Non-local preparation in entanglement swapping experiments

[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

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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.

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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?

 

[DrChinese]

The correlations predicted by QM are not disputed. …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.

I hear of the existence of these “accounts”. And I literally have a hundred+ bookmarks for various ones making similar claims. I cannot find anything at all that actually* maintains strict local/Einsteinian causality.

Local information transfer/update to explain remote delayed choice swapping? Basically, that’s a straight out violation of Bell’s Theorem.


*They gotta explain swapping without hand-waving. Nonlocal influences will do the trick of course. But even those need boundaries.

 

[PeterDonis]

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 think the answer is yes (but see my question below)--or more precisely yes for the state of the overall 4 photon system in the entanglement swapping experiment. The usual formulation of NRQM doesn't cover such cases, but I think QFT can. If the two photons you describe are photons 1&4 in an entanglement swapping experiment (which is possible in principle, though still well beyond our practical capabilities), then I think you can pick out appropriate spacetime events and appropriate quantum field operators to describe the experiment and the 4 photon system that it is an experiment on. In QFT a "state" does not have to be a state at a particular time. I think any combination of QFT degrees of freedom can in principle describe a "state", though of course the vast majority of such combinations have no practical use.

That does raise a question, though: @DrChinese, do you know of any reference that develops the kind of formulation I just described, that can cover an entanglement swapping experiment of the kind @martinbn described? I'm curious as to how much of what I just hand-waved has actually been rigorously investigated.

[Edit--I see the reference @DrChinese gave in post #45, I'll take a look.]

 

[PeterDonis]

if two events are not connected causally (space-like separated)

In the case @martinbn described, the events of photon 1 being emitted and absorbed could be in the past light cone of the events of photon 1 being emitted and absorbed. But it's true that they wouldn't have to be; it would be possible to set things up so those events were spacelike separated (though expensive, since you'd have to have a lab at least a light year wide).

 

[Morbert]

What do these authors propose to interpret the entanglement correlations?

Fuchs and Peres read QM as a theory of macroscopic tests and preparations, and not as a realistic theory of the microscopic. They maintain that nonlocal influence is necessary to postulate only when attempting to reproduce QM with a realistic theory of the microscopic. Entanglement is a characteristic of states, and hence they interpret it as a characteristic of preparations, giving rise to Bell-inequality-violating correlations under the right tests.

Brun and Griffiths read QM as a realistic theory, but introduce a restriction on the construction of logical propositions about quantum systems. They argue that this restriction eliminates the need to infer nonlocal influence. https://arxiv.org/abs/0908.2914

Note that none of these approaches premise "no nonlocal influence" on coincident pasts of subsystems. As such, papers like the one referenced by @DrChinese in post #45 don't pose a novel challenge to these approaches.

 

[DrChinese]

That does raise a question, though: @DrChinese, do you know of any reference that develops the kind of formulation I just described, that can cover an entanglement swapping experiment of the kind @martinbn described? I'm curious as to how much of what I just hand-waved has actually been rigorously investigated.

[Edit--I see the reference @DrChinese gave in post #45, I'll take a look.]

A couple of additional comments. Obviously, there are some limits to the amount of separation that can be achieved on the planet Earth*. There have been a number of experiments where the swaps are separated by larger distances than the one I referenced previously. That one was only about 1 meter. This one is a much larger distance:

Field test of entanglement swapping over 100-km optical fiber with independent 1-GHz-clock sequential time-bin entangled photon-pair sources

Depending on how you calculate the distance between Alice and Bob, they are either 12.5 km apart (physical distance) or about 65 km apart (virtual distance including coiled fiber, my best estimate). In this particular experimental setup, the relative times and ordering can be adjusted arbitrarily. I was unable to deduce what the experimenters' actual timing was for this paper.

There have also been earth-to-satellite tests, but I don't think those citations would add much.


*A millisecond translates to 300 km of distance at c.