I Non-local preparation in entanglement swapping experiments

[kurt101]

TL;DR Summary

In entanglement swapping experiments, if you consider the Bell test of 2&3 as a form of preparing entanglement between 1&4, how is this practically different than local preparation such as with SPDC in an entanglement experiment of the type Bell considered in his non-locality proofs?

There is one question that I would like to get an answer to in regards to the discussion between @DrChinese and @iste in the thread:
https://www.physicsforums.com/threa...ion-of-quantum-mechanics.1060576/post-7138288

In the case where the Bell state test is done on photons 2&3 before the measurement of photons 1&4; we know that the statistics of entanglement will be found between 1&4 for whatever orientation that is used to measure 1&4.

1) How is this situation practically different than the normal entanglement experiment where two photons are entangled through local preparation such as SPDC (Spontaneous Parametric Down Conversion)? We don't really know that non-locality isn't involved in the internal details of SPDC. So in a practical sense, SPDC is no different than the preparation of the bell test of 2&3 in that both methods are used to create truly entangled photon pairs.

In other words we consider the photons entangled through SPDC to be truly entangled, because of Bell's argument based on how we intend to measure these photons and their measurement results, but not how the photons were prepared. So why would we treat the non-local preparation case (i.e. bell test at 2&3) any different?

So in this scenario (i.e. measurement of 1&4 done last), how could anyone ( @iste ?) take the position that the entanglement between 1&4 is anything but a true non-local phenomena between 1&4. Wouldn't they fundamentally be arguing against Bell's work?

2) In the original Aspect experiment performed in 1983, the orientation of measurement was changed at the last moment. Has the same thing been done in entanglement swapping experiments?

FWIW, I happen to take the unusual position where I agree with @DrChinese in one scenario and agree with @iste in the other scenario. It is the only position that makes sense to me. That said, if I have a misunderstanding I am happy to change my position. So don't think good arguments will be wasted on me.

 

[martinbn]

Just to point out that the full set of results of measurements on 1&4 do not show any correlations. Only the subsets with the same outcome of the measurements on 2&3.

 

[pines-demon]

Can somebody provide some sort of diagram or picture, I am not sure I get what all the numbers refer to at this point.

 

[pines-demon]

2) In the original Aspect experiment performed in 1983, the orientation of measurement was changed at the last moment. Has the same thing been done in entanglement swapping experiments?

Yes there are many Bell tests. My understanding is that there are various tests using entanglement swapping, Google throw down a couple, I think this is the one to look at: Żukowski et al 1993

Edit: see also this news article from 2015 about the Delft Bell test experiment: https://www.nature.com/articles/nature.2015.18255

 

[DrChinese]

Can somebody provide some sort of diagram or picture, I am not sure I get what all the numbers refer to at this point.

For entanglement swapping, one of the main papers being discussed is:

Experimental delayed-choice entanglement swapping (2012)
Xiao-song Ma, Stefan Zotter, Johannes Kofler, Rupert Ursin, Thomas Jennewein, Časlav Brukner, and Anton Zeilinger

 

[pines-demon]

For entanglement swapping, one of the main papers being discussed is:

Experimental delayed-choice entanglement swapping (2012)
Xiao-song Ma, Stefan Zotter, Johannes Kofler, Rupert Ursin, Thomas Jennewein, Časlav Brukner, and Anton Zeilinger

I am sure that there are less technical diagrams of entanglement swapping out there...
Edit: I am talking about figure 2, figure 1 is the opposite, it is too simple.

 

[martinbn]

I am sure that there are less technical diagrams of entanglement swapping out there...
Edit: I am talking about figure 2, figure 1 is the opposite, it is too simple.

Wikipedia is sometimes not credible, but I think this is presented accurately.

https://en.wikipedia.org/wiki/Quantum_teleportation#Algorithm_for_swapping_Bell_pairs

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

 

[Morbert]

In entanglement swapping experiments, if you consider the Bell test of 2&3 as a form of preparing entanglement between 1&4, how is this practically different than local preparation such as with SPDC in an entanglement experiment of the type Bell considered in his non-locality proofs?

[...]

So in this scenario (i.e. measurement of 1&4 done last), how could anyone take the position that the entanglement between 1&4 is anything but a true non-local phenomena between 1&4. Wouldn't they fundamentally be arguing against Bell's work?

The protocol followed for obtaining the 2-particle Bell state isn't important provided the protocol is reliable and the 2-particle system can be sufficiently isolated from the systems involved in preparation afterwards. This 2-particle system will exhibit Bell nonlocality.

The dispute is over whether the success of entanglement swapping protocols necessarily imply action at a distance, where an external influence on one region can immediately affect a spatially distant region.

 

[pines-demon]

Wikipedia is sometimes not credible, but I think this is presented accurately.

https://en.wikipedia.org/wiki/Quantum_teleportation#Algorithm_for_swapping_Bell_pairs

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

View attachment 354654

This is too simplified, I was thinking more of something like this:

This images show also the classically controlled operations.

Taken from previous discussion: Ways to understand the delayed entanglement swapping. But I do not know how OP or the rest are labelling the qubits.

 

[martinbn]

This is too simplified, I was thinking more of something like this:

View attachment 354656
This images shows the classical controlled operations.

Taken from previous discussion: Ways to understand the delayed entanglement swapping. But I do not know how OP or the rest are labelling the qubits.

1, 2, 3, and 4 from top to bottom on your picture.

 

[DrChinese]

In the case where the Bell state test is done on photons 2&3 before the measurement of photons 1&4; we know that the statistics of entanglement will be found between 1&4 for whatever orientation that is used to measure 1&4.

1) How is this situation practically different than the normal entanglement experiment where two photons are entangled through local preparation such as SPDC (Spontaneous Parametric Down Conversion)? We don't really know that non-locality isn't involved in the internal details of SPDC. So in a practical sense, SPDC is no different than the preparation of the bell test of 2&3 in that both methods are used to create truly entangled photon pairs.

In other words we consider the photons entangled through SPDC to be truly entangled, because of Bell's argument based on how we intend to measure these photons and their measurement results, but not how the photons were prepared. So why would we treat the non-local preparation case (i.e. bell test at 2&3) any different?

So in this scenario (i.e. measurement of 1&4 done last), how could anyone ( @iste ?) take the position that the entanglement between 1&4 is anything but a true non-local phenomena between 1&4. Wouldn't they fundamentally be arguing against Bell's work?

2) In the original Aspect experiment performed in 1983, the orientation of measurement was changed at the last moment. Has the same thing been done in entanglement swapping experiments?

3) FWIW, I happen to take the unusual position where I agree with @DrChinese ...

1) So, how is one conceptually different from the other? In some ways, entanglement is entanglement. Obviously, in the swapping scenario there are 4-fold "simultaneous" detections while with normal 2 photon PDC there are 2-fold detections. Either way, an entangled pair that itself has a nonlocal spatial extent results. Either way, you can demonstrate violation of a Bell inequality, and/or show "perfect" correlations. So yes, I would say denial of swapping as creating entanglement is of course denying Bell. You can't have entanglement with only classical elements.

But certainly we have to appreciate that in the swapping scenario, conceptually at least: Any two photons - created anywhere at anytime - could become entangled. This is an oversimplification of course, but it should raise eyebrows for anybody. Even Peres, Zeilinger, and the many great scientists who first explored this must have been astounded in the possibilities for experimental variations to explore nonlocality so explicitly.


2) Yes, there is an important "loophole free" experiment that does this, not sure if it will meet your needs exactly. This paper and its methodology is quite complex (at least to me). It uses a significantly different form of entanglement generation than PDC, but the 4 fold coincidence detection is implemented with choice of spin basis made spacetime independently for A and B (corresponding to Alice and Bob in many experiments).

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

EDIT: I see now that this is the same underlying paper referred to in the post by @pines-demon.

3) Notice how I cleverly cut the quote short to make it appear completely different than you intended...

 

[DrChinese]

How is this situation practically different than the normal entanglement experiment where two photons are entangled through local preparation such as SPDC (Spontaneous Parametric Down Conversion)? We don't really know that non-locality isn't involved in the internal details of SPDC.

Interestingly: In type I PDC, there are 2 nonlinear crystals placed next to each other. One outputs |HH>, the other outputs |VV>. I.e. neither separately are entangled! But when the output streams are combined/overlapped so the source crystal is not distinguishable, the result is |HH>+|VV> - which is an Entangled state. This is precisely the same thing which occurs in the BSA component of an entanglement swap. The 2 & 3 sources are not distinguishable.

 

[iste]

how could anyone ( @iste ?) take the position that the entanglement between 1&4 is anything but a true non-local phenomena between 1&4. Wouldn't they fundamentally be arguing against Bell's work?

My thoughts are not strictly speaking that it "not non-local" but that the non-locality in entanglement swapping does not require any other non-local phenomena additionally beyond the non-local behaviors of 1&2 and then 3&4 as distinct entanglements.

 

[pines-demon]

My thoughts are not strictly speaking that it "not non-local" but that the non-locality in entanglement swapping does not require any other non-local phenomena additionally beyond the non-local behaviors of 1&2 and then 3&4 as distinct entanglements.

As far as it is written in sources above (Delft 2015), the entanglement swapping allows one to be sure that there is no 'communication loophole', meaning that the electrons are unable to conspire with each other (share local hidden variables) in order to produce the entanglement. This is important when doing the experiment with massive particles like electrons, but I am not so sure what it add for the case of photons where you can put detectors as far as you want. What I can say is that both types of entanglement violate local-realism, but with entanglement swapping you are even more certain that it is the case.

Edit: for electrons it allows to close both the locality loophole and the detection loophole.

 

[iste]

As far as it is written in sources above (Delft 2015), the entanglement swapping allows one to be sure that there is no 'communication loophole', meaning that the electrons are unable to conspire with each other (share local hidden variables) in order to produce the entanglement. This is important when doing the experiment with massive particles like electrons, but I am not so sure what it add for the case of photons where you can put detectors as far as you want. What I can say is that both types of entanglement violate local-realism, but with entanglement swapping you are even more certain that it is the case.

Edit: for electrons it allows to close both the locality loophole and the detection loophole.

Well I did assert non-locality in my post, but we probably have different interpretations if what non-locality might actually mean.

 

[pines-demon]

Well I did assert non-locality in my post, but we probably have different interpretations if what non-locality might actually mean.

I am trying to use "no local realism" to encode all possible meanings of a Bell inequality violation including "non-locality".

 

[Morbert]

Bell outlines what he means by nonlocal in his "La Nouvelle Cuisine" article.

A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a space-time region 3. [...] Ordinary quantum mechanics is not locally causal.

This nonlocality stipulated by Bell is well established, and entanglement swapping experiments indeed close loopholes, and Bell states prepared either by conventional means or by entanglement swapping are truly nonlocal in this sense.

What is instead debated is whether Bell's definition is an appropriate understanding of nonlocality or, similarly, if quantum mechanics, independent of interpretation, necessitates a stronger Einsteinian nonlocality, where external influences on one region can immediately affect another space-like separated region. Various interpretations of QM are local in this latter sense (instrumentalist, consistent histories, Deutsch's + Wallace's many-worlds etc) and "nonlocalists" like Tim Maudlin and (I *think*) @DrChinese maintain that these interpretations are deficient in important ways.

 

[iste]

I am trying to use "no local realism" to encode all possible meanings of a Bell inequality violation including "non-locality".

Yes but you can still have a different interpretation of non-(local realism) depending on your interpretation of quantum mechanics. A Bohmian might interpret it in terms of direct communication of hidden variables, Barandes might attribute it to remembered correlations of hidden variables, others are agnostic and say there is no hidden-variables and the wave-function is just inexplicably non-separable and perhaps even retrocausal, Everettians may have another alternative perspective I am not entirely sure of.

 

[DrChinese]

Bell outlines what he means by nonlocal in his "La Nouvelle Cuisine" article. … and (I *think*) @DrChinese maintain that these interpretations are deficient in important ways.

The diagram in your #17 is my reference. Agreed that it well represents the ideas Bell wanted to all to analyze and discuss. However… sadly he died before a critical series of theorems and experiments made their way into canon. That new science actually makes the famous diagram either outdated - or even somewhat misleading.

In current scientific terms: the diagram should not include any area of overlap in the backwards light cones of 1 and 2. There is no requirement there be such.

So the point I am making: If an interpretation addresses this old (pre-1990) Bell diagram, they are about 25+ years behind. It’s time to tackle these issues straight on. As mentioned, I have no idea how nature does it or how best to interpret the science.

 

[martinbn]

In current scientific terms: the diagram should not include any area of overlap in the backwards light cones of 1 and 2. There is no requirement there be such.

This is impossible in Minkowski space-time! The past light cones of any two events will overlap.

 

[DrChinese]

This is impossible in Minkowski space-time! The past light cones of any two events will overlap.

That's true, but meaningless. The future light cones of any two events will also overlap, also a meaningless statement. The relevant issue is: the photon examined in area 1 never co-exists/overlaps with the photon in area 2.

 

[PeterDonis]

The past light cones of any two events will overlap.

That's true, but irrelevant to the point under discussion. Bell's point, as shown in the diagram in post #17, was that in what he calls a "locally causal" theory, you can specify data in the past light cone of just one event, i.e., "above" the region of overlap (region 3 in the diagram) that makes it irrelevant what is in the overlap region, or anywhere else; the data in region 3 alone is sufficient to determine all measurement results in region 1.

And, as Bell says, QM is not "locally causal" in this sense; if there is entanglement between what is measured in region 1 and what is measured in region 2, then knowing all the data in region 3 is not sufficient to determine all experimental results in region 1.

 

[PeterDonis]

The relevant issue is: the photon examined in area 1 never co-exists/overlaps with the photon in area 2.

That's not the issue Bell was illustrating with his diagram. That issue is what I described in post #22.

To give a precise formulation of what you say in the quote above, you need to give a precise definition of what "never co-exists/overlaps" means. Is there a reference that does that?

 

[DrChinese]

To give a precise formulation of what you say in the quote above, you need to give a precise definition of what "never co-exists/overlaps" means. Is there a reference that does that?

Somehow I am not surprised at your request.

I have such a definition: There is no spacetime region that both particles ever occupy. But in the published paper, the authors state: "The resulting correlations between particles that do not share any common past are
strong enough to violate a Clauser-Horne-Shimony-Holt (CHSH) inequality." They do not provide a definition such as you request, as presumably they and the reviewers felt it was sufficiently obvious that no definition was required.

Note that some versions of the Bell diagram we are referencing (see for example Fig. 1 HERE) include λ as being the "hidden variables" in the overlap region. I am simply pointing out there are experiments where there are no overlap regions, and therefore cannot contain such variables.

 

[martinbn]

Somehow I am not surprised at your request.

I have such a definition: There is no spacetime region that both particles ever occupy.

I will be pedantic again and point out that this is wrong. Take a very big region, for example the whole Minkowski space-time.

Can i suggest the following. Take one particle, which was created, call that event C and later distroyed, call that event D. Then consider the intersection of the future light cone of C and the past light cone of D. It is a diamond like region and it is bounded. Pergaps you want to say that the two particles have disjoint diamond regions. Or not only that they are disjoint but all events in one of them is space-like seperated with any event from the other.

 

[PeterDonis]

There is no spacetime region that both particles ever occupy.

What counts as a "spacetime region"? If you make the region large enough, obviously both particles will occupy it.

particles that do not share any common past

As this quote illustrates, they use the term "do not share a common past", which is different than the term you used. Is your intent that your "never coexist/overlap" should be identical to their "do not share a common past"?

They do not provide a definition such as you request, as presumably they and the reviewers felt it was sufficiently obvious that no definition was required.

Presumably, but that doesn't make it right. Vague ordinary language terms should never be given a critical role in physics papers. There should be some explicit, testable definition. If I had been a peer reviewer for the paper you cite, I would have pointed that out as an issue.

If I try to come up with an explicit definition of "do not share a common past" from the paper, what I get is this:

Consider the source and measurement events for the two particles (in the entanglement swapping experiments under discussion here, these would be photons 1 & 4), and look at the region of spacetime consisting of the intersection of the future light cone of the source event, and the past light cone of the measurement event, for each particle. If those two regions do not overlap, then the particles do not share a common past.

Does this definition look acceptable to you?

 

[DrChinese]

If I try to come up with an explicit definition of "do not share a common past" from the paper, what I get is this:

Consider the source and measurement events for the two particles (in the entanglement swapping experiments under discussion here, these would be photons 1 & 4), and look at the region of spacetime consisting of the intersection of the future light cone of the source event, and the past light cone of the measurement event, for each particle. If those two regions do not overlap, then the particles do not share a common past.

Does this definition look acceptable to you?

Certainly.

And we can now agree that there are no hidden variables in any common past of the photons, and they have never interacted. They become entangled even though they share no common past. This is non-local preparation of entanglement, as contemplated by the OP. In the experiment, those are the 1 & 4 photons.

---

Note that there is also no requirement that even the twins of the final entangled pair overlap (share a common past). You can chain N>2 pairs, with no theoretical upper limit. For example, you could have 3 pairs of initially entangled photons: 1&2, 3&4, 5&6 and end up with 1 & 6 entangled. You perform a Bell State Measurement on 2&3 and on 4&5, which can be done on mutually unbiased polarization bases (say H/V and +/-). The final entangled 1 & 6 pair will be entangled on all polarization bases: H/V, +/-, L/R, etc. But their initially associated twins (the 2 & 5 photons) share no common past.

Multistage Entanglement Swapping (2008)

"We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements (BSMs) one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an entangled state, as characterized by an entanglement witness."

A quirk of this setup is that the time ordering of the various pair creation events (there are 3 of these) and the photon detection events (there are 6 of these - making 9 total) can be altered without changing the essential final entanglement of photons 1 & 6. Although that was not actually performed in this particular experiment, all of the following are feasible:

a) Basic version with 1 & 6 measured after the intermediate BSMs.
b) Delayed choice version, with the 4&5 BSM occurring after 1 & 6 are measured.
c) Same as b) but with photon 1 measured (and therefore ceasing to exist) before the 5&6 pair is even created.

Note that the final entangled pair (1 & 6) are polarization entangled on every basis (conceptually an infinite number). On the other hand, their final resulting net Bell state is only 1 of 2 potentially differentiated Bell states, |Ψ−> or |Ψ+>. In other words, the final identifiable Bell state is only one of two possible. But the entanglement is on a multitude of bases. Meaning the intermediate BSMs do not allow for any kind of exchange of "hidden" information - there isn't a large enough channel. Also, the direction of any possible information flow is muddied, since you can order all 9 events in nearly any desired order.

---

So where does this leave us? The OP asked if there was something conceptually different about non-local preparation of entanglement via swapping as opposed to more traditional entanglement from a single PDC source. While the resulting entanglement is the same, it is difficult to characterize the creation mechanism in any kind of classical terms. And by "classical terms", I mean in terms of trying it back to anything respecting Einsteinian causality - with the exception that you cannot signal FTL of course.

I would say that there is a big difference, because Einsteinian causality is being tested to the max. And that is what the Bell diagram (see @Morbert #17 above) seeks to challenge us to consider. But others might not see it that way, it's subjective. I wonder what Bell himself would have made of all this.

 

[martinbn]

Certainly.

And we can now agree that there are no hidden variables in any common past of the photons, and they have never interacted. They become entangled even though they share no common past. This is non-local preparation of entanglement, as contemplated by the OP. In the experiment, those are the 1 & 4 photons.

Strictly they are not entangled. The results of the measurements on 1&4 has a subset that is statistically the same as that of an entangled pair. But the definition of entangled pair is that the combined system has a nonfactorisable state. If those two have never coexisted they don't have any state let alone nonfactorisble.

So where does this leave us? The OP asked if there was something conceptually different about non-local preparation of entanglement via swapping as opposed to more traditional entanglement from a single PDC source. While the resulting entanglement is the same, it is difficult to characterize the creation mechanism in any kind of classical terms. And by "classical terms", I mean in terms of trying it back to anything respecting Einsteinian causality - with the exception that you cannot signal FTL of course.

I would say that there is a big difference, because Einsteinian causality is being tested to the max. And that is what the Bell diagram (see @Morbert #17 above) seeks to challenge us to consider. But others might not see it that way, it's subjective. I wonder what Bell himself would have made of all this.

What do you call Einstein causality?

 

[DrChinese]

Strictly they are not entangled. The results of the measurements on 1&4 has a subset that is statistically the same as that of an entangled pair.

They are entangled. There is no such thing as the subset you describe. Independent pairs - 1&2 and 3&4 - are never entangled unless a swap is executed. Read the reference by the Nobel laureate.

 

[martinbn]

They are entangled. There is no such thing as the subset you describe. Independent pairs - 1&2 and 3&4 - are never entangled unless a swap is executed. Read the reference by the Nobel laureate.

I read it. I am quoting it! They say that the set of measurments on 1&4 shows no correlation. Only the subset for those trials on which Victor obtained a one of the possible outcomes of his measurment.

 

[martinbn]

If you insist that they are entangled what is the state of the system 1&4?

ps What do you call Einstein causality?

 

[javisot20]

Does something in QM prevent two particles that have never interacted in any sense or share preparation from acting in a quantum-correlated way in experiments by chance? Or is it simply improbable?

 

[pines-demon]

Does something in QM prevent two particles that have never interacted in any sense or share preparation from acting in a quantum-correlated way in experiments by chance? Or is it simply improbable?

That’s the whole point of this discussion. Do you consider that in entanglement swapping particles 1 and 4 interacted in any way?

 

[javisot20]

That’s the whole point of this discussion. Do you consider that in entanglement swapping particles 1 and 4 interacted in any way?

I don't have enough knowledge to answer... but after reading this thread and the one on interpretations of quantum mechanics I needed that answer to understand the conversation that is being held here. (I can't find the explicit answer in the papers)

 

[Morbert]

The position I have argued the various times it has come up here is entanglement swapping experiments do not present additional challenges to mainstream local* interpretations of QM like those laid out by Asher Peres or Robert Griffiths.

* Local in the sense of no superluminal influence responsible for Bell-inequality-violating correlations.

 

[DrChinese]

I don't have enough knowledge to answer [whether the 1 & 4 particles interacted in any way]... but after reading this thread and the one on interpretations of quantum mechanics I needed that answer to understand the conversation that is being held here. (I can't find the explicit answer in the papers)

Perhaps I can help, at least discussing the cases of whether the 1&4 or 2&3 photons interact in any way. This is the 2012 paper by Zeilinger's team, in which the 2 & 3 interaction variable is the primary objective of the paper - and no interaction between 1 & 4.
Φ

---

Re: 1&4 photons interacting:

In no cases do the 1 & 4 photons ever interact. They are created at separate locations (different PDC crystals) about .5 meter apart and fed into fiber, and measured about 35ns later. There is no time or place for them to interact. From Figure 2 of the paper:

"Photons 1 and 4 are directly subject to the polarization measurements performed by Alice and Bob (green blocks".

In other experiments, the separation of photons 1 and 4 are more clearly delineated than in this particular experiment. But obviously: If the independent variable is what happens at the BSM, then any hypothetical interaction can't really matter to our conclusion.

---

Re: 2&3 photons interacting:

1. To execute a swap via the BSM, the 2 & 3 photons must arrive at the beam splitter within a narrow time window. The same time window is applied whether an Entangled State (ES) measurement is to result, or a Separable (non-entangled) State (SS) measurement is to occur. The decision to make it ES or SS is made randomly by automation on a case by case basis. The time window is measured by clicks at the BSM in 2 detectors.

2. There are 4 possible Bell states that result from a entanglement swap. For a variety of mostly technical reasons, only a single state is reported in the experiment. That is the |φ-> state. That state is indicated when the BSM registers either two H clicks or two V clicks at the BSM. Note that to get the two clicks |HH> or |VV>, that can result only from the 2 & 3 photons being both reflected or both transmitted at the beam splitter (BS). The only entangled stats being reported are from this one Bell state for ES scenario. No other Bell states are being combined with the entangled |Φ-> state numbers. Similarly, the SS scenario also looks at |HH> or |VV> results at the BSM. So the statistics are "apples to apples". The key here is that we are going to compare the ES and SS (entangled vs non-entangled) correlations. From the paper:

"After all the data had been taken, we calculated the polarization correlation function of photons 1 and 4. It is derived from their coincidence counts of photons 1 and 4 conditional on projecting photons 2 and 3 to |Φ−〉23 = (|𝐻𝐻〉23 − |𝑉𝑉〉23)/√2 when the Bell-state measurement was performed, and to |𝐻𝐻〉23 or |𝑉𝑉〉23 when the separable state measurement was performed."

3. Here is exactly how the physical variable changes that creates the ES (entangled) or SS (non-entangled) results: There are 2 Electro-Optical Modulator (EOM 1 and EOM 2, see figure 2) that together change the beam splitter between 2 possible configurations. To get ES outcomes, the beam splitter operates in a 50:50 mode - that is, 50% transmitted and 50% reflected. To get SS outcomes, the beam splitter operates in a 0:100 mode - that is, 0% transmitted and 100% reflected (i.e. a mirror).

There IS entanglement when the 2 & 3 photons can overlap in the beam splitter within the time window, but you cannot know whether both photons were transmitted - or both were reflected (50:50). I.e. the 2 & 3 photons are indistinguishable. There is NO entanglement when the 2 & 3 photons cannot overlap in the beam splitter within the time window, because both were reflected (0:100) before they could possibly cross. I.e. now the 2 & 3 photons are easily distinguishable according to which side's detectors click.

This is the only difference between the statistics reported in Figure 3 between the a) side [left 3 bars] and the b) side [right 3 bars]. The easiest to see is the middle of the 3 bars on each side. These are the associated click outcomes for the |RR>/|LL> correlations at the Alice and Bob stations. The middle bars have the Alice and Bob stations only measuring circular polarization R or L. When there is |Φ-> entanglement, Alice and Bob should get identical results on any same basis, so you would expect mostly RR> or LL> outcomes and few LR> or RL> outcomes. Without entanglement, Alice and Bob should not see any correlation. Note that correlation is calculated as C=(Matches - Mismatches)/(Matches + Mismatches) and can vary from 1 to -1.

When the Entangled State was selected randomly, you expect significant correlation (theoretically perfect would be C=1.0). When the Separable State was selected, you expect no significant correlation (theoretically perfect would be C=0.0).

The actual entangled (ES) correlation is about 0.603+/-0.071, while the actual separable (SS) correlation is about 0.010+/-0.072. These results are clearly saying: If a physical change is made at the BSM, then there is a corresponding observable change of the overall statistics - as predicted by QM.

So the answer is: When there is an entanglement swap, the 2&3 photons are allowed to physically interact (but they aren't if a separable state is to be generated). The only thing varied in the results a) vs b) is that setup at the BSM. So the difference in statistics, according to norms in experimental science, is the independent variable. Which is selected and chosen well after the Alice and Bob perform their measurements on photons 1 & 4.

You can make of this what you like.

 

[DrChinese]

If you insist that they are entangled what is the state of the system 1&4?

ps What do you call Einstein causality?

In the 2012 Ma experiment, the 1 & 4 system is |Φ-> for all the reported cases in Figure 3a). For the reported Separable State cases in 3b), they are either |HH> or |VV> which of course is not entangled.

Einsteinian causality requires causes to occur before effects, with limits of propagation through spacetime of cause to effect not to exceed c. Obviously, the predictions of QM do not satisfy this condition. This has been known for a long time, as a future nonlocal context is the sole factor/determinant for the quantum expectation value in many scenarios. For example, the well known cos^2(theta) function for entanglement matches.

 

[DrChinese]

I read it. I am quoting it! They say that the set of measurments on 1&4 shows no correlation. Only the subset for those trials on which Victor obtained a one of the possible outcomes of his measurment.

You failed to quote anything that you actually interpreted correctly. Yes, measurements on photons 1 & 4 alone show no correlation in these experiments UNLESS there is a specific outcome at the BSM - AND there is interaction (interference) between 2 & 3 at the BSM as well.

Please read my #36 above which explains everything in detail. Please note again the independent variable in this scientific experiment.

 

[PeterDonis]

If you insist that they are entangled what is the state of the system 1&4?

In the interpretation @DrChinese is using, where the quantum state describes individual runs of the experiment, the state of the system 1&4 for each individual run is the appropriate Bell state induced by the swap operation on 2&3 for that run.

In a statistical interpretation, the state you assign depends on what subset of runs you are doing statistics on. If you take the entire set of runs, without picking out any subsets, then the state of 1&4 is the appropriate mixed density matrix that shows no correlations. If you pick out subsets of runs corresponding to particular outputs of the swap operation on 2&3, then the state of 1&4 for those subsets is the corresponding Bell state, as above.

What you can't do is take the entire set of runs, point out that that set shows no correlation between 1&4, and then use that as a basis for an assertion that 1&4 are not entangled in individual runs. The "no correlation" statistics are only relevant for a statistical interpretation. On an interpretation that assigns quantum states to individual runs, there is no such thing as "no correlation"; every run (or more precisely every run where a swap takes place, but that's sufficient for this discussion) puts 1&4 into some definite Bell state. There are no runs where a swap takes place but there is no correlation between 1&4.

In other words, as far as I can tell, you and @DrChinese are talking past each other because you are using different, incompatible interpretations.

 

[martinbn]

In the interpretation @DrChinese is using, where the quantum state describes individual runs of the experiment, the state of the system 1&4 for each individual run is the appropriate Bell state induced by the swap operation on 2&3 for that run.

In a statistical interpretation, the state you assign depends on what subset of runs you are doing statistics on. If you take the entire set of runs, without picking out any subsets, then the state of 1&4 is the appropriate mixed density matrix that shows no correlations. If you pick out subsets of runs corresponding to particular outputs of the swap operation on 2&3, then the state of 1&4 for those subsets is the corresponding Bell state, as above.

What you can't do is take the entire set of runs, point out that that set shows no correlation between 1&4, and then use that as a basis for an assertion that 1&4 are not entangled in individual runs. The "no correlation" statistics are only relevant for a statistical interpretation. On an interpretation that assigns quantum states to individual runs, there is no such thing as "no correlation"; every run (or more precisely every run where a swap takes place, but that's sufficient for this discussion) puts 1&4 into some definite Bell state. There are no runs where a swap takes place but there is no correlation between 1&4.

In other words, as far as I can tell, you and @DrChinese are talking past each other because you are using different, incompatible interpretations.

My question about the state meant to point out that it makes no sense to talk about it since they have never coexisted. If 1&4 have never coexisted what does it mean to be in a given state!

If @DrChinese is using an interpretation, then i have no problem with his claims. But it seems to me that he insists that his discription is the only posssible one.

 

[pines-demon]

My question about the state meant to point out that it makes no sense to talk about it since they have never coexisted. If 1&4 have never coexisted what does it mean to be in a given state!

Even if two particles have never interacted you can write their state quantum mechanically. In the case of entanglement swapping, the math of QM tells us how to write the state.

 

[martinbn]

Even if two particles have never interacted you can write their state quantum mechanically. In the case of entanglement swapping, the math of QM tells us how to write the state.

I am not talking about particles that haven't interacted, but about particles that haven't coexisted. If you have a photon that was emitted and absorbed a year ago and another that was emitted and absorbed today, does it make sense to talk about the state of the two photon system?

 

[pines-demon]

I am not talking about particles that haven't interacted, but about particles that haven't coexisted. If you have a photon that was emitted and absorbed a year ago and another that was emitted and absorbed today, does it make sense to talk about the state of the two photon system?

I might need to check this with spacetime plots, but if two worldlines that are not casually tied can't you just find a reference frame where both are simultaneous?

 

[DrChinese]

If @DrChinese is using an interpretation, then i have no problem with his claims. But it seems to me that he insists that his discription is the only posssible one.

My “interpretation” is just standard QM, I.e. the predictions thereof. It predicts perfect correlation in certain situations, in principle with each and every run. But limitations in real world experiments do not achieve that.

The combination of the theoretical predictions and the actual results lead to some clear descriptions. However, there are multiple alternative ways to describe the situation too. My point is simply that one should start at one spot (obvious signs of nonlocality) first. But each person is free to start where they like.

Some hold Einsteinian causality higher than QM, for example. I would say these each have their own domain of application, neither supercedes the other.

 

[DrChinese]

I am not talking about particles that haven't interacted, but about particles that haven't coexisted. If you have a photon that was emitted and absorbed a year ago and another that was emitted and absorbed today, does it make sense to talk about the state of the two photon system?

And yet such 2 photon state has been so described, and has been produced experimentally. Publication: Phys. Rev. Lett. 110, 210403 (2013), so hopefully not too much to question here.

Entanglement Between Photons that have Never Coexisted

"According to this description, the timing of each photon is merely an additional label to discriminate between the different photons, and the time in which each photon is measured has no effect on the final outcome. The first photon from the first pair (photon 1) is measured even before the second pair is created (see Fig. 1). After the creation of the second pair, the Bell projection occurs and only after another delay period is the last photon from the second pair (photon 4) detected. Entanglement swapping creates correlations between the first and last photons non-locally not only in space, but also in time. ...

"In conclusion, we have demonstrated quantum entanglement between two photons that do not share coexistence. Although one photon is measured even before the other is created, full quantum correlations were observed by measuring the density matrix of the two photons, conditioned on the result of the projecting measurement [into Bell states |φ+> or |φ−>]. This is a manifestation of the non-locality of quantum mechanics not only in space, but also in time."

 

[DrChinese]

I might need to check this with spacetime plots, but if two worldlines that are not casually tied can't you just find a reference frame where both are simultaneous?

It is not true that 2 distant events in spacetime A & B must necessarily demonstrate some reference frame in which order is reversed. It is dependent on the distance between them in both space and time.

Suppose A and B start with synchronized clocks. At T=0, A makes her measurement. At T=3 nanoseconds, B makes his measurement. If A and B are separated by less than a meter (approximately), there is no reference frame (accelerated or not) in which B appears to occur before A.

I am not so well versed in Special Relativity regarding accelerated reference frames. If I am incorrect, please set me on the right path.

 

[Morbert]

My “interpretation” is just standard QM, I.e. the predictions thereof. It predicts perfect correlation in certain situations, in principle with each and every run. But limitations in real world experiments do not achieve that.

The correlations predicted by QM are not disputed. What's disputed is their significance re/ nonlocal influence. It is my position - and Peres's, Fuchs's, Brun's, Griffiths's et al - that ordinary QM doesn't necessarily imply nonlocal influence.

And yet such 2 photon state has been so described, and has been produced experimentally. Publication: Phys. Rev. Lett. 110, 210403 (2013), so hopefully not too much to question here.

Entanglement Between Photons that have Never Coexisted

"Entanglement swapping creates correlations between the first and last photons non-locally not only in space, but also in time. ...

Similarly, what these experiments show is that we can induce Bell-inequality-violating correlations between outcomes of measurements on photons that never coexisted, but we can give accounts of these correlations without recourse to nonlocal influence.

 

[pines-demon]

It is not true that 2 distant events in spacetime A & B must necessarily demonstrate some reference frame in which order is reversed. It is dependent on the distance between them in both space and time.

Suppose A and B start with synchronized clocks. At T=0, A makes her measurement. At T=3 nanoseconds, B makes his measurement. If A and B are separated by less than a meter (approximately), there is no reference frame (accelerated or not) in which B appears to occur before A.

I am not so well versed in Special Relativity regarding accelerated reference frames. If I am incorrect, please set me on the right path.

Nevermind reversing the order, if two events are not connected causally (space-like separated) you can always find a non-accelerated frame when you can treat the two events as if the events started at the same time.

 

[pines-demon]

The correlations predicted by QM are not disputed. What's disputed is their significance re/ nonlocal influence. It is my position - and Peres's, Fuchs's, Brun's, Griffiths's et al - that ordinary QM doesn't necessarily imply nonlocal influence.

What do these authors propose to interpret the entanglement correlations?

Similarly, what these experiments show is that we can induce Bell-inequality-violating correlations between outcomes of measurements on photons that never coexisted, but we can give accounts of these correlations without recourse to nonlocal influence.

Coexistence does not matter much if you use nonlocal interactions...

 

[DrChinese]

Nevermind reversing the order, if two events are not connected causally (space-like separated) you can always find a non-accelerated frame when you can treat the two events as if the events started at the same time.

If you can’t flip the order in some reference frame, they cannot be made to look simultaneous either.

It’s a question of distance apart in spacetime. I gave you a specific example. Why don’t you address that one, and show some reference frame where the A and B events are simultaneous?