General argument that entanglement can only be created locally

[greypilgrim]

Hi.

As far as I know, entanglement can initially only be created locally, for example by creating two photons at one place in a crystal, or by local forces. Sure, there's entanglement swapping, but the initial entanglement was still created locally.

But I only know examples. Is there a general mathematical argument that proves this?

 

[Vanadium 50]

If youy define "true" entanglement as having been "created locally", aren't you done?

No trus Scotsman puts sugar on his porridge.

 

[greypilgrim]

Well it's mathematically decidable if a given state is entangled or not, without referring to its generation.

 

[DrChinese]

Sure, there's entanglement swapping, but the initial entanglement was still created locally.

A swap here creates entanglement there. How can you dismiss this obviously non-local phenomena? The swap can be performed after detection of entangled photons that never even existed in a common light cone.

 

[greypilgrim]

But swaps have to be performed locally as well, don't they? The photons have to be "at the same place" for a Bell basis measurement?

 

[DrChinese]

But swaps have to be performed locally as well, don't they? The photons have to be "at the same place" for a Bell basis measurement?

The swapped photons (ones becoming entangled) are elsewhere, not local to the swap itself.

And even the photons participating in the swap are not exactly local. They are near to each other for a short period of time before they are detected at different detectors. They do not directly interact (and in fact may have orthogonal polarizations). They must instead be indistinguishable as to the source.

 

[Morbert]

A swap here creates entanglement there. How can you dismiss this obviously non-local phenomena? The swap can be performed after detection of entangled photons that never even existed in a common light cone.

The instrumentalist approach would frame the entanglement swapping as causally local, as the entangled photons exist in the common light cone of the preparation procedure (The preparation procedure in this case consisting of a preparation of two photon pairs [1,2] and [3,4] and a measurement of one photon pair [2,3]).

 

[vanhees71]

A swap here creates entanglement there. How can you dismiss this obviously non-local phenomena? The swap can be performed after detection of entangled photons that never even existed in a common light cone.

Not again! Also the choice of the entangled subensembles in the entanglement-swapping protocol are due to local measurements on two photons (one from the one initially entangled pair, one from the other). For the so chosen (and the choice can be made as delayed as you wish!) sub-ensembles you have entanglement between photon pairs, which were never in causal/local contact. We've discussed this at length before. There are no non-local interactions, only correlations between far-distant parts! That's even true without thinking by construction of QED as local relativistic QFT!

 

[DrChinese]

For the so chosen (and the choice can be made as delayed as you wish!) sub-ensembles you have entanglement between photon pairs, which were never in causal/local contact. ... There are no non-local interactions, only correlations between far-distant parts! That's even true without thinking by construction of QED as local relativistic QFT!

We agree on almost everything, including your "without thinking" part. You might consider re-thinking that, it's good to take the occasional opportunity to question your own (entrenched) position. Read on below...

The instrumentalist approach would frame the entanglement swapping as causally local, as the entangled photons exist in the common light cone of the preparation procedure (The preparation procedure in this case consisting of a preparation of two photon pairs [1,2] and [3,4] and a measurement of one photon pair [2,3]).

Yes, it is true that photons [2,3] are observed to be very near (within a range of about 0.25 to 1.5 meters apart) to each other, so near that you cannot distinguish [2] from [3]. However: in half of the "chosen" cases, these photons are orthogonal and yet the (remote/distant/non-local) swap occurs.

a) Can you explain how orthogonal photons manage to interact?
b) Can you explain how the outcomes of a measurement "here" (locally) cause the entanglement of distant photons?
c) Can you explain how the entanglement of distant photons is "caused" long after those other photons are measured?
d) Can you explain at what time the [1] photon ceased being entangled with [2], and started being entangled with [4]? (Keeping in mind that the [4] photon need not even be in existence at any time you select.)

The thing I keep pointing out is the obvious contradiction between so-called local* interpretations** and the experimentally verified quantum rules, those being: entanglement of photons from independent sources, entanglement of photons outside a common light cone, entanglement via remote swapping, entanglement via delayed swapping, inability of orthogonal photons to interact, and of course Monogamy of Entanglement***. Perhaps the theoretical view espoused by @vanhees71 needs refinement in light of overwhelming evidence to the contrary?*Despite the published conclusions of thousands of experimentalists demonstrating quantum non-locality, stating that their conclusions are orthodox QM.

** Or any viewpoint that claims the swap is merely correlation or coincidence, and does not represent a non-local change to the overall system under study.

***MoE: Which prevents photon [1] from being entangled with photons [2] and [4] simultaneously.

 

[Morbert]

@DrChinese Before I answer, can you relink the paper? I'm having trouble finding it. I want to make sure I remember the procedure right.

 

[Morbert]

Let's first consider a single pair of particles, prepared in the state $|\phi^+\rangle\langle\phi^+|$. The pair are moving away from each other such that at a joint measurement carried out by two appropriately aligned SG instruments in space-like separated spacetime regions will yield a correlation uu+dd (where '+' denotes an 'exclusive or' operator) over several experimental runs (I.e. if one particle emerges in the upper beam of its SG instrument, the other particle must also do the same). We have a cause (the preparation), and an effect (the observed correlation in joint-measurements). The effect is spatially nonlocal (the instruments measuring the correlated property of the particles are spacelike separated) but causally local (The union of the past light cones of the particles contains the causal event, the preparation. See figure 1 here).

We can see that the entanglement swapping experiment is analogous. Our preparation of the two pairs in the state $|\psi^+_{12}\psi^+_{34}\rangle\langle\psi^+_{12}\psi^+_{34}|$ is the causal event. This time, the joint measurement is a measurement of the particle pairs [1,4] and [2,3] in the bell basis, that will yield the correlation $\psi^+_{14}\psi^+_{23}+\psi^-_{14}\psi^-_{23}+\phi^+_{14}\phi^+_{23}+\phi^-_{14}\phi^-_{23}$. Like before, we have an effect that is spatially nonlocal, but causally local, as the union of past light cones of the 4 particles contain the preparation (the cause).

Now, iirc in the original paper, no measurement is carried out on particle pair [1,4], so no joint measurement of the pairs can be carried out and analyzed for correlations. In this case our effect is limited to the measurement result of [2,3], and we cannot say anything about the [1,4] pair as it is never objectified through experiment.

It goes without saying that the above limitation of objective facts to experiments that are actually done is one interpretation of QM, the instrumentalist interpretation of QM, and other interpretations might conclude some causal nonlocality in addition to spatial locality. But it's a consistent, unambiguous interpretation.

So to answer your questions with this interpretation in mind

a) Can you explain how orthogonal photons manage to interact?
b) Can you explain how the outcomes of a measurement "here" (locally) cause the entanglement of distant photons?
c) Can you explain how the entanglement of distant photons is "caused" long after those other photons are measured?
d) Can you explain at what time the [1] photon ceased being entangled with [2], and started being entangled with [4]? (Keeping in mind that the [4] photon need not even be in existence at any time you select.)

a) No photons interact with each other. Only with the preparation procedure.
b + c) If joint measurements on [1,4] and [2,3] are carried out, we will see correlations, but this "correlation event" is caused by the preparation event. And this cause is local, as the union of the past light cones of all the particles contain the preparation. The individual outcomes of the measurements are not cause by each other.
d) There is no moment where the photons [1] and [4] become entangled. It is not an objective property of the world. There are only the correlations yielded by joint measurements. Nor can we say that [1,4] have been prepared in an entangled state, because we would need a way to bin the [1,4] pairs of each experimental run in accordance with the outcomes of measurement on [2,3].

 

[DrChinese]

@DrChinese Before I answer, can you relink the paper? I'm having trouble finding it. I want to make sure I remember the procedure right.

https://arxiv.org/abs/quant-ph/0201134
Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping
Quantum teleportation strikingly underlines the peculiar features of the quantum world. We present an experimental proof of its quantum nature, teleporting an entangled photon with such high quality that the nonlocal quantum correlations with its original partner photon are preserved. This procedure is also known as entanglement swapping. The nonlocality is confirmed by observing a violation of Bell's inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted our results directly confirm the quantum nature of teleportation.

In this paper, the photons are labeled 0-3 rather than 1-4, but I will continue the labels as 1-4. Of course, the [1, 4] pair does have a Bell test performed on it to demonstrate entanglement.https://arxiv.org/abs/1209.4191
Entanglement Between Photons that have Never Coexisted
The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime.
This uses the 1-4 labels. Same experiment, but the [1] photon is detected before the [3, 4] pair is even created. Keep in mind that MoE does not allow the [1] photon to be maximally entangled with both the [2] and the [4] photons at the same time.

a) Your concept that there is an "initial preparation" that has [1,4] entangled is not justified by any interpretation of QM. Keep in mind that [1,4] will show perfect correlations at all (an infinity of?) angle settings, something no unentangled photon pairs will do. A swap here - and only a swap here - physically causes the [1,4] entanglement; and it does so at a spacetime distance not limited by Einsteinian causality.

b) Further: it should be obvious that the indistinguishability requirement on [2,3] could be waived if there is no physical event occurring. They obviously don't interact when they are orthogonal! And you obviously don't think the swap procedure changes anything at [1, 4]! And yet... no indistinguishability, no swap. Hmmm. Why do you think that is? Answer: Spooky action at a distance, let's just call it for what it is.

c) IMPORTANT: There is no requirement that the [2] & [3] photons ever appear in the same light cone. There can be additional intermediate swaps, which actually occurs with quantum repeaters. I imagine you can hand waive that away by saying that there are now 4+2 photons as part of the initial preparation procedure; but I hope you can see that the time ordering issue becomes a serious problem as the final swap can be performed after all four of [1,2,3,4] are recorded. (Or not, as the experimenter decides.)

 

[DrChinese]

a) We can see that the entanglement swapping experiment is analogous. Our preparation of the two pairs in the state $|\psi^+_{12}\psi^+_{34}\rangle\langle\psi^+_{12}\psi^+_{34}|$ is the causal event. This time, the joint measurement is a measurement of the particle pairs [1,4] and [2,3] in the bell basis, that will yield the correlation $\psi^+_{14}\psi^+_{23}+\psi^-_{14}\psi^-_{23}+\phi^+_{14}\phi^+_{23}+\phi^-_{14}\phi^-_{23}$. Like before, we have an effect that is spatially nonlocal, but causally local, as the union of past light cones of the 4 particles contain the preparation (the cause).

b) Now, iirc in the original paper, no measurement is carried out on particle pair [1,4]...

It goes without saying that the above limitation of objective facts to experiments that are actually done is one interpretation of QM, the instrumentalist interpretation of QM, and other interpretations might conclude some causal nonlocality in addition to spatial locality. But it's a consistent, unambiguous interpretation.

c) So to answer your questions with this interpretation in mind
a) No photons interact with each other. Only with the preparation procedure.
b + c) If joint measurements on [1,4] and [2,3] are carried out, we will see correlations, but this "correlation event" is caused by the preparation event. And this cause is local, as the union of the past light cones of all the particles contain the preparation. The individual outcomes of the measurements are not cause by each other.
d) There is no moment where the photons [1] and [4] become entangled. It is not an objective property of the world. There are only the correlations yielded by joint measurements. Nor can we say that [1,4] have been prepared in an entangled state, because we would need a way to bin the [1,4] pairs of each experimental run in accordance with the outcomes of measurement on [2,3].

This should be obvious, but I will repeat this (same result as vanhees71 and I agreed upon earlier this year on this subject):
Subensemble Before (Initial Preparation): $$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}.$$

Subensemble After Swap: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

Objectively: $$\hat{\rho}_{12} \otimes \hat{\rho}_{34} <> \hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

This change to the quantum state is a result of a physical action - the remote entanglement swap.

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

a) I agree that the swap is spatially non-local. That's my point, it's action at a distance! How you manage to call this "causally local" is a mystery to me though. You can do the swap after [1,4] become entangled. That would actually be called retrocausal (not that I am espousing retrocausality), and certainly not "causally local".

b) You just missed this in the paper. A full Bell test is always performed on the [1,4] pairs. The nonlocality proof would be meaningless without this. The reference being "Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping" by one of Zeilinger's teams.

c) If you carry your view of the swap creating [1,4] entanglement to its logical conclusion: all entangled particles from independent sources anywhere are also prepared in the same initial state - just waiting for those "correlations" to be revealed. Any photon pair that passes a Bell test must also evidence perfect correlations at all identical angles. That is a large - if not infinite - amount of correlations. And in your mind, those perfect correlations are just waiting to be revealed with any of thousands of potential photon sources. After all, we could pair [1,2] - instead of with [3,4] - with [5,6] or [7,8] or [9,10] etc.

Hmmm, that is as big a violation of Monogamy of Entanglement (MoE) as I could imagine. MoE says that if [1,2] are maximally entangled, they cannot be entangled at all with any other quantum particle. Or perhaps you deny MoE?

https://arxiv.org/abs/quant-ph/9907047
This is one of the seminal papers on MoE, referred to as CKW.

https://arxiv.org/pdf/quant-ph/0604168.pdf
Proof of MoE

 

[vanhees71]

We agree on almost everything, including your "without thinking" part. You might consider re-thinking that, it's good to take the occasional opportunity to question your own (entrenched) position. Read on below...
Yes, it is true that photons [2,3] are observed to be very near (within a range of about 0.25 to 1.5 meters apart) to each other, so near that you cannot distinguish [2] from [3]. However: in half of the "chosen" cases, these photons are orthogonal and yet the (remote/distant/non-local) swap occurs.

The photons [2,3] interacted with the polarizing beam splitter and were then detected. I don't understand, what you mean by "orthogonal". Of course with some probability one of these photons turn out to be in orthogonal polarization states. What has this to do with their interactions with the beam splitter and the detectors? After all the state of these two photons simply is $1/4 \hat{1} \otimes \hat{1}$. They are not entangled before the measurement. The purpose of this measurement is to select them in an entangled state. For each of the four possible entangled states then also the photon pair [1,4], which were never anywhere in causal/local contact, is in one of the four specific Bell states. This is however due to the entanglement of the pairs [1,2] and [3,4] and not due to any "spooky actions at a distance".

a) Can you explain how orthogonal photons manage to interact?

I don't understand this question. The photons interact with the beam splitter and the detectors, no matter in which polarization state they are found in this measurement. I don't know, what you mean by "interact" in connection with the orthonality of the measured polarization states. We don't discuss photon-photon scattering here. That's way too small to be detected in such an experiment. In fact it has only been detected very recently in ultra-relativistic ultra-peripheral Pb-Pb collisions at the LHC.

b) Can you explain how the outcomes of a measurement "here" (locally) cause the entanglement of distant photons?

As said above, that's due to the entanglement of the pairs [1:2] and [3:4] before the measurement. The two pairs among themselves are not entangled at all. In the initial state you have
$$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}$$.
After making a Bell measurement on photons 2 and 3 and projecting the four-photon system in any state, where photons 2 and 3 were found in one of the four Bell states, the photons 1 and 4 are also projected to such a Bell state. There was no interaction at a distance. It was just selection of a sub-ensemble due to the local measurement on photons 2 and 3 and the original entanglement of photons 1 and 2 and photons 3 and 4. This correlation is already there with the original preparation. There's no need to envoke some "spooky actions at a distance", which contradict QED. QED itself is sufficient to explain the outcomes of this entanglement and thus the validity of the entanglement swapping protocol.

c) Can you explain how the entanglement of distant photons is "caused" long after those other photons are measured?

The same as answering b). It doesn't matter, when I select the sub-ensembles. The correlations needed to explain the entanglement of photons 1 and 4 after the local measurement on photons 2 and 3 were already there with the preparation of these four photons. The possibility of post-selection together with locality of QED demonstrates that there's no causal effect of the local measurement on photons 2 and 3 on the state of photons 1 and 4, because there's no causal connection between the latter photons with the measurement appartus used for the measurement on the former.

d) Can you explain at what time the [1] photon ceased being entangled with [2], and started being entangled with [4]? (Keeping in mind that the [4] photon need not even be in existence at any time you select.)

There's no temporal order in this. That's the whole point of this experiment! Your can only say: It's the split into subensembles, which come into being at the moment the pair [2,3] has been detecting as being in one of the four Bell states.

The thing I keep pointing out is the obvious contradiction between so-called local* interpretations** and the experimentally verified quantum rules, those being: entanglement of photons from independent sources, entanglement of photons outside a common light cone, entanglement via remote swapping, entanglement via delayed swapping, inability of orthogonal photons to interact, and of course Monogamy of Entanglement***. Perhaps the theoretical view espoused by @vanhees71 needs refinement in light of overwhelming evidence to the contrary?

Locality is a property of theories, and in relativistic QFT it has a well-defined mathematical meaning, namely the microcausality constraint being fulfilled for all local observable operators. There's no interpretation involved here. I've no idea, what you mean by the "inability of orthogonal photons to interact". Of course, any photon can interact with the optical equipment with the corresponding probability. There's nothing the prevents such an interaction only because there's another photon being in an orthogonal polarization state.

*Despite the published conclusions of thousands of experimentalists demonstrating quantum non-locality, stating that their conclusions are orthodox QM.

The experimentalists demonstrate the validity of local relativistic QFTs again and again. It's the most successful theory ever.

Of course with QM, being a non-relativistic theory, there's no contradiction with actions at a distance. There's of course no microcausality constraint in non-relativistic Q(F)T. It's not even possible to formulate such a principle in non-relativistic physics.

** Or any viewpoint that claims the swap is merely correlation or coincidence, and does not represent a non-local change to the overall system under study.

I'm clearly in this camp, because that's what local relativistic QFT describes by construction.

***MoE: Which prevents photon [1] from being entangled with photons [2] and [4] simultaneously.

In none of the states (at the original preparation nor for the sub-ensembles after projection of photons [2,3] to one of the four Bell states) is photon 1 being entangled with photons 2 and 4 simultaneously. I never claimed such a thing.

 

[martinbn]

Subensemble Before (Initial Preparation): $$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}.$$

Why do you call this a subensemble? Isn't that the full ensemble?

Subensemble After Swap: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

This is for a subensemble.

Objectively: $$\hat{\rho}_{12} \otimes \hat{\rho}_{34} <> \hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

This change to the quantum state is a result of a physical action - the remote entanglement swap.

This doesn't follow. There are two different ensembles here and two different states.

 

[vanhees71]

The change is due to selection based on local measurements on photons 2 and 3, and of course $\hat{\rho}_{12} \otimes \hat{\rho}_{34}$ describe the full ensemble while $\hat{\rho}_{23} \otimes \hat{\rho}_{14}$ describes one of 4 sub-ensembles after projection of photons 2 and 3 to one of the four Bell states. The full ensemble is always described by the former state!

 

[DrChinese]

a) The photons [2,3] interacted with the polarizing beam splitter and were then detected. I don't understand, what you mean by "orthogonal".

Of course with some probability one of these photons turn out to be in orthogonal polarization states. What has this to do with their interactions with the beam splitter and the detectors? After all the state of these two photons simply is $1/4 \hat{1} \otimes \hat{1}$. They are not entangled before the measurement. The purpose of this measurement is to select them in an entangled state. For each of the four possible entangled states then also the photon pair [1,4], which were never anywhere in causal/local contact, is in one of the four specific Bell states. This is however due to the entanglement of the pairs [1,2] and [3,4] and not due to any "spooky actions at a distance".

a) 2 of the 4 Bell states require their photon detections to be orthogonal. The other 2 states require them to be the same (parallel). This relationship couldn't be simply a result of a typical interaction with a polarizer for [2] individually and independently and for [3] individually and independently. For if it were, you would not get a Bell inequality violated (or perfect correlations) by the [1,4] pairs.

b) In your view: [1, 4] are entangled already - we just don't know which of the 4 states they are entangled in until the Bell state measurement (BSM) is performed. A successful BSM - which is all [2,3] pairs that are observed within the coincidence time window - is merely the method to distinguish one Bell State from the other. That tells us whether [1,4] are perfectly correlated or anti-correlated.

But that view is not possible! MoE forbids this exact situation. [1,4] cannot be entangled if [1,2] are simultaneously entangled.

I've given the references (most recently in post #13), and no person disagreeing with me has provided a single reference refuting Monogamy of Entanglement. That's because MoE is generally accepted, regardless of interpretation. That prevents/precludes an explanation requiring [1,4] entanglement existing from the [1,2]*[3,4] preparation. Moderators, isn't there a burden here? I again challenge anyone to present a specific quote from a suitable paper that explains entanglement swapping as vanhees71 has done.

And just to be clear, the title of the well known Zeilinger paper on the subject is entitled: "Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping" which leaves nothing to the imagination. "Nonlocality" being the key word here...

 

[DrChinese]

It of course goes without saying that the correlations between 1 and 4 can be deeper than the correlations between the distant socks.

There are no quantum correlations of any kind whatsoever between systems that are prepared independently in a Product state. This is fundamental, and there is really nothing to debate about this. And why you would mention the classical socks example is beyond me. In your world, the swap operation is apparently not even necessary. How about, once again, providing a reference that matches your completely wrong assessment of the initial Product State $|\psi^-_{1,2}\psi^-_{3,4}\rangle$ and says it embeds 4 Bell States inside it without needing to perform a swap operation.

It completely puzzles me why I produce references that state what I assert nearly verbatim (Zeilinger: "Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping"; and you fail to produce any remotely close reference matching your position (which you claim is standard - so it should be easy). You should re-think your entrenched position in light of the references I have provided, especially those about MoE.

The instrumentalist will say that the photons never have any inherent property of being entangled or not entangled. A state like $|\psi^-_{1,2}\psi^-_{3,4}\rangle$ is not a statement about the photons per se. It is a statement about their preparation, and can be used to predict correlations in detector outcomes.

There is no treatment anywhere that says photons [1,4] are "pre-entangled" in any way, shape or form when prepared as in the reference. The swap does more than identify the Bell State; it creates it, and is a necessary step.

And the idea that [1,2] pairs are not prepared in an entangled state is laughable - of course it is an inherent property of a such a system. Show me any experimentalist who says otherwise in their entanglement paper.

 

[martinbn]

And just to be clear, the title of the well known Zeilinger paper on the subject is entitled: "Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping" which leaves nothing to the imagination. "Nonlocality" being the key word here...

No one disagrees with that. They say, already in the abstract you quoted, "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations." Which means that by nonlocality, they mean violation of Bell's inequality. You mean something stronger. You cannot support your claim by just quoting a paper that uses the same word "nonlocality" , but with a different meaning.

 

[PeterDonis]

Thread closed for moderation.

 

[berkeman]

@Morbert has been thread banned for continued off-topic posts and the thread is reopened.

 

[Cthugha]

I've given the references (most recently in post #13), and no person disagreeing with me has provided a single reference refuting Monogamy of Entanglement. That's because MoE is generally accepted, regardless of interpretation. That prevents/precludes an explanation requiring [1,4] entanglement existing from the [1,2]*[3,4] preparation. Moderators, isn't there a burden here? I again challenge anyone to present a specific quote from a suitable paper that explains entanglement swapping as vanhees71 has done.

And just to be clear, the title of the well known Zeilinger paper on the subject is entitled: "Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping" which leaves nothing to the imagination. "Nonlocality" being the key word here...

Just to be clear: The most famous proponent of @vanhees71 version is Zeilinger himself:
https://arxiv.org/ftp/arxiv/papers/1203/1203.4834.pdf

As he states on page 6:
"If one views the quantum state as areal physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge”. Then the state is a probability list for all possible measurement outcomes, the relative temporal order of the three observer’s events is irrelevant and no physical interactions whatsoever between these events, especially into the past, are necessary to explain the delayed-choice entanglement swapping. What, however, is important is to relate the lists of Alice, Bob and Victor’s measurement results. On the basis of Victor’s measurement settings and results, Alice and Bob can group their earlier and locally totally random results into subsets which each have a different meaning and interpretation. This formation of subsets is independent of the temporal order of the measurements. According to Wheeler, Bohr said: “No elementary phenomenon is a phenomenon until it is a registered phenomenon.” We would like to extend this by saying: “Some registered phenomena do not have a meaning unless they are put in relationship with other registered phenomena.”"

Indeed Zeilinger leaves nothing to the imagination. He clearly favours @vanhees71 version.

The whole MoE discussion is a red herring based on an argument that is only valid when assuming a realistic interpretation. Based on that prior assumption, it indeed becomes important. However, we are not in the interpretations forum here.

 

[vanhees71]

Sure, Zeilinger is clearly a no-nonsense experimentalist, sticking to the physical facts and thus demystifies all the philosophical clouds over the quantum-foundations community. As far as the physical foundations are concerned, there are indeed no contradictions between the experimental outcomes and the locality of the relativistic QFT and thus also not with causality. There are no faster-than-light causal actions and of course no retrocausal paradoxes due to the possibility of post-selecting sub-ensembles from a combination of local measurement protocols as used, e.g., in the delayed-choice quantum-eraser experiment or entanglement swapping.

The monogamy of quantum entanglement, as described in Wikipedia,

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

is a preparability constraint and pretty straight forward to prove, as seen even in the Wikipedia article. It is in clear accordance with the minimal statistical interpretation.

Also, I guess the misunderstanding leading to bringing up the argument with the monogamy of entanglement may be again not to clearly distinguish between correlations and causations. It's of course clear that in the here discussed entanglement-swapping experiment that preparation of the full ensemble has the form
$$\hat{\rho}_{1234}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}$$
with $\hat{\rho}_{jk}$ being pure Bell states. So the pairs (13), (1,4), (2,3) and (2,4) are not entangled as can easily be shown by calculating the corresponding reduced density matrix.

Entanglement swapping, however is just selcecting subsenembles by doing a projection measurement on the pair (23) to one of the four possible Bell states of this pair. Then the preparation in the above state implies that for this sub-ensemble no also (14) is in a Bell state, as demonstrated by the experiments. This is of course no contradiction to the monogamy, because by this selection the subensemble is now in the state
$$\hat{\rho}_{1234}'=\hat{\rho}_{14} \otimes \hat{\rho}_{23},$$
i.e., in this sub-ensemble the pairs (12), (13), (42), and (43) are all not entangled, in accordance to the monogamy constraint, i.e., also the entanglement swapping is not a preparation procedure that can violate the monogamy of entanglement.

As usual, with the minimal statistical interpretation there's no paradox in any way. BTW, Zeilinger's reference to the quantum state as the "catalogue of our knowledge" is already due to Schrödinger. Schrödinger was much more clear concerning foundational issues than the entire Copenhagen gang ever was. He never "entangled" his dissatisfaction with QT with the physical meaning following from QT. His quibble was purely philosophical too, i.e., as Einstein he could not accept the conclusion from the discovery of QT that Nature is inherently probabilistic. As concerning Einstein, I'd be really interested to know, how Schrödinger would have reacted to Bell's work and Zeilinger's et al's findings about Bell tests!

 

[DrChinese]

Just to be clear: The most famous proponent of @vanhees71 version is Zeilinger himself:
https://arxiv.org/ftp/arxiv/papers/1203/1203.4834.pdf

a) As he states on page 6:
"If one views the quantum state as areal physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge”. Then the state is a probability list for all possible measurement outcomes, the relative temporal order of the three observer’s events is irrelevant and no physical interactions whatsoever between these events, especially into the past, are necessary to explain the delayed-choice entanglement swapping. What, however, is important is to relate the lists of Alice, Bob and Victor’s measurement results. On the basis of Victor’s measurement settings and results, Alice and Bob can group their earlier and locally totally random results into subsets which each have a different meaning and interpretation. This formation of subsets is independent of the temporal order of the measurements. According to Wheeler, Bohr said: “No elementary phenomenon is a phenomenon until it is a registered phenomenon.” We would like to extend this by saying: “Some registered phenomena do not have a meaning unless they are put in relationship with other registered phenomena.”"

b) He clearly favours @vanhees71 version.

c) The whole MoE discussion is a red herring based on an argument that is only valid when assuming a realistic interpretation.

a) This is a pretty good quote, but the sense of it is not presented as I might. I'd like to parse out a different portion of the same paragraph: "i) Whether these two particles are entangled or separable has been decided after they have been measured. ii) If one views the quantum state as a real physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. iii) However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge".

i) This is my assertion, perfectly phased.
ii) This too is my assertion. I prefer to refer to it as "quantum nonlocality" or "spooky action at a distance" rather than focus on any retrocausal element. That's because it is the entire experimental context (which is nonlocal obviously) that must be considered, and as they state: "quantum mechanical predictions are completely indifferent to the temporal order". Note that they base this on the assumption that the quantum state is a real physical object. The 2011 PBR paper "On The Reality of the Quantum State" says that it is (published near simultaneous with your reference).
iii) As long as the nonlocality of the full context is acknowledged, I have no issue with this statement. However, I dispute any inference that this the swap does not play an active role in the full context. b) Likewise, I dispute any inference that Zeilinger et al are saying that the [1,4] pair was entangled in any way as a part of the initial preparation, as @vanhees71 claims. There are no statements to that effect here. So no, Zeilinger is not "favouring" him in any relevant way. c) Sorry, there is no interpretational issue involved in MoE. This is well accepted by all interpretations AFAIK. Again, here are my references and I welcome anyone who provides a quote/reference otherwise:

i) CKW: "there is a trade-off between A's entanglement with B and its entanglement with C"
https://arxiv.org/abs/quant-ph/9907047

ii) Proof of monogamy of entanglement: "A simple example is the Bell state..."
https://arxiv.org/pdf/quant-ph/0604168.pdf

iii) Wikipedia & Quantiki (not provided as a technical reference, but just to show MoE is generally accepted):

"In order for two qubits A and B to be maximally entangled, they must not be entangled with any third qubit C whatsoever."
https://en.wikipedia.org/wiki/Monogamy_of_entanglement

"If two qubits A and B are maximally quantumly correlated they cannot be correlated at all with a third qubit C."
https://www.quantiki.org/wiki/monogamy-entanglement

I'm not sure how many hoops you are going to make me jump through on this straightforward statement regarding the initial preparation that @vanhees71 completely incorrectly describes as containing the seeds of [1,4] entanglement. Because of MoE, it can't be correct.

Since [1,2] are prepared in a Bell state initially, [3,4] cannot in any way, shape or manner be entangled with [1,2], including the consideration that one might not know how they are entangled. There is nothing ambiguous here.

 

[Cthugha]

No, sorry. I have no time or energy to join that game.
I read your posts for some months now and there are repeating patterns.

a) This is a pretty good quote, but the sense of it is not presented as I might. I'd like to parse out a different portion of the same paragraph: "i) Whether these two particles are entangled or separable has been decided after they have been measured. ii) If one views the quantum state as a real physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. iii) However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge".

i) This is my assertion, perfectly phased.
ii) This too is my assertion. I prefer to refer to it as "quantum nonlocality" or "spooky action at a distance" rather than focus on any retrocausal element. That's because it is the entire experimental context (which is nonlocal obviously) that must be considered, and as they state: "quantum mechanical predictions are completely indifferent to the temporal order". Note that they base this on the assumption that the quantum state is a real physical object. The 2011 PBR paper "On The Reality of the Quantum State" says that it is (published near simultaneous with your reference).
iii) As long as the nonlocality of the full context is acknowledged, I have no issue with this statement. However, I dispute any inference that this the swap does not play an active role in the full context.

No, the 2011 PBR paper does not say that. You are misrepresenting it badly. The PBR paper says that "any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory." and finishes with "For these reasons and others, many will continue to view the quantum state as representing information. One approach is to take this to be information about possible measurement outcomes, and not about the objective state of a system".

The authors phrase it even simpler: "The argument depends on few assumptions. One is that a system has a “real physical state”". The paper shows elegantly that if one starts from the basic assumption of realism, then a model that considers the quantum state to represent information only will fail. This is a case for the interpretations forum.

b) Likewise, I dispute any inference that Zeilinger et al are saying that the [1,4] pair was entangled in any way as a part of the initial preparation, as @vanhees71 claims. There are no statements to that effect here. So no, Zeilinger is not "favouring" him in any relevant way.

Let us see what @vanhees71 really posted:

Also, I guess the misunderstanding leading to bringing up the argument with the monogamy of entanglement may be again not to clearly distinguish between correlations and causations. It's of course clear that in the here discussed entanglement-swapping experiment that preparation of the full ensemble has the form
$$\hat{\rho}_{1234}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}$$
with $\hat{\rho}_{jk}$ being pure Bell states. So the pairs (13), (1,4), (2,3) and (2,4) are not entangled as can easily be shown by calculating the corresponding reduced density matrix.

So you claim that he stated that the [1,4] pair was initially entangled which is clearly the opposite of what @vanhees71 actually said. You then go on to fight that straw man argument. That is pointless.

c) Sorry, there is no interpretational issue involved in MoE. This is well accepted by all interpretations AFAIK. Again, here are my references and I welcome anyone who provides a quote/reference otherwise:

i) CKW: "there is a trade-off between A's entanglement with B and its entanglement with C"
https://arxiv.org/abs/quant-ph/9907047

ii) Proof of monogamy of entanglement: "A simple example is the Bell state..."
https://arxiv.org/pdf/quant-ph/0604168.pdf

iii) Wikipedia & Quantiki (not provided as a technical reference, but just to show MoE is generally accepted):

"In order for two qubits A and B to be maximally entangled, they must not be entangled with any third qubit C whatsoever."
https://en.wikipedia.org/wiki/Monogamy_of_entanglement

"If two qubits A and B are maximally quantumly correlated they cannot be correlated at all with a third qubit C."
https://www.quantiki.org/wiki/monogamy-entanglement

I'm not sure how many hoops you are going to make me jump through on this straightforward statement regarding the initial preparation that @vanhees71 completely incorrectly describes as containing the seeds of [1,4] entanglement. Because of MoE, it can't be correct.

Since [1,2] are prepared in a Bell state initially, [3,4] cannot in any way, shape or manner be entangled with [1,2], including the consideration that one might not know how they are entangled. There is nothing ambiguous here.

This is another straw man. You claim that people dispute monogamy of entanglement. Nobody does that. You just interpret it to mean something that it does not. You discuss in detail the physics of two separate photon pairs, while the relevant physics here is about the density matrix of the full 4-photon state which is really at the heart of the experimental scenario.

The bounds of monogamy of entanglement are derived and valid for bipartite entanglement. Monogamy of entanglement provides an upper bound for how bipartite entanglement can be shared in a multipartite system. The relevant quantity telling us how much bipartite entanglement can be distilled from a multipartite state is either the entanglement of assistance or the concurrence of assistance (see, e.g. https://arxiv.org/abs/quant-ph/0506229 ). You do not need to prepare a state where any entanglement between photons 1 and 4 is present beforehand. Nobody claimed that and I have no idea why you repeatedly put up this straw man. You need to prepare a state with sufficient entanglement of assistance to distill the entanglement between photons 1 and 4. The analysis (outlined for example on page 4 of the paper linked above) shows that the assisted generalized concurrence for the states used in typical entanglement swapping experiments achieves exactly that.
If you intend to claim that photons 1 and 4 need to be entangled beforehand in order to see entanglement between them after a swapping process in entanglement swapping experiments, please provide a peer-reviewed source to back up your claim. This goes very much against the scientific consensus. As pointed out in the paper above, the achievable bipartite entanglement between photon 1 and 4 is given only by the generalized concurrence of assistance of the initially prepared multipartite state - which simultaneously fulfills all bounds given by monotonicity of entanglement.

You repeatedly misrepresent what others state and even when they tell you that you are misrepresenting them, you put up straw man arguments to support your point in a discussion which might probably be suitable for the interpretations forum, but certainly not for the quantum physics forum - and even in the interpretations forum misrepresenting others and the literature is not okay.

I do not see how this style of discussion is suitable for the quantum physics part of these forums and I really do not understand why the moderators let your repeated misrepresentation of what others wrote slip.

 

[vanhees71]

a) This is a pretty good quote, but the sense of it is not presented as I might. I'd like to parse out a different portion of the same paragraph: "i) Whether these two particles are entangled or separable has been decided after they have been measured. ii) If one views the quantum state as a real physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. iii) However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge".

i) This is my assertion, perfectly phased.
ii) This too is my assertion. I prefer to refer to it as "quantum nonlocality" or "spooky action at a distance" rather than focus on any retrocausal element. That's because it is the entire experimental context (which is nonlocal obviously) that must be considered, and as they state: "quantum mechanical predictions are completely indifferent to the temporal order". Note that they base this on the assumption that the quantum state is a real physical object. The 2011 PBR paper "On The Reality of the Quantum State" says that it is (published near simultaneous with your reference).
iii) As long as the nonlocality of the full context is acknowledged, I have no issue with this statement. However, I dispute any inference that this the swap does not play an active role in the full context.

Sigh, I thought you finally accepted the mathematical facts, i.e., the relativistic local QFT is by construction local. That's why it's called local! You can have a lot of philosophical prejudices, but they must be consistent with the mathematical content of the theory to make sense.

b) Likewise, I dispute any inference that Zeilinger et al are saying that the [1,4] pair was entangled in any way as a part of the initial preparation, as @vanhees71 claims. There are no statements to that effect here. So no, Zeilinger is not "favouring" him in any relevant way.

I do not claim anything like that. I've made this clear several times. The full ensemble is prepared in a state, where [1,4] are not entangled. That's the whole point of the entanglement-swapping, which is done by selecting a sub-ensemble by projecting the pair [2,3] (by local manipulations as described above) to one of the four Bell states. In this sub-ensemble also the pair [1,4] is in a Bell state. That does not imply that before the projection measurement this pair has been entangled. To the contrary the whole point of the experiment is that it was not!

c) Sorry, there is no interpretational issue involved in MoE. This is well accepted by all interpretations AFAIK. Again, here are my references and I welcome anyone who provides a quote/reference otherwise:

i) CKW: "there is a trade-off between A's entanglement with B and its entanglement with C"
https://arxiv.org/abs/quant-ph/9907047

ii) Proof of monogamy of entanglement: "A simple example is the Bell state..."
https://arxiv.org/pdf/quant-ph/0604168.pdf

iii) Wikipedia & Quantiki (not provided as a technical reference, but just to show MoE is generally accepted):

"In order for two qubits A and B to be maximally entangled, they must not be entangled with any third qubit C whatsoever."
https://en.wikipedia.org/wiki/Monogamy_of_entanglement

"If two qubits A and B are maximally quantumly correlated they cannot be correlated at all with a third qubit C."
https://www.quantiki.org/wiki/monogamy-entanglement

I'm not sure how many hoops you are going to make me jump through on this straightforward statement regarding the initial preparation that @vanhees71 completely incorrectly describes as containing the seeds of [1,4] entanglement. Because of MoE, it can't be correct.

I DID NOT CLAIM such a thing. It's very bad style of discussion to claim things I never said!

Since [1,2] are prepared in a Bell state initially, [3,4] cannot in any way, shape or manner be entangled with [1,2], including the consideration that one might not know how they are entangled. There is nothing ambiguous here.

Please don't claim things I never said. I precisely said what you write in words here in clear mathematical terms. It would help a lot, if you'd read everybody's postings with the necessary diligence and not claiming the opposite of what has been really said!

 

[vanhees71]

So you claim that he stated that the [1,4] pair was initially entangled which is clearly the opposite of what @vanhees71 actually said. You then go on to fight that straw man argument. That is pointless.

Thanks for setting the record straight. What @DrChinese does is nothing less than scientific misconduct here, claiming I stated the opposite of what I really have written!

This is another straw man. You claim that people dispute monogamy of entanglement. Nobody does that. You just interpret it to mean something that it does not. You discuss in detail the physics of two separate photon pairs, while the relevant physics here is about the density matrix of the full 4-photon state which is really at the heart of the experimental scenario.

The bounds of monogamy of entanglement are derived and valid for bipartite entanglement. Monogamy of entanglement provides an upper bound for how bipartite entanglement can be shared in a multipartite system. The relevant quantity telling us how much bipartite entanglement can be distilled from a multipartite state is either the entanglement of assistance or the concurrence of assistance (see, e.g. https://arxiv.org/abs/quant-ph/0506229 ). You do not need to prepare a state where any entanglement between photons 1 and 4 is present beforehand. Nobody claimed that and I have no idea why you repeatedly put up this straw man. You need to prepare a state with sufficient entanglement of assistance to distill the entanglement between photons 1 and 4. The analysis (outlined for example on page 4 of the paper linked above) shows that the assisted generalized concurrence for the states used in typical entanglement swapping experiments achieves exactly that.
If you intend to claim that photons 1 and 4 need to be entangled beforehand in order to see entanglement between them after a swapping process in entanglement swapping experiments, please provide a peer-reviewed source to back up your claim. This goes very much against the scientific consensus. As pointed out in the paper above, the achievable bipartite entanglement between photon 1 and 4 is given only by the generalized concurrence of assistance of the initially prepared multipartite state - which simultaneously fulfills all bounds given by monotonicity of entanglement.

You repeatedly misrepresent what others state and even when they tell you that you are misrepresenting them, you put up straw man arguments to support your point in a discussion which might probably be suitable for the interpretations forum, but certainly not for the quantum physics forum - and even in the interpretations forum misrepresenting others and the literature is not okay.

I do not see how this style of discussion is suitable for the quantum physics part of these forums and I really do not understand why the moderators let your repeated misrepresentation of what others wrote slip.

I don't think that it is suitable for any part of these forums!

 

[DrChinese]

@vanhees71:

Ok, so we agree that the initial preparation lacks 1,4 entanglement of any kind, and contains no subensembles with 1,4 entanglement. Correct? I keep thinking we agree on this, and then you seem to backtrack on the point. My apologies for misrepresenting your position.

Because you keep mentioning locality. And yet, it takes a nonlocal distant swapping operation to create 1,4 entanglement. 1,4 need never have existed in a common light cone, and don’t need to be anywhere near the 2,3 swap - which can be performed at any time. And in fact 2,3 don’t need to ever exist in a common light cone either, as an intermediate repeater can be present.

So how is 1,4 entanglement being created when 1,2,3,4 are all distant from each other?

 

[PeterDonis]

If you intend to claim that photons 1 and 4 need to be entangled beforehand in order to see entanglement between them after a swapping process in entanglement swapping experiments

Please note that @DrChinese himself has never made that claim. Others responding to him, in other threads, have, repeatedly. If @vanhees71 is not claiming that, that's good; that means this discussion is going better than many previous ones on this topic have.

 

[PeterDonis]

the relativistic local QFT is by construction local

For a particular meaning of "local", yes--that spacelike separated measurements commute. But not for another meaning of "local"--that the Bell inequalities are not violated. That means the term "local" should not even be used in discussions on this topic, since it is ambiguous. You should use the more technical term that clearly states what you actually mean.

 

[PeterDonis]

So how is 1,4 entanglement being created when 1,2,3,4 are all distant from each other?

Note that this question assumes realism--that entanglement is something that has to be "created". In other words, it is interpretation dependent, as @Cthugha has pointed out.

 

[PeterDonis]

As far as I know, entanglement can initially only be created locally

As the discussion here has shown, this is not true, in the sense that two particles can be entangled without ever having undergone a common local interaction. That is an experimental fact.

How that fact is interpreted is a matter of QM interpretation, and discussion of that, as has been remarked, belongs in the interpretations subforum.

And with that, this thread is closed. Thanks to all who participated.