Exploring Entanglement Swapping: Post-Selection vs. BSM?

[DrChinese]

I am starting this thread to focus on a point discussed in a QP thread. The relevant experiment is referenced below, which is a very complex experiment intending to remove some of the "loopholes" in Bell tests. For this thread, those loopholes don't matter and we won't reference that element. What matters is that entanglement is demonstrated (S=2.4 for CHSH calculation). The entanglement is created by a "traditional" Bell State Measurement (BSM) performed on 2 photons, whose near-simultaneous arrival heralds a psi- state (maximal entanglement, with opposite polarizations) for the pair used for the Bell test. Importantly in this experiment, the BSM (at location C) occurs AFTER the entangled pairs are recorded (at locations A and B)

https://arxiv.org/pdf/1508.05949.pdf
Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
Hensen et al, 2015.

I. The question being posed is as follows: Is Entanglement Swapping a result of a) Post-Selection, or b) a result of the BSM operation? In other words: is swapping a) simply identifying photon pairs that will demonstrate entanglement; or b) is swapping a result of a physical quantum interaction? Here are two opposing interpretations (reference Figure 1):

@vanhees71 takes position a): "If I understand it right, the point is to use entanglement swapping to select (or post-select, which doesn't really matter, if QT is correct, and there's no reason to doubt it, including the result of this experiment!) entangled electron pairs. Without this selection the electron pairs are not entangled at all!"

I say: b) Only a physical operation, performed after the fact, causes the entanglement swap to occur in this experiment. This is a demonstration of quantum nonlocality, which defies the normal cause-effect nature of classical physics. (Note that there is no possibility of sending an FTL signal here. Also note that if you are a fan of "acausal" interpretations, then my position is nothing special.)

Obviously, there are answers provided by various interpretations. But is there an experimental way to discern between a) and b)? Maybe there is. Here is my shot. a) and b) agree that a successful swap occurs when the following criteria are met (as they are in the experiment):

i) A polarized photon from location A and a similarly polarized photon from location B pass through a beam splitter (FBS), and emerge on opposite output ports. Both are transmitted, or both are reflected.
ii) The photons cause the both of the detectors positioned outside the output ports to click simultaneously, where simultaneously is defined as being within a suitably small time window (perhaps on the order of 10 to 50 nanoseconds).
iii) Either the A photon was reflected to the "left" detector and the B photon was reflected to the "right" detector; exclusive or (XOR)
iv) The A photon was transmitted to the "right" detector and the B photon was transmitted to the "left" detector.

In the a) interpretation championed by vanhees71: the above are apparently the only requirements. All that occurs is that we are post-selecting a group that comes along about once an hour. There is no quantum interaction that occurs that defies local causality. There is no expectation that the photon from A has any kind of quantum interaction with the photon from B that is a requirement for identifying an entanglement swap.

In the b) interpretation championed by me DrChinese: there is an additional requirement v), namely that it must not be possible to determine the source of the photon arriving at the "left" detector (which of course would immediately tell us the source of the photon arriving at the "right" detector). This indistinguishability requirement is physical, and is only satisfied when the physical setup does not allow the iii) and the iv) to be distinguished.

Now I'm sure the a) proponents would agree that v) is one of their requirements too, but why? Imagine this scenario, we'll call Alt-BSM. In the Alt-BSM setup, requirements i) ii) iii) and iv) are met - but NOT requirement v) physical indistinguishability. Here is how we will create this. The photons from location A and the photons from location B will be routed to separate but otherwise identical BSM setups. We will record the results and make note of the pairs that meet the requirements of i) ii) iii) and iv) above. We still expect the both to be reflected, or both to be transmitted. We still expect them to arrive simultaneously (within the small time window). However, we will always know which photon comes from the A location, and which comes from the B location, and they will have never had a chance to interact. So the v) requirement (physical interaction) is definitely NOT met. Nonetheless, we will have otherwise satisfied the requirements needed for those who say that the post-selection process merely reveals the small proportion (1 per hour) of pairs in which entanglement had occurred (since the A & B outcomes are recorded before the C outcomes). On the other hand, I say the related A/B pairs will NOT violate a Bell inequality and will have an S value below 2. Thus proving that the v) requirement of physical indistinguishability is essential, and that the only reasonable interpretation is the b) position: the BSM performs a physical operation (entanglement swapping), which violates local causality.

II. Now I know that my friends the a) advocates will kick and scream at my characterization of v), but here is my final proof (actually not a proof, but an experimentally testable question which should provide proof). We already know that the rate of coincidences in the actual experiment are 245 in a 220 hour run. Let's call that 1 per hour. If a) is correct, then if we perform the Alt-BSM version we must get a lot more than 1 qualifying event per hour. Perhaps we would get 3 per hour: 1 of which (a subset) would have also satisfied the actual BSM criteria (thus "post-selecting" the entangled pairings), and maybe a 2 more that would NOT have met the more restrictive criteria (no entanglement). This would demonstrate that only those events in which v) is satisfied are those in which entanglement occurs. On the other hand, if the rate of coincidence remains at about 1 per hour: then we know for a fact that the BSM is a physical operation that violates local causality when it is performed after entangled A and B are detected (as in this experiment). For a) to be valid, there must be a difference in the rate between the performed BSM experiment and my hypothetical Alt-BSM experiment.

So my question to experimenters: run the Hensen et al experiment in the Alt-BSM mode, and tell us the rate of seeing qualifying events. And while you are at it: whether the S value indicates entanglement (S=2.42+/-), no entanglement, or some entanglement. Thoughts?

 

[StevieTNZ]

I will muse over your experiments. I should note that in the past I emailed Bill Wootters, where I asked if entanglement between systems A and B, and systems C and D, is required, in order for it to be swapped to B and C (therefore A and D) - even in the delayed choice experiment. He answered yes.

My thoughts are that entanglement between A and B (and likewise C and D) is not broken by a detection of systems A and D. Merely what occurs is entanglement of those systems with the macroscopic apparatus' (so the entanglement is now between the apparatus and B (and apparatus and C)). That would enable entanglement to still exist in order to be swapped.

 

[PeterDonis]

My thoughts are that entanglement between A and B (and likewise C and D) is not broken by a detection of systems A and D. Merely what occurs is entanglement of those systems with the macroscopic apparatus'

This view only works for no collapse interpretations of QM, such as the MWI. It does not work if collapse is an actual physical process, since such a process would have to break entanglement.

 

[PeterDonis]

The entanglement is created by a "traditional" Bell State Measurement (BSM) performed on 2 photons, whose near-simultaneous arrival heralds a psi- state (maximal entanglement, with opposite polarizations) for the pair used for the Bell test. Importantly in this experiment, the BSM (at location C) occurs AFTER the entangled pairs are recorded (at locations A and B)

I'm not quite getting all of this from what is described in the paper you linked to. In particular, it doesn't seem to be consistent with the spacetime diagram in Fig. 2a.

Here is what I am getting from that diagram and its accompanying text. I will describe the events in "stages", each of which consists of one or more events which can be taken to be spacelike separated from each other, but in which each "stage" is timelike separated from every other.

(1) At each of points A and B, an electron undergoes a "spin reset" operation.

(2) At each of points A and B, the spin of the electron that got the "spin reset" in phase 1, above, is entangled with a photon, which is emitted towards point C, timed such that the two photons from A and B will arrive at C at the same instant, to within as tight an accuracy as possible. (Note that it is not actually necessary that these two phase 2 events are spacelike separated, but I will treat them as if they are since their time ordering is irrelevant to the rest of the experiment.)

(3) At points A and B, a "measurement" sequence is initiated on the electron at that point, consisting of an RNG generation of an input bit, the input bit determining the direction of a spin measurement, and a spin measurement time window being started. At point C, the two photons from points A and B are received, their detection times are recorded, and, if they meet a particular coincidence detection pattern, an "event ready" signal is generated indicating that this run of the experiment is valid.

(4) The spin measurement time windows end at points A and B and the results are recorded. (Note that this is in a separate phase, because the spin measurement time windows are long enough that the events in this phase are in the future light cone of all the events in phase 3 above.)

Since phase 4 comes after phase 3, the results of the spin measurements at A and B are not recorded before the photon detection at C is done. The RNG generation and the start of the spin measurement windows at A and B are spacelike separated from the photon detection at C (all of these are in phase 3, above).

 

[StevieTNZ]

This view only works for no collapse interpretations of QM, such as the MWI. It does not work if collapse is an actual physical process, since such a process would have to break entanglement.

So if entanglement is observed after swapping, what implications do the current experimental results have on that stance?

 

[PeterDonis]

if entanglement is observed after swapping, what implications do the current experimental results have on that stance?

Such a stance would take the view that the measurement at C did break an entanglement, since before that measurement we have two entangled pairs (the electron and photon that originated from A, and the electron and photon that originated from B), whereas after the measurement we have only one such pair (the electrons at A and B). It's just not possible in this case to describe this as breaking a single identified entanglement, because of the swapping aspect; one can only describe it, heuristically, as "reducing the number of entanglements by one".

 

[StevieTNZ]

Such a stance would take the view that the measurement at C did break an entanglement, since before that measurement we have two entangled pairs (the electron and photon that originated from A, and the electron and photon that originated from B), whereas after the measurement we have only one such pair (the electrons at A and B). It's just not possible in this case to describe this as breaking a single identified entanglement, because of the swapping aspect; one can only describe it, heuristically, as "reducing the number of entanglements by one".

I'm referring to original entanglement between the systems (before swapping). If entanglement needs to remain between the original systems, if it is broken by a physical process prior to swapping what entanglement is there to swap? The fact that Bell's inequality was violated after swapping indicates what about the physical collapse interpretation?

Bernard d'Espagnat, back in 2013, emailed me regarding https://www.nature.com/articles/nphys2294:

Concerning the first measurement (on 1 and 4), you rightly pointed out that they result in entanglements with the instruments. But since the outcomes are registered we may consider that collapses have taken place so that we are left with a quantum system composed of but two particles and which is not in a pure state. It is a mixture the elements of which may be considered separately. I considered those corresponding to what was actually measured in the Vienna experiment. The theoretical outcomes happen to fit the experimental ones. But their interpretation is quite different from the one given in the article in that particles 1 and 4 cannot be considered having been entangled (due to delayed entanglement swapping) before they were measured. In fact I'm afraid there is neither delay nor swapping…

 

[PeterDonis]

I'm referring to original entanglement between the systems (before swapping).

The measurement of the photons, on the view I described, would indeed break both of those original entanglements, as will be evident from the fact that after that measurement, the remaining entanglement is between the electrons only.

if it is broken by a physical process prior to swapping what entanglement is there to swap?

The same physical process does both things: breaks the original entanglements, and creates the new "swapped" entanglement. There is nothing in the "measurements break entanglements" view I described that forbids this.

 

[StevieTNZ]

The same physical process does both things: breaks the original entanglements, and creates the new "swapped" entanglement. There is nothing in the "measurements break entanglements" view I described that forbids this.

What about in the delayed choice experiment? The swapped entanglement is apparently created after detection of systems A and D. Those two systems are not the ones we're interested in to do 'delayed choice entanglement swapping'. That would be systems B and C interacting, to achieve that.

 

[PeterDonis]

What about in the delayed choice experiment?

You'll have to give a reference to a specific experiment if you want to discuss that.

 

[grzegorzsz830402]

I say: b) Only a physical operation, performed after the fact, causes the entanglement swap to occur in this experiment. This is a demonstration of quantum nonlocality, which defies the normal cause-effect nature of classical physics. (Note that there is no possibility of sending an FTL signal here. Also note that if you are a fan of "acausal" interpretations, then my position is nothing special.)

Or, we have low resolution model for light "photon" that works great at long distances, yet fails at short ones.

Point "assumption" about photon (massless particle), is a useful simplification for low resolution model, that removes all complexity about nature of energy delivery.

Yet, that complexity have to be unpacked if we want to find unified understanding.

We have instantaneous (bulk- all at once) energy delivery assumption.
If, we allow ourself to entertain possibility of gradual energy delivery, take under consideration energy threshold requirements for detection, then we can see possibility for physical operation happening with some delay, allowing insufficient energy for detection to reach detectors unaffected by physical operation, (No detection), and we can observe only detection of energy, afected by physical operation.

With speed of light being roughly around 300 000 km/s, 818m distance between cause and effect can be seen as neglecteble in that context (although not intuitively at first). Especially, if speed of energy propagation and speed on internal processes of that phenomenon, would have to be taken under consideration for complete understanding of delay, in affected spin.

There would be possibility to test that, if we have ability, to adjust detection apparatus sensitivity, in a way that could expose energy reduction caused by delay. If, it would be sufficiently higher, than standard energy fluctuation of emitted fotons.

If, technology is within our reach, we would have "no detection", when "successful entanglement swapping" criteria, would be met.

 

[DrChinese]

I'm not quite getting all of this from what is described in the paper you linked to. In particular, it doesn't seem to be consistent with the spacetime diagram in Fig. 2a.

...

(3) At points A and B, a "measurement" sequence is initiated on the electron at that point, consisting of an RNG generation of an input bit, the input bit determining the direction of a spin measurement, and a spin measurement time window being started. At point C, the two photons from points A and B are received, their detection times are recorded, and, if they meet a particular coincidence detection pattern, an "event ready" signal is generated indicating that this run of the experiment is valid.

(4) The spin measurement time windows end at points A and B and the results are recorded. (Note that this is in a separate phase, because the spin measurement time windows are long enough that the events in this phase are in the future light cone of all the events in phase 3 above.)

Since phase 4 comes after phase 3, the results of the spin measurements at A and B are not recorded before the photon detection at C is done. The RNG generation and the start of the spin measurement windows at A and B are spacelike separated from the photon detection at C (all of these are in phase 3, above).

You are correct about the sequencing. I misread some of the elements of the diagrams. Thanks for correcting me.

For their purposes (strict Einsteinian locality), it is essential that the random number generation (RNG) and choice of measurement basis at A be performed too late to affect anything at B (and vice versa - for the Bell test). In the Figure 2.a., the sequencing of the A & B detections (over a span of about 4 microseconds) relative to the BSM at location C varies. To my eyes, it appears some of the C BSMs occur before the A/B detections, while some occur after.

For the purposes of this thread: let's pretend/assume that the lab location C is located sufficiently far away from A and B such that the BSM is guaranteed to be performed AFTER the A and B detections have been recorded in ALL cases. That would require a delay of the BSM by about 3 microseconds, requiring location C to be about 0.9 km further away from both A and B.

Also, here is the paper related to other delayed choice entanglement swapping reference by @StevieTNZ in post #7. On this version, the BSM always occurs after the Bell test, and does so in all reference frames.

https://arxiv.org/abs/1203.4834
Experimental delayed-choice entanglement swapping
Ma et al (2012)
"In Peres’ words: “if we attempt to attribute an objective meaning to the quantum state of a single system, curious paradoxes appear: quantum effects mimic not only instantaneous action-at-a-distance but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded." This being a restatement of the b) position in this thread.

"However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge." This being a restatement of the a) position in this thread.

 

[PeterDonis]

For their purposes (strict Einsteinian locality), it is essential that the random number generation (RNG) and choice of measurement basis at A be performed too late to affect anything at B (and vice versa - for the Bell test).

I think they also want the BSM at C to be spacelike separated from the RNG and choice of measurement basis at A and B. (The exact coordinate times in the frame in which Fig. 2.a. is drawn don't matter as long as spacelike separation of the events is maintained.)

In the Figure 2.a., the sequencing of the A & B detections (over a span of about 4 microseconds) relative to the BSM at location C varies.

The length of time the actual A & B detection processes take makes it impossible, given the spatial layout, for those processes to complete while being entirely spacelike separated from each other (or from the BSM at C). The spacelike separation can only apply to the starting of those processes (the RNG and choice of measurement basis).

here is the paper related to other delayed choice entanglement swapping reference by @StevieTNZ in post #7. On this version, the BSM always occurs after the Bell test, and does so in all reference frames.

The key observation here (made in the comments under Figure 1) is that Alice and Bob can only sort their measurement results into subsets and run the appropriate tests to verify the predicted correlations after they receive Victor's measurement results. That is why FTL signaling is not possible, and it is also why the spacetime relationship between the BSM and the other measurements doesn't actually matter. And, of course, that is consistent with the math of QM.

The same restriction exists in the other paper's setup (the A and B results cannot be tested against QM predictions until the C results are obtained), but in that paper, since the spacetime relationship between the BSM and the other measurements is different, by the time the A and B measurements are completed, the result of the C measurement is already available. In other words, the only real difference between the two setups is that in the "delayed choice" setup, Alice and Bob have to wait longer (until they receive Victor's result) to run their statistical tests and verify the QM predictions. But the final outcomes are the same in both cases.

 

[PeterDonis]

The question being posed is as follows: Is Entanglement Swapping a result of a) Post-Selection, or b) a result of the BSM operation?

In the light of the actual experiments we have looked at, the answer is obviously: both! You need both an operation like the BSM operation that can swap the entanglement (since the A and B particles as originally prepared are not entangled with each other) and a post-selection process that uses the observed result of the BSM operation (or whatever operation you are using to do the swapping) to sort the A and B measurements into subsets that correspond to whether the entanglement swap actually happened or not.

 

[PeterDonis]

iii) Either the A photon was reflected to the "left" detector and the B photon was reflected to the "right" detector; exclusive or (XOR)
iv) The A photon was transmitted to the "right" detector and the B photon was transmitted to the "left" detector.

In the paper referenced in your OP, this isn't even applicable because the A and B particles are electrons, not photons. Which means your additional requirement v) can't be right since it can't even cover this kind of scenario, while "entanglement swapping" is certainly occurring in it.

The photons from location A and the photons from location B will be routed to separate but otherwise identical BSM setups.

Wouldn't this invalidate the whole scheme? The point of having a single BSM setup is that otherwise there is no way to get A and B entangled at all. There must be a single operation that involves something entangled with A and something entangled with B, in order to swap entanglements to make A and B entangled.

 

[DrChinese]

1. In the paper referenced in your OP, this isn't even applicable because the A and B particles are electrons, not photons. Which means your additional requirement v) can't be right since it can't even cover this kind of scenario, while "entanglement swapping" is certainly occurring in it.

2. Wouldn't this invalidate the whole scheme? The point of having a single BSM setup is that otherwise there is no way to get A and B entangled at all. There must be a single operation that involves something entangled with A and something entangled with B, in order to swap entanglements to make A and B entangled.

1. No, the photons are from A and from B going to C (where the BSM is performed). At C (in the diagram it is marked as "a fibre-based beam splitter (FBS)":

iii) Either the A photon was reflected to the "left" detector and the B photon was reflected to the "right" detector; exclusive or (XOR)
iv) The A photon was transmitted to the "right" detector and the B photon was transmitted to the "left" detector.

2. Well of course I agree that no BSM occurs unless there is a single setup - the BSM is a real and physical quantum operation in my book. But for those who say that all we are doing is revealing some photon characteristics (that must already exist) when the observations at C occur, why should it be necessary for the photons to be analyzed by the single common setup? Why not two identical setups instead? Since the properties we seek to learn are i) what time do they arrive; and ii) do they transmit or reflect at the beam splitter.

 

[PeterDonis]

At C (in the diagram it is marked as "a fibre-based beam splitter (FBS)":

iii) Either the A photon was reflected to the "left" detector and the B photon was reflected to the "right" detector; exclusive or (XOR)
iv) The A photon was transmitted to the "right" detector and the B photon was transmitted to the "left" detector.

Ah, I see; this is the "event ready" signal. Or, to put it another way, the result of this measurement is used to sort the A and B results into two subsets, one of which is predicted to show "entangled" statistics and the other of which is predicted to show "separable" statistics.

This kind of measurement at C, and the post-selection of the A and B results based on it, are both necessary for entanglement swapping to be detected.

I'm not sure how anything @vanhees71 has claimed is inconsistent with that, but he might not be correctly describing the experimental setup to begin with. For example, here is the phrase you associate with him in the OP:

"If I understand it right, the point is to use entanglement swapping to select (or post-select, which doesn't really matter, if QT is correct, and there's no reason to doubt it, including the result of this experiment!) entangled electron pairs. Without this selection the electron pairs are not entangled at all!"

This is not correct: entanglement swapping is not used to select the subsets of the A and B results, it is an observed result of the A and B correlations for one of the subsets. I don't think the BSM operation by itself can be described as "entanglement swapping"; I think that is a property of the whole arrangement, including the selection of the subsets of the A and B results and the computation of their statistics.

 

[DrChinese]

1. This kind of measurement at C, and the post-selection of the A and B results based on it, are both necessary for entanglement swapping to be detected.

2. I'm not sure how anything @vanhees71 has claimed is inconsistent with that...

3. This is not correct: entanglement swapping is not used to select the subsets of the A and B results, it is an observed result of the A and B correlations for one of the subsets. I don't think the BSM operation by itself can be described as "entanglement swapping"; I think that is a property of the whole arrangement, including the selection of the subsets of the A and B results and the computation of their statistics.

1. The BSM is enough for the swap. The A and B results are needed as proof only.

2. Everything @vanhees71 says is inconsistent with a physical operation of the BSM. That would violate his "microcausality" condition (what he often wrongly refers to as "local causality"). See post #19 below.

3. I deny that swapping doesn't occur independently of a Bell test. In fact, one of the principles of quantum repeaters ( is that swapping can theoretically be performed from system to system without limit (of course there are practical considerations limiting that). No Bell test is required - ever. And every one of the swaps can be performed after the fact, making the entire chain of teleportation depend on future to past action.

Again, this is dependent on whether you are in the a) camp or the b) camp, and I am in the b) camp: Entanglement swapping is objectively real, and therefore it mimics action at a distance (as Peres says). The experimental realization of the experiment I propose above - which is well within reach with no additional technology required - will confirm the answer we seek.

 

[DrChinese]

So is the quantum state "no more than a “catalogue of our knowledge" as position a) holds? And therefore nothing *physical* occurs with the BSM which causes the A/B entanglement (since that would imply backwards in time causation) ?

If so: then nothing we do as part of the BSM (when performed after the related Bell test data for that run is recorded) can "cause" the entanglement. All we are doing is identifying (at location C) which NV pairs at locations A and B will yield psi- Bell state entanglement statistics. This occurred 245 times during the 220 hours of runtime for the experiment, or about once every 54 minutes. So the qualifying events are rare, since there are maybe 25,000,000* non-qualifying events in between. The non-qualifying events primarily occur because the event ready signals at A and B do not occur such that the photons arrive at C within the requisite narrow time window (perhaps 1 microsecond, if I am reading the chart correctly.) But when they do occur within the time window, there are 4 permutations possible at the beam splitter (with near equal frequency):

i) both A and B transmitted;
ii) both A and B reflected;
iii) A transmitted, B reflected
iv) A reflected, B tranmitted

Only the first 2 are of interest to us (as they indicate the psi- Bell state), and when either of those events occurs, 2 detectors will flash. Why do they need to interact at the BS if all we seek to learn is that either i) or ii) occurred? Why is quantum indistinguishability necessary if we are merely uncovering a pre-existing quantum property that cannot possibly affect the outcome of an entanglement test at locations A and B?

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

My assertion is that the sum of the i) and ii) cases will be about the same regardless of whether there is a dual BSM (Alt-BSM) setup or the standard BSM setup. That is, 1 qualifying event every 54 minutes. The difference would be that when the Alt-BSM setup is used, there will be no entanglement (and S will be less than 2).

On the other hand, if I am wrong: there should be many more qualifying events under the Alt-BSM regimen because most of those events will not indicate that there will be entanglement seen from the Bell test. (Only 245 accomplish that.) Perhaps 1 qualifying event every 13 minutes (this is an arbitrary number I made up), let's say 1015 to be specific (derived from the 1 in 13 minutes rate for 220 hours). After all, those 1015 events would include the same 245 that demonstrate (reveal) entanglement, but as a subset. But it would also include other 770 other events that presumably would reduce the CHSH S value (since we require that only the 245 yield an S>2). The number of "additional events" over the 245 must be enough to pull the S value below 2. Again I don't know that number, but it must be enough to be discerned in an experiment.

Otherwise you would conclude that the BSM is a physical operation which causes the entanglement swap, even though that entanglement occurred in the past. That would be a demonstration of action at a distance, where the distance is distance in spacetime. None of this would be contradicted by anything predicted by QM, since there is no indicated causal direction in quantum mechanical predictions.*My estimate assumes that there are 10,000 spin resets per second. I could not find a specific rate in the paper. It takes at least 15 microseconds for a full cycle.

 

[PeterDonis]

1. The BSM is enough for the swap. The A and B results are needed as proof only.

For the particular type of interpretation you are taking, yes, you could take this view. I was talking about the experimental facts independent of any interpretation. Experimentally, you can only detect the entanglement swap when you sort the A and B results into subsets based on the C result and do statistics on them. When (and possibly even "if"--I'm not sure that interpretations like the MWI would even describe this process as "entanglement swapping") the swap "actually occurs" will be interpretation dependent.

 

[PeterDonis]

My assertion is that the sum of the i) and ii) cases will be about the same regardless of whether there is a dual BSM (Alt-BSM) setup or the standard BSM setup.

This doesn't make sense to me: with two BSMs how can you even have any of these cases? The cases are for what happens when photons coming from A and B encounter a single beam splitter.

 

[PeterDonis]

Everything @vanhees71 says is inconsistent with a physical operation of the BSM. That would violate his "microcausality" condition

I don't see how, since the "microcausality" condition refers to measurements commuting. All of the measurements involved in these experiments commute (their results are independent of their ordering), so they all obviously meet the "microcausality" condition. (Indeed, as the "delayed choice" experiment shows, they meet this condition even if they are not spacelike separated, so they meet a stronger condition than the usual commutation condition in QFT, which only applies to measurements that are spacelike separated.)

I agree that "microcausality" is a poorly chosen name for this condition, since it doesn't actually say anything about "causality" in the usual sense, because in that usual sense of causality, a cause and its effect clearly cannot commute (the cause must come before the effect). But that's a problem with the words used to describe the condition, not the condition itself. At the very least, if this condition is claimed to tell us something useful about "causality", somebody should publish an argument for why. I'm not aware of anyone having done so. But that doesn't change the facts about what measurements do or do not meet the actual condition, i.e., which measurements do or do not commute.

 

[PeterDonis]

is the quantum state "no more than a “catalogue of our knowledge" as position a) holds? And therefore nothing *physical* occurs with the BSM

This is a non sequitur. Whether or not the BSM "does something physical" is a separate question from how we interpret the quantum state. The BSM obviously does do something physical because we can change the statistics of experimental results by putting it in or taking it out. That is independent of any QM interpretation we adopt.

 

[StevieTNZ]

You'll have to give a reference to a specific experiment if you want to discuss that.

As DrChinese has already linked to, I'd refer to this experiment: https://www.nature.com/articles/nphys2294 (https://arxiv.org/abs/1203.4834)

 

[PeterDonis]

As DrChinese has already linked to, I'd refer to this experiment: https://www.nature.com/articles/nphys2294 (https://arxiv.org/abs/1203.4834)

Got it.

The swapped entanglement is apparently created after detection of systems A and D.

That doesn't change the fact that the only possible process that could do the swapping is the measurement at C/Victor. There is no other process that involves something entangled with A/Alice and something entangled with B/Bob. (There is no "D" anywhere in the experiments we are discussing; it's A, B, and C in the experiment in the OP, and Alice, Bob, and Victor in the delayed choice version.)

Of course this kind of thing would not be possible with classical causality. That just means that whatever kind of "causality" QM has, it can't be the same as classical causality, at least not when entanglement is involved.

 

[StevieTNZ]

Got it.That doesn't change the fact that the only possible process that could do the swapping is the measurement at C/Victor. There is no other process that involves something entangled with A/Alice and something entangled with B/Bob. (There is no "D" anywhere in the experiments we are discussing; it's A, B, and C in the experiment in the OP, and Alice, Bob, and Victor in the delayed choice version.)

Of course this kind of thing would not be possible with classical causality. That just means that whatever kind of "causality" QM has, it can't be the same as classical causality, at least not when entanglement is involved.

There are four systems involved - A, B (maximally entangled) and C and D (maximally entangled). Systems B and C interact, supposedly causing entanglement swapping to A and D (Alice and Bob). But if there is no longer any entanglement between A and B (likewise C and D) because A and D are measured prior to B and C interacting, what is being swapped?

 

[DrChinese]

Whether or not the BSM "does something physical" is a separate question from how we interpret the quantum state. The BSM obviously does do something physical because we can change the statistics of experimental results by putting it in or taking it out. That is independent of any QM interpretation we adopt.

The question I pose is whether the BSM merely reveals entanglement, or actually creates it. If it creates entanglement, it must be physical - and therefore the quantum state is objectively real (in the words of Peres and Zeilinger et al).

It sounds like you agree.

 

[DrChinese]

This doesn't make sense to me: with two BSMs how can you even have any of these cases? The cases are for what happens when photons coming from A and B encounter a single beam splitter.

Well, the photons arriving at a beam splitter are either both reflected or both transmitted in either scenario. The photons arrive near simultaneously. If we are simply *identifying* the rare case (once every 54 minutes) that these attributes occur, why do they need the opportunity to appear in the same beam splitter in an overlapping region of spacetime?

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

I say: the reason they need to appear in the same beam splitter in an overlapping region of spacetime (and obviously they do) is that this is a quantum interaction that causes the entanglement swap - for the entangled systems used in the Bell test - even though the Bell inequality violating results were already cast in stone. This is an example of quantum nonlocality, action at a distance (in spacetime) which violates Einsteinian locality. It cannot be described in terms of local causality, nor does quantum theory demand that it should.

If we were using the words of @RUTA he would say this is an example of quantum mechanics demonstrating its "acausal" nature. I would guess @Demystifier might agree but use somewhat different words to describe what is occurring. But regardless, I don't think it is really interpretation dependent at this point when describing a delayed choice entanglement swap: it's physical and contradicts any causal explanation (where cause precedes effect). There is only a quantum context, and the context spans spacetime in a manner that does not respect Einsteinian limits.

 

[PeterDonis]

The question I pose is whether the BSM merely reveals entanglement, or actually creates it.

I'm not sure the question is well posed; at the very least, whether or not it is well-posed seems to me to be interpretation dependent.

If it creates entanglement, it must be physical - and therefore the quantum state is objectively real (in the words of Peres and Zeilinger et al).

This might be a map-territory confusion. "Quantum states" are parts of our quantum models of reality. That doesn't necessarily mean they are part of reality itself. Again, the answer to this question, or whether it is even well-posed enough to have an answer, might be interpretation dependent.

 

[DrChinese]

As DrChinese has already linked to, I'd refer to this experiment: https://www.nature.com/articles/nphys2294 (https://arxiv.org/abs/1203.4834)

Quoting from that: "Whether Alice’s and Bob’s photons can be assigned an entangled state or a separable state depends on Victor’s later choice. In Peres’ words: “if we attempt to attribute an objective meaning to the quantum state of a single system, curious paradoxes appear: quantum effects mimic not only instantaneous action-at-a-distance but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded.”

Stevie, in that reference, the mapping of the locations/actors is as follows:

Location A == Alice (who measures photon 1)
Location B == Bob (who measures photon 4)
Location C == Victor (who chooses to perform the entanglement swap by performing the successful BSM on photons 2 and 3)

Keep in mind that what we loosely refer to as photons 1 and 2 (or 3 and 4) are actually biphotons (systems of 2 entangled and non-separable photons). There is no specific point in time when you can say the photons we label 1 and 4 become the biphoton of 1 and 4 (as opposed to being members of earlier biphotons). Regardless of which specific experiment we cite, these are essentially the same experiment for the purposes of this thread.

 

[PeterDonis]

the photons arriving at a beam splitter are either both reflected or both transmitted in either scenario.

Yes, but if there are two beam splitters, the photons can't be put into a Bell state by being both reflected or both transmitted. This seems to me to be an obvious fact about the two different experimental setups. If it creates some sort of problem, I'm not sure what.

I don't think it is really interpretation dependent at this point when describing a delayed choice entanglement swap: it's physical and contradicts any causal explanation (where cause precedes effect).

I think one has to be extremely careful to distinguish what we actually can verify in experiments from what we can't.

We can verify in experiments that the initial processes at A and B each produce a pair of particles (one electron and one photon in the OP experiment, two photons in the post #12 "delayed choice" experiment) that, if we just measure them without doing anything else to them, are entangled within each pair, but the pairs are not entangled with each other.

We can verify in experiments that, if we do not do anything to the particles in each pair that are headed for C--i.e., we do not do a BSM or anything else, we just let those photons fly off into the environment and never be heard from again--then measurements of the left-over particles at A and B (the electrons in the OP experiment, or the photons in the post #12 experiment) will show them to be not entangled. We can similarly verify in experiments that if we do separate measurements on the two particles headed for C--such as separate beam splitters for each instead of them both passing through the same one--then, again, measurements of the left-over particles at A and B will show them to be not entangled.

We can verify in experiments that if the two photons at C both pass through a single beam splitter, then we will obtain at C one of two possible results ("event ready" or not) which allow us to separate the results at A and B into two subsets, one of which (the "event ready" one) shows statistics consistent with entanglement of A and B, and the other of which shows statistics consistent with A and B not being entangled.

We can record the times of the A, B, and C measurements, and we can verify that the above statistical results work out the same regardless of the spacetime relationships of those measurements.

We cannot verify in experiments "when the entanglement swap occurs".

We cannot verify in experiments "what the quantum state is" in between the preparations and measurements in the above scenarios.

I'll leave it to you to respond as to whether you think what I've said above is consistent with the statement of yours that I quoted.

 

[DrChinese]

1. Yes, but if there are two beam splitters, the photons can't be put into a Bell state by being both reflected or both transmitted. This seems to me to be an obvious fact about the two different experimental setups. If it creates some sort of problem, I'm not sure what.

2. I think one has to be extremely careful to distinguish what we actually can verify in experiments from what we can't.

We can verify in experiments that the initial processes at A and B each produce a pair of particles (one electron and one photon in the OP experiment, two photons in the post #12 "delayed choice" experiment) that, if we just measure them without doing anything else to them, are entangled within each pair, but the pairs are not entangled with each other.

We can verify in experiments that, if we do not do anything to the particles in each pair that are headed for C--i.e., we do not do a BSM or anything else, we just let those photons fly off into the environment and never be heard from again--then measurements of the left-over particles at A and B (the electrons in the OP experiment, or the photons in the post #12 experiment) will show them to be not entangled. We can similarly verify in experiments that if we do separate measurements on the two particles headed for C--such as separate beam splitters for each instead of them both passing through the same one--then, again, measurements of the left-over particles at A and B will show them to be not entangled.

We can verify in experiments that if the two photons at C both pass through a single beam splitter, then we will obtain at C one of two possible results ("event ready" or not) which allow us to separate the results at A and B into two subsets, one of which (the "event ready" one) shows statistics consistent with entanglement of A and B, and the other of which shows statistics consistent with A and B not being entangled.

3. We can record the times of the A, B, and C measurements, and we can verify that the above statistical results work out the same regardless of the spacetime relationships of those measurements.

We cannot verify in experiments "when the entanglement swap occurs".

We cannot verify in experiments "what the quantum state is" in between the preparations and measurements in the above scenarios.

I'll leave it to you to respond as to whether you think what I've said above is consistent with the statement of yours that I quoted.

1. I know this, and everyone agrees it is true (including of course me). But why does distinguishability matter if you AREN'T changing what happened in the past, you are merely selecting the 245 A/B pairs that already demonstrate entanglement? If one argues (quoting @vanhees71 but he is not the only person saying this):

...the point is to use entanglement swapping to select (or post-select, which doesn't really matter, if QT is correct, and there's no reason to doubt it, including the result of this experiment!) entangled electron pairs. Without this selection the electron pairs are not entangled at all!"

Entanglement swapping is not a "selection"! It's an action, an operation, and this experiment (and others like it) demonstrate so clearly. He even says that without this action (misleadingly labeled "selection"), the entanglement swap fails. 2. I agree with all of this and have never implied otherwise.3. I agree with all of this and have never implied otherwise.

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

Who/what I am attacking is very simple: those who claim a delayed entanglement swap merely reveals which As and Bs are entangled. Were that true - and it's not - then there should be no need to do anything more on the photons arriving at C other than to test whether they are both transmitted (or both reflected) and whether they arrive near simultaneously. Why would you need to do anything else (like require them to overlap so they become indistinguishable) ? Again, *I* know that failing to have them overlap (so they are indistinguishable) means there is no swap. But for those that believe that a delayed swap can't affect the past (which it can), they must explain their reasoning here as to why the overlap is necessary - when the other requirements are otherwise met.

The photons from A and B arrive at C. There are 2 event qualifying possibilities (assuming near-simultaneous arrival times):

i) A is transmitted and B is transmitted, causing the "left" detector and the "right" detector to both click.
ii) A is reflected and B is reflected, causing the "left" detector and the "right" detector to both click.
If both detectors click, then you won't know whether it was case i) or case ii). We know this is a requirement (indistinguishability) per quantum theory, I am not questioning this point in any way. This scenario occurs once in 54 minutes on the average.

But why would indistinguishability (overlap) be a requirement if the action at C was not physically a part/cause of the A/B entanglement? So what if you learned whether it was scenario i) or scenario ii)? Would that identify different A/B pairs than the 245 that qualified? After all, you would be arguing that what occurred in the past was already fixed and in no way dependent on what you chose to do (or not do) at a later time. That's what I am asking - a defense of the contrary view.

Because I don't see that anything I am discussing is in fact interpretation dependent. It's the same facts in all interpretations, all interpretations require indistinguishability (again no one questions this). And yet indistinguishability can't really matter unless the entangled A/B pairs depend on that to become entangled, which requires an action in the future to affect the past. That must therefore be an element of any interpretation. Interpretations may describe it somewhat differently, but the essentials must be the same.

 

[vanhees71]

1. I know this, and everyone agrees it is true (including of course me). But why does distinguishability matter if you AREN'T changing what happened in the past, you are merely selecting the 245 A/B pairs that already demonstrate entanglement? If one argues (quoting @vanhees71 but he is not the only person saying this):

...the point is to use entanglement swapping to select (or post-select, which doesn't really matter, if QT is correct, and there's no reason to doubt it, including the result of this experiment!) entangled electron pairs. Without this selection the electron pairs are not entangled at all!"

Entanglement swapping is not a "selection"! It's an action, an operation, and this experiment (and others like it) demonstrate so clearly. He even says that without this action (misleadingly labeled "selection"), the entanglement swap fails.

The "entanglement-swapping protocol" is a typical selection process using projective measurement. You start with two entangled uncorrelated pairs. Then you use one piece of one pair and one piece of the other and perform a (local) measurement on these two pieces allowing to find these two pieces in the possible entangled states. Projecting out only one of these entangled state, i.e., working further with the two other pieces according to the local measurement, selects an entangled state of these two other pieces. The amazing thing is that these two now entangled pieces, which were before entirely uncorrelated, need not have to be in any causal contact to get entangled.

It's also irrelevant, whether you do the projective measurement with one of the pair before or after the measurement on the other (distant) pair or even when the two measurments are space-like separated.

My interpretation, arguing with microcausality of relativistic QFT is, that all this is just due to the entanglement of the initial pairs, i.e., the preparation of the objects you measure, before any of these measurements. There is no mutual causal action due to the measurement processes themselves.

2. I agree with all of this and have never implied otherwise.3. I agree with all of this and have never implied otherwise.

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

Who/what I am attacking is very simple: those who claim a delayed entanglement swap merely reveals which As and Bs are entangled. Were that true - and it's not - then there should be no need to do anything more on the photons arriving at C other than to test whether they are both transmitted (or both reflected) and whether they arrive near simultaneously. Why would you need to do anything else (like require them to overlap so they become indistinguishable) ? Again, *I* know that failing to have them overlap (so they are indistinguishable) means there is no swap. But for those that believe that a delayed swap can't affect the past (which it can), they must explain their reasoning here as to why the overlap is necessary - when the other requirements are otherwise met.

The photons from A and B arrive at C. There are 2 event qualifying possibilities (assuming near-simultaneous arrival times):

i) A is transmitted and B is transmitted, causing the "left" detector and the "right" detector to both click.
ii) A is reflected and B is reflected, causing the "left" detector and the "right" detector to both click.
If both detectors click, then you won't know whether it was case i) or case ii). We know this is a requirement (indistinguishability) per quantum theory, I am not questioning this point in any way. This scenario occurs once in 54 minutes on the average.

But why would indistinguishability (overlap) be a requirement if the action at C was not physically a part/cause of the A/B entanglement? So what if you learned whether it was scenario i) or scenario ii)? Would that identify different A/B pairs than the 245 that qualified? After all, you would be arguing that what occurred in the past was already fixed and in no way dependent on what you chose to do (or not do) at a later time. That's what I am asking - a defense of the contrary view.

Because I don't see that anything I am discussing is in fact interpretation dependent. It's the same facts in all interpretations, all interpretations require indistinguishability (again no one questions this). And yet indistinguishability can't really matter unless the entangled A/B pairs depend on that to become entangled, which requires an action in the future to affect the past. That must therefore be an element of any interpretation. Interpretations may describe it somewhat differently, but the essentials must be the same.

 

[DrChinese]

1. The "entanglement-swapping protocol" is a typical selection process using projective measurement. You start with two entangled uncorrelated pairs. Then you use one piece of one pair and one piece of the other and perform a (local) measurement on these two pieces allowing to find these two pieces in the possible entangled states. Projecting out only one of these entangled state, i.e., working further with the two other pieces according to the local measurement, selects an entangled state of these two other pieces. The amazing thing is that these two now entangled pieces, which were before entirely uncorrelated, need not have to be in any causal contact to get entangled.

It's also irrelevant, whether you do the projective measurement with one of the pair before or after the measurement on the other (distant) pair or even when the two measurments are space-like separated.

2. My interpretation, arguing with microcausality of relativistic QFT is, that all this is just due to the entanglement of the initial pairs, i.e., the preparation of the objects you measure, before any of these measurements. There is no mutual causal action due to the measurement processes themselves.

1. Agreed, except for the 2 words in bold. These are loaded with meaning that is subject to debate.

2. The entanglement of A/B is caused by the later BSM at C. It cannot be otherwise. You are essentially saying the photons arrive at C with their quantum properties predetermined AND local (unable to be affected by anything outside a light cone). This violates everything we know about quantum mechanics post-Bell, and does not fit in with any interpretation I am aware of... other than yours.

-------

I was hoping you would address my explicitly constructed example (OP) with a spirited defense of your ideas. There were 245 events in which the criteria were met for a swap. In your view, when the 2 photons arrive at C, they already possessed the following attributes (in addition to arriving near simultaneously and like polarized):

i) A is transmitted and B is transmitted at a BS, causing the "left" detector and the "right" detector to both click; XOR...
ii) A is reflected and B is reflected at a BS, causing the "left" detector and the "right" detector to both click.

They must fulfill one of the above, regardless of whether they were indistinguishable, because that was precisely what was tested in the actual experiment. The requirement that they be indistinguishable is an ADDITIONAL requirement. So presumably, all 245 events would have also been identified in the less restrictive criteria when the additional requirement is waived. That is basic logic within the locally causal world you advocate.

Of course, if you have a less restrictive set of criteria, you might also pick up additional events over and above the 245 that were actual swaps. The additional number of events, X, might include events in which the A/B Bell test did not include entanglement. And for your idea to make sense, X would need to be large enough that the CHSH calculation on the (245+X) events would fall below 2. That because the X events are not entangled and are presumably uncorrelated.

I am not certain, but I think the CHSH S value for random polarized unentangled pairs is 0. Can anyone confirm? If so, I think you can see the problem here. When you average in the X events with an S of 0 with 245 events with an S of 2.42 (per the actual experiment) you still get a value above 0. But the CHSH calculation on the (245+X) events will be above 0. I say that if this experiment were to be performed, there will be no swaps at all. So you would see S=0 or whatever the expectation would be for uncorrelated A/B.

I say that if you are correct, waiving the indistinguishability requirement for a BSM swap will identify 245+X qualifying pairs in a 220 hour run, yielding an S>0 (due to the 245 entangled pairs in the mix). If I am correct, I say the S value will instead be near 0 (indicating no correlation, since there is no swap and therefore 0 entangled pairs). Not sure how many events to expect but I might guess around 245.

This experiment is physically realizable with no new technology required. It would be helpful if you addressed the substance of my argument.

 

[PeterDonis]

why does distinguishability matter if you AREN'T changing what happened in the past, you are merely selecting the 245 A/B pairs that already demonstrate entanglement?

I should have added this to the list of things we can't verify experimentally. We can't even verify that these are the only two possibilities.

If one argues (quoting @vanhees71 but he is not the only person saying this):

...the point is to use entanglement swapping to select (or post-select, which doesn't really matter, if QT is correct, and there's no reason to doubt it, including the result of this experiment!) entangled electron pairs. Without this selection the electron pairs are not entangled at all!"

Entanglement swapping is not a "selection"! It's an action

What you quote here seems to me to be saying that "entanglement swapping" is both a selection and an action. (Shimmer is a floor wax and a dessert topping...) It is a selection because the results of the C measurement are used to select the subsets of the A/B results. It is an action because, per the quote, "Without this selection the electron pairs are not entangled at all!" In other words, without the C measurement the A/B results will always show no entanglement. I don't think this contradicts any of the things I said, which you said you agreed with.

those who claim a delayed entanglement swap merely reveals which As and Bs are entangled.

Per the above, I don't think @vanhees71 is claiming this. If it were true, the A/B results would show entanglement even if the C measurement were never made. But of course they won't. And I don't think @vanhees71 was claimng that they would.

I don't see that anything I am discussing is in fact interpretation dependent

None of the things that I said can be verified by experiments are interpretation dependent (they can't be if they can be verified by experiments).

The things that I said cannot be verified by experiments are interpretation dependent.