter 6 “Quantum entanglement” of his book “Do We Really Understand Quantum Mechanics?”:

6.1 A purely quantum property
In quantum mechanics, the relation between parts and the whole is very special, and certainly non-intuitive. We have already mentioned that Schrödinger was the first to use the words “quantum entanglement” in 1935, when he wrote (page 555 of [233]): “When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled......
Another way of expressing the peculiar situation is: the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts, even though they may be entirely separate and therefore virtually capable of being 'best possibly known', that is, of possessing, each of them, a representative of its own. The lack of knowledge is by no means due to the interaction being insufficiently known — at least not in the way that it could possibly be known more completely — it is due to the interaction itself.”

As respects to entanglement swapping, one now has to rethink Schrödinger’s statement as systems can become entangled that have never previously interacted. “Entanglement swapping is a procedure in which entanglement may be 'swapped' from a pair of jointly measured particles to a pair of particles lacking common preparation.” (David Glick in “Timelike Entanglement For Delayed-Choice entanglement Swapping”)

 

[Cthugha]

A lot of interpretations (not saying yours does) that preserve locality try to "sneak by" on this point; "revealing pre-existing correlations" and the like. They can't be pre-existing (if you preserve locality) unless you reject Bell.

Can you provide a reference for this statement? This claim is contrary to pretty much every single reference in the field. Just to make the terminology clear: "pre-existing correlations" does not mean that the individual measurement results are pre-existing, but their correlations are. If you prepare a state of momentum-entangled photons, you will always find that the sum of the two photons sums up to the same value (up to some small uncertainty). If you prepare a state of energy-entangled photons, you will find that their energies always sum up to the same value. This sum of energies (or momenta) is the pre-existing correlation. "Revealing pre-existing correlations" amounts only to conservation of energy (or momentum) and means, e.g., that the sum of the energies of the entangled photons in PDC is equal to the energy of the input photon. In other words, it means that you can predict the sum of the two entangled photon energies in PDC before the experiment is performed if you know the energy of the input photon (but of course not the individual photon energies).

Your statement is equivalent to stating that conservation of energy and momentum do not apply in experiments on entanglement, which is a very strong statement that should be backed up.

 

[DrChinese]

Can you provide a reference for this statement? This claim is contrary to pretty much every single reference in the field. Just to make the terminology clear: "pre-existing correlations" does not mean that the individual measurement results are pre-existing, but their correlations are. ... "Revealing pre-existing correlations" amounts only to conservation of energy (or momentum) and means, e.g., that the sum of the energies of the entangled photons in PDC is equal to the energy of the input photon. In other words, it means that you can predict the sum of the two entangled photon energies in PDC before the experiment is performed if you know the energy of the input photon (but of course not the individual photon energies).

Surely there is no need to provide references for the fact that Bell precludes both locality and realism. A person who holds on to locality must reject realism to comply with Bell. And nowhere do I make any claim whatsoever about conservation rules, and certainly don't reject them. Anything otherwise is not my assertion, and I don't really see how it applies here. I follow orthodox QM and generally reject Bell realism AND accept quantum non-locality (as that what QM looks like to me).

I think the issue here is terminology - I mentioned "pre-existing correlations" and I meant "pre-existing something" where each interpretation fills in the something in order to get to the predicted correlations. There are a number of interpretations that claim - in one fashion or another - that swapping experiments represent an "updating" or "revealing" of pre-existing conditions. If they preserve locality then they must reject realism, but a reading of their tenets is not completely clear on this point. Generally, I would refer to these as "wave function is epistemic" interpretations. Are these interpretations rejecting realism, or not? You asked for references:

1. QBism: Local with epistemic realism (reality is based on user beliefs)
https://arxiv.org/pdf/1810.13401.pdf
Locality: "... when we consider the highly specialized character of what is actually meant by realism in this context, keeping the local turns out to be the natural move."
Realism: "A quantum state encodes a user’s beliefs about the experience they will have as a result of taking an action on an external part of the world."

2. Consistent Histories: Local with epistemic realism (reality is stochastic)
https://plato.stanford.edu/entries/qm-consistent-histories/#LocSpeRel
Locality: "No such nonlocal influences are present in the histories interpretation, which is perfectly compatible with special relativity."
Realism: "First, quantum dynamics is treated as stochastic or probabilistic. ... In other words, given a measurement outcome [m^k] at t2 one can be certain that the prior state of the particle at t1 was [s^k]."

In their words, not mine. I call this "skirting Bell" because these interpretations do not do a very strong job of rejecting EPR elements of reality (Bell realism). They keep with the idea that there was a single reality prior to the act of measurement.

If anyone here denies the quotes above, I'd be happy to learn more. I don't consider myself well-versed in all interpretations, I mainly know what folks here have told me about there views (and which school they belong to).

 

[martinbn]

In the foundations of QM realism means existence of values of observables, not the philosophical existence of objective reality. I think that QM is non realistic by itself. And one needs to work hard to have a realistic interpretation. So rejecting realism (in this sense) is not a problem at all.

 

[mattt]

I think that nobody here has asserted the realistic position (that quantum observables have definite values all the time, regardless of the act of measurement or context) as unavoidable, just the opposite is true.

At most only bohmian mechanics defenders (or any other non-local realistic interpretation) may have mentioned it as a possibility only.

What I (and many others in this thread) have asserted is that this experiment and the mathematics that describes and explains it, adds nothing essentially new to the mathematics of entanglement (the CHSH Theorem and similar ones, the fact that the mathematics of quantum mechanics violates Bell inequalities, quantum teleportation, ...)

In all these cases, the state (the mathematical object that characterizes the statistics of) the initial ensemble of identically prepared copies, shows you that those correlations are there in the mathematical expression of the state, and they will be revealed experimentally if we happen to apply the pertinent experimental procedures suggested by that same mathematical expression of the initial state.

I see nothing new in this sense.

 

[DrChinese]

I think that nobody here has asserted the realistic position (that quantum observables have definite values all the time, regardless of the act of measurement or context) as unavoidable, just the opposite is true.

At most only bohmian mechanics defenders (or any other non-local realistic interpretation) may have mentioned it as a possibility only.

What I (and many others in this thread) have asserted is that this experiment and the mathematics that describes and explains it, adds nothing essentially new to the mathematics of entanglement (the CHSH Theorem and similar ones, the fact that the mathematics of quantum mechanics violates Bell inequalities, quantum teleportation, ...)

In all these cases, the state (the mathematical object that characterizes the statistics of) the initial ensemble of identically prepared copies, shows you that those correlations are there in the mathematical expression of the state, and they will be revealed experimentally if we happen to apply the pertinent experimental procedures suggested by that same mathematical expression of the initial state.

I see nothing new in this sense.

I agree with this. The only difference is the part where you say that this experiment shows nothing that wasn't already present before. I think the issue is: A particle (1) that was monogamously entangled with another (2) had its quantum state changed remotely so it was maximally entangled with yet another (4), without ever interacting with any other system at all.

That dynamic is not included in your description. This is relatively new (about 20+/- years), obviously now is well-accepted (the experiment, not necessarily the interpretation that swapping is objectively "action at a distance"). Then there is the PBR theorem (circa 2011), which says the wave function is itself "real".

https://arxiv.org/abs/1201.6554
"Broadly speaking, physicists today view the quantum state in one of two ways: in correspondence with the real physical state of affairs [Ontic] or as representing only an agent’s knowledge or information about some aspect of the physical situation [Epistemic]. The latter ‘epistemic’ viewpoint is primarily motivated by the obvious parallel between the quantum process of instantaneous wavefunction collapse, and the classical procedure of instantaneous updating of a probability distribution, both of which occur upon the acquisition of information regarding the outcome of a measurement process. The epistemic view has a long history of illustrious advocates..." Those advocates including Einstein, Popper, Ballentine, Zeilinger and Spekkens (plus many greats whose names are not mentioned).

Not surprisingly, and despite experimental realization, there are some who don't accept the PBR theorem on a variety of grounds. But when you combine the swapping experiment with the PBR theorem, yes, I think we are in a very new world when it comes to interpretations. If you aren't suitably familiar with these, I think you might want to make sure your favored interpretation complies with these... without hand-waving.

 

[gentzen]

Then there is the PBR theorem (circa 2011), which says the wave function is itself "real".

And because the wave function has this aspect of reality, the density matrix is so important to me and other instrumentalists. In fact, only after I learned about the density matrix in the context of partial coherence in optics, did I guess (around 2006) that I might finally be able to understand quantum mechanics, if I would give it a second try. Which turned out to be true.

Scott Aaronson nicely explains what is going on in the PBR theorem: The quantum state cannot be interpreted as something other than a quantum state

I recommend reading the preprint if you haven’t done so yet; it should only take an hour. PBR’s main result reminds me a little of the No-Cloning Theorem: it’s a profound triviality, something that most people who thought about quantum mechanics already knew, but probably didn’t know they knew. (Some people are even making comparisons to Bell’s Theorem, but to me, the PBR result lacks the same surprise factor.)

By contrast, pure states—states with perfect quantum coherence—seem intuitively much more “objective.” Concretely, suppose I describe a physical system using a pure state |ψ>, and you describe the same system using a different pure state |φ>≠|ψ>. Then it seems obvious that at least one of us has to be flat-out wrong, our confidence misplaced! In other words, at least one of us should’ve assigned a mixed state rather than a pure state. The PBR result basically formalizes and confirms that intuition.

 

[DrChinese]

Scott Aaronson nicely explains what is going on in the PBR theorem: The quantum state cannot be interpreted as something other than a quantum state

That blog entry came out very shortly after the original PBR paper, and I would not call it particularly insightful or definitive. Without trying to hype its significance, I would point instead to the 2014 review by Leifer (88 pages).

https://arxiv.org/abs/1409.1570

The original paper has about 1000 citations, and I would call it generally accepted. The significance of it may be in dispute, but not the proof itself. "If the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory." This is an anti-realist position (even as it espouses the reality of the wave function), and I would rate it as fairly severe.

 

[Cthugha]

Surely there is no need to provide references for the fact that Bell precludes both locality and realism. A person who holds on to locality must reject realism to comply with Bell.

I do not see how this is relevant for my remark. It was aimed especially at the term "pre-existing correlations" and your statement "They can't be pre-existing (if you preserve locality) unless you reject Bell."

I think the issue here is terminology - I mentioned "pre-existing correlations" and I meant "pre-existing something" where each interpretation fills in the something in order to get to the predicted correlations. There are a number of interpretations that claim - in one fashion or another - that swapping experiments represent an "updating" or "revealing" of pre-existing conditions. If they preserve locality then they must reject realism, but a reading of their tenets is not completely clear on this point. Generally, I would refer to these as "wave function is epistemic" interpretations. Are these interpretations rejecting realism, or not?

"Pre-existing something" is ill-defined. Pre-existing correlations are a clear-cut technical term with a well defined meaning: One can take, e.g., Mermin's take from "What is quantum mechanics trying to tell us", where he states:
"By correlations among subsystems I have in mind the mean values, at any given time, of all system observables (hermitian operators) that consist of products over subsystems of individual subsystem observables. Among the observables of a subsystem are the projection operators onto its linear subspaces, so the set of all correlations among the subsystems contains the set of all joint probability distributions over subsystems."
One example of such a system variable that consists of products over subsystems is the sum of the energies of the two detected photons in a PDC process. This sum energy is a correlation in the full technical sense of this word. The value of this sum energy can be predicted beforehand (if the input photon energy is known) with 100% certainty. It is therefore an element of reality. Most importantly, the fact that the correlation (the sum of energies) is an element of reality does not imply that the individual energies are an element of reality as well. This is what inspired Mermin's "Correlations have physical reality. That which they correlate does not".

Therefore, your statement "[correlations] can't be pre-existing (if you preserve locality) unless you reject Bell" is not tenable. The individual values of the photon energies surely cannot be pre-existing in this case. The sum of the values (and therefore the correlations) can. This is trivially not at odds with Bell at all. You can even formulate uncertainty relations about that. Just like you can either prepare states with well-defined momentum or position, you can either prepare states with well-defined correlations (so you have entanglement) or well defined individual properties (so you have some kind of single photon coherence). This has been shown by Teich in his famous 2001 PRA (Phys. Rev. A 63, 063803 (2001), https://arxiv.org/abs/quant-ph/0112065 ).

Just to summarize: my point is that "pre-existing correlations" are not "pre-existing something", but a well-defined technical term that should not be used in a loose manner as its meaning may easily get altered completely when doing so.

 

[DrChinese]

Just to summarize: my point is that "pre-existing correlations" are not "pre-existing something", but a well-defined technical term that should not be used in a loose manner as its meaning may easily get altered completely when doing so.

Wow @Cthugha , I think your focus on the word "correlations" (or "something") is way overboard, quite out of the ordinary for you. If you want to make something of the significance of momentum entanglement (as opposed to polarization entanglement) in PDC pairs and how it relates to conservation rules: Start a thread and we can discuss. But you will quickly find that it is not a factor in swapping experiments (or their interpretation), at least not one that changes anything discussed in this thread. Entanglement is entanglement, regardless of basis. Conservation is conservation as well, and nothing I say challenges this. I have written enough in this thread that trying to french fry me over a word is ridiculous. If you have something of substance, then present it.
-------------------------------

So... I wasn't specifically trying to make the point about correlations when I wrote it, but if you want to press it: let me be explicit:

DrC: The final (1 & 4) correlations are not pre-existing independent of the BSM. Only the initial (1 & 2) correlations existed prior to that (due to MoE*). Correlations that violate CHSH are indicative of entanglement*, and vice versa.

Reference on "correlation" as you requested (the one we've been using and you apparently didn't read entirely):
https://arxiv.org/abs/0809.3991

"We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4. Violation of a CHSH inequality is not only of fundamental interest because it rules out local-hidden variable theories. It also proves that the swapped states are strongly entangled... The resulting correlations between particles that do not share any common past are strong enough to violate a Clauser-Horne-Shimony-Holt (CHSH) inequality."

Case closed, my words stand as written. You can argue with the authors over semantics if you like, but I'm done on your point in this thread. You aren't even disputing that the BSM is action at a distance.*Already referenced, and not a single counter-reference presented to date in these threads. I am not going to keep presenting references over and over.

 

[Fra]

I call this "skirting Bell" because these interpretations do not do a very strong job of rejecting EPR elements of reality (Bell realism). They keep with the idea that there was a single reality prior to the act of measurement.

I think most interpretations holds variations but I think that qbist stances(at least not all) does not strictly "keep the idea of objective reality". To me at least i would say it is compatible with objective reality but does not rely on it. This is a world of difference! I would even say objective reality cant be ruled out, so its allowed, but the agent interations is indifferent to it. A solid illusion is indistinguishable from objective reality from the perspective of any inferring agent.

This is to me the KEY to bypass/skirting? the premises of bells theorem - isolated HV may exist and add explanatory value, but they does not influence the physics as long as they are isolate not only from the physicist but from every part of the experimental setup.

But I see no problem with this "skirting"?

Realism is allowed, but wether its just an illusion doesnt matter. Its impossible to tell and that is fine. Also, the point for an agent is that even IF objective reality exists, that adds no value, unleas the agent has inferred it.

Otherwise its like say you know the answer to somerhing! Its only that you forgotten it. Or you have a superalgorithm that you clom gives the answer it just takes the lifetime of a universe to compute it.

Well then you dont know. And your decision must be made.

/Fredrik

 

[Nullstein]

We have established many times that the initial 1 & 4 state is uncorrelated and unentangled, and that there is no relationship between them - hidden or otherwise.

We also have established many times that the final 1&4 state is uncorrelated and unentangled.

Yes, it is trivially true that if you look at the 1 & 4 pairs and don't know their Bell state, no pattern pops out. I guess we need to tell this team that they are wasting their time when they run the experiment and announce: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4. Violation of a CHSH inequality is not only of fundamental interest because it rules out local-hidden variable theories. It also proves that the swapped states are strongly entangled and, as a result, distillable."

All I can say is "wow". Hundreds of teams out there are working to create quantum networks using swapping from point to point to point. They all seem to think there is entanglement, and they all seem to think the 2 & 3 BSM had something to do with it.

The aim of these teams is just to verify the predictions of QM, nothing more. Your personal goal, which is different from the goal of these teams, is to somehow infer causal relationships from the data. These teams have reached their goal, while you have failed to reach yours. Nobody doubts that there is entanglement swapping. The discussion in this thread is solely about causal inference.

I have quoted extensively on Monogamy and referenced papers.

We have already established that your application of MoE is wrong. You are trying to somehow show that the full ensemble of 1&4 is entangled after the BSM. We have established that it is in a product state. No appeal to MoE can invalidate this. The papers you quoted don't support your opinion.

 

[PeterDonis]

Thread closed for moderation.

 

[DrClaude]

We'll leave the thread closed. Thanks to all that have participated.