# Ways to understand the delayed entanglement swapping

• B
• Joao
In summary, the various interpretations of quantum mechanics all predict entanglement swapping, and this event would even show that those interpretations are wrong.

#### Joao

Hi everyone! Sorry for the bad English!

Please, is entanglement swapping "understood" in the most famous QM interpretations?

To me, it seems that any of the interpretations really helps much...
Even more: I guess this event would even show that those interpretations are wrong.

But of course I'm wrong, I'm just putting my view to see if anyone can help me understand where I'm wrong...

I mean, for example, let's take a 4 photons experiment, and photon 1 and 4 are entangled if photon 2 and 3 are projected into bell state:

Copenhagen:
The wave function of the first foton collapsed as it was detected and... somehow... if photon 2 and 3 got projected into bell states, it will show that it was collapsed in a way that shows that photon 1 and 4 are entangled.
(How did the wave that collapsed in the detector 1 got influenced by photon 3 and 2 being projected into bell states?)

Many worlds:
Photon 1 is traveling is it's wave function... it interacts with it's detector and the universe unfolds into many universe, one for each probability of detection... photon 2 and 3 got projected into bell states and... somehow... out of an infinite numbers of universes, ours is the one that have the photon 1 and 4 in bell states.
(Are we just that lucky that we are in the universe that, by blind chance, collapsed all the waves "just right" to all photons 1 be entangled with photon 4?)

De broigle pilot wave: our photon 1 is being carried by a pilot wave... and it hits it's detector... and if photon 2 and 3 are projected into bell states, somehow that wave took the photon in just the spots that show entanglement between photon 1 and 4.
(How the pilot wave got influenced by the future event of photon 2 and 3 getting entangled? )

And so on with all the interpretations...

Thanks all! =)

Entanglement swapping is predicted by quantum mechanics. Interpretations implement quantum mechanics. Therefore every interpretation predicts, and is consistent with, entanglement swapping.

For reference, this is the entanglement swapping procedure:

But the above is actually a cleaned up screenshot of a circuit in my quantum circuit simulator Quirk, which computes the output state by simply going through the gates in order and applying them to the input state one by one. So I can say with pretty high confidence that nothing magical is going on, since the smulator is reproducing the results in a pretty straightforward fashion.

It's also worth pointing out that there is in fact a path for information to propagate from Bob to Alice (and vice versa) during the entanglement swapping (just follow the lines from bottom to top without going left). It's just that part of the path is classical, since it passes through a measurement. For some reason this confuses people; like they think the experimenter deciding whether or not to flip over a qubit (or doing so after-the-fact during the analysis, sometimes trickily via post-selection) can't count as a communication mechanism w.r.t. the analysis.

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Joao
Joao
Oh you're talking about the delayed experiment. The key to understanding these experiments is to realize that the way Alice and Bob's qubits collapse implies different resulting states for Charlie's qubits. The "entanglement swapping" measurement is just an obfuscated way of distinguishing between those various cases.

If the delayed choice stuff is confusing you, I recommend reading this blog post: A Classical Delayed Choice Experiment.

As you can see in the above diagram, Bob's die rolls depend on Alice's choice and coin results. When Alice shook the box, we see a flat distribution for Bob's die rolls. When Alice didn't shake the box, we see banded disributions.

Therefore, by the same logic people use when explaining the DCQE, Alice's choice to shake the box has reached backwards in time and changed Bob's die roll.

...

Just kidding.

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DrChinese and Joao
Hi everyone! Thanks for the answers! =)

Strilanc, thanks a lot for the demonstrations and the classical analogy! I'm still trying to figure it all out! It's quite complicated hehehehe!

I guess it will take me a couple of days to understand the Quirk! I'll post back as soon as I understand it! =)

Strilanc said:
If the delayed choice stuff is confusing you, I recommend reading this blog post: A Classical Delayed Choice Experiment.

A nice analogy, but I don't think it would be fair to compare that directly to the DCQE. There are a number of critical differences:

1. In the real DCES (entanglement swapping): Alice can make her decision either before or after Bob takes his actions. This clearly indicates that there is no causal direction to consider. In the classical version, there is causal direction and the results are NOT the same if reversed.

2. In the real DCES: If Alice makes her decision prior to Bob performing any tests on the pair of particles (1 & 4) headed to him, then they are perfectly correlated. Bob can choose ANY identical angle to test them at, and will get the expected correlation with certainty. ONLY entangled particles have that attribute, and yet there is no underlying physical reason they are entangled EXCEPT for what Alice does. They need never have been in causal contact, for example, for that to be true. And this same point applies still when Alice executes the swapping operation AFTER Bob measure 1 & 4.

So the entanglement of 1 & 4 must be related to what is done (or not done) to 2 & 3; and causal order is not important.

Joao
DrChinese said:
1. [...] Alice can make her decision either before or after Bob takes his actions. [...]

2. [...] Bob can choose ANY identical angle to test them at, and will [get different correlations] [without causal contact] [...].

For (1): instead of Bob preparing the coin and die, trusted Trent prepares a boxed die and boxed coin. He then hands the boxed die to Bob and the boxed coin to Alice. Bob can now delay opening his box and writing down the value of the die for as long as he wants. More generally, we can make Alice and Bob symmetric by making the boxes more complicated. For example, give each box two compartments (1 and 2) and a mechanism that causes opening one compartment to shake/tumble the other compartment. Trent then puts correlated coins in compartments A1:B1 and correlated coins in compartments A2:B2.

For (2): Yes! The ability to get a few specific partial correlations, while spacelike separated, is key to what quantum mechanics unmistakably does differently than classical mechanics in these experiments. On the other hand, I think that by the time you have made sure to get all of those details right, ensuring a classical system can't produce the same results, your experiment is better described as a Bell test rather than a DCQE.

Joao
Strilanc said:
For (1): instead of Bob preparing the coin and die, trusted Trent prepares a boxed die and boxed coin. He then hands the boxed die to Bob and the boxed coin to Alice. Bob can now delay opening his box and writing down the value of the die for as long as he wants. More generally, we can make Alice and Bob symmetric by making the boxes more complicated. For example, give each box two compartments (1 and 2) and a mechanism that causes opening one compartment to shake/tumble the other compartment. Trent then puts correlated coins in compartments A1:B1 and correlated coins in compartments A2:B2.

One of the difficulties here is that you can't always successfully model quantum systems using classical mechanisms. So discussing the original analogy will have a limit somewhere. One idea of the analogy, as I understood it, was to show that there was no retrocausal action - that was simply an artifact of how you chose to interpret things. The example indicated that Alice was simply creating chaos by shaking the box, thereby erasing the correlations. If Alice does nothing, then the "order" appears. So I see you are attempting to modify the analogy, which is perfectly fine.

But if we want to model this more accurately, I think we need to acknowledge that 1 and 4 are prepared independently. It is 1 & 2 that are prepared together, and 3 & 4 prepared together. And if Alice does nothing, then chaos results. While if Alice does something, there there is more "order". What does Alice do to cause 1 & 4 to bring order to the results? I guess the analogy then becomes that she is able to compare elements of 2 & 3 (which are essentially copies of 1 & 4). If she looks at 2 & 3 and sees a subset that possesses a specific attribute that relates them, then that might allow us to make the analogy work. Say if she looks at 2 & 3 and they are both yellow, then that means their 1 & 4 partners will correlate. So that would complete the analogy (I think) and the timing of the what Alice does would not be an issue.

Of course we might not be able to get the right statistics with this scheme, but at least the idea is there. I will post some comments outside of the analogy itself separately.

Joao
So here is the basic idea of the analogy Strilanc presented. Alice looks at particle pairs 2 & 3 and learns something that identifies the 1 & 4 pairs as possessing an attribute. That being that 1 & 4 are entangled. In this scenario, Alice does NOT bring about any change to 1 & 4. I would agree that IF she doesn't change 1 & 4. then the timing of her observations of 2 & 3 does not matter. Thus the delayed element of this is a red herring.

BUT...

I don't think that is a fair assessment at all. I believe Alice's actions CAN and DO change the relationship of 1 & 4, which are now quite remote to Alice. The fact is, the Bell State Measurement Victor performs (it's Alice in the analogy and Victor in the paper below) must be doing something to particles 1 & 4. If they aren't, the analogy is good. But if we can demonstrate that in fact something Victor does different is changing 1 & 4, then the Classical Analogy fails.

https://arxiv.org/vc/arxiv/papers/1203/1203.4834v1.pdf

So what can Victor do to change what happens at 1 & 4, and how can we prove that occurred? Clearly, looking at a stream of 1s and 4s by itself - no subsets identified - yields no information, pattern, or correlations. But Victor can split the 1 & 4 series into 2 subsets - one in which the pairs are what I call + and another which I call -. Each of those subsets can be split yet again by Victor: + separable (VV) and + entangled(Phi +), or - separable (HH) and - entangled (Phi -). Figure 1 of the paper also presents these 4 states (although they are labeled differently, as I show in parentheses).

The key here is that Victor can choose to report only the + subset (which is almost perfectly 50% of the total) to Alice and Bob, and ask them to do a Bell test on those only. Obviously, Victor can ALSO choose to cast some of those pairs into an entangled state (2 & 3 are indistinguishable), or none at all (separable because 2 & 3 are distinguishable). And those results will be different because the entangled state statistics are different from product state statistics. I.e. when Alice and Bob compare their results, they can see if Victor cast some pairs into an entangled state or not. This is inconsistent with the idea that Victor is a passive observer.

Because one cannot cast 2 & 3 into a Bell State every time, Victor cannot produce streams of 1 & 4 that have all entangled state pairs (i.e. a pure entangled stream). There will always be some that are product state. On the other hand, Victor can create 1 & 4 pairs that are 100% product state (pure separable) simply by keeping 2 & 3 separated and not allowing them to interact in any way. Hopefully what I am trying to say is clear and makes a degree of sense.

Joao
Attached is Figure 1 from the paper. This let's you see the 4 possible states: 2 are entangled, 2 are separable. The question: is does Victor do anything that changes anything at Alice and Bob's neck of the woods?

Note that even if the answer is "Yes" (which I believe it is), you still cannot send a FTL message. Funny how everything comes back to that same conclusion.

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Joao
One would assume that entanglement exists (between photons 1 and 2, and 3 and 4), when the bell-state measurement occurs. Matthias Egg relays in his article that no entanglement is swapped because measurement has taken place on photons 1 and 4 (while entangled with their original partners) - thus entanglement no longer exists.

In principle, QM applies to macroscopic apparatus'. Johannes sent me a Mathematica file demonstrating how the experiment is calculated. They input into the interferometer photons 2 and 3 as if they're already entangled, to calculate the result. When I modified the file to describe the actual situation (ie entanglement between photons 1 and 2), you get a different outcome.

EDIT: corrected an error, and reformatted.

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Joao and DrChinese
Here's how I would make a classical analogy for the delayed entanglement swapping. Dr. Chinese, you can compare and contrast it with the setup you had in mind:

1. Alice and Bob are separated.
2. Alice and Bob each have a coin. They flip it, getting result A and B respectively. They write down the result.
3. Alice prepares a coin in state A in a box and send it to Victor. Bob does the same for B.
4. Victor decides whether or not to shake the boxes.
5. Victor opens the boxes and writes down whether the coins were DIFFERENT or SAME.

We repeat this many times, and then get everyone together to compare notes. We notice that, when Victor decided to shake the box, his DIFFERENTs and SAMEs are unrelated to Alice and Bob's results. It's as if Alice and Bob had separable coins. But when you post-select down to the case where Victor didn't shake the box and wrote down DIFFERENT, Alice and Bob's coin flips were in fact different. Similarly for no-shake and SAME. So in this case they had correlated coins.

Joao
Strilanc said:
Here's how I would make a classical analogy for the delayed entanglement swapping. Dr. Chinese, you can compare and contrast it with the setup you had in mind:

1. Alice and Bob are separated.
2. Alice and Bob each have a coin. They flip it, getting result A and B respectively. They write down the result.
3. Alice prepares a coin in state A in a box and send it to Victor. Bob does the same for B.
4. Victor decides whether or not to shake the boxes.
5. Victor opens the boxes and writes down whether the coins were DIFFERENT or SAME.

We repeat this many times, and then get everyone together to compare notes. We notice that, when Victor decided to shake the box, his DIFFERENTs and SAMEs are unrelated to Alice and Bob's results. It's as if Alice and Bob had separable coins. But when you post-select down to the case where Victor didn't shake the box and wrote down DIFFERENT, Alice and Bob's coin flips were in fact different. Similarly for no-shake and SAME. So in this case they had correlated coins.

Well I guess I would point out a few things.

a. Certainly we agree that if Alice is doing the same measurement as Victor, which is the same measurement as Bob, then Alice and Bob together know what Victor will see. Certainly we can say that Victor can separate his results into Alice/Bob pairs that match, and pairs that do not match. Finally, we agree that Victor is not changing anything that Alice or Bob see as correlated, which remains a constant.

b. In the actual experiment: Alice and Bob can perform an large/infinite number of different measurements. Victor always performs the same measurement, other than choosing to entangle (attempt to entangle) or not. No other variation, sorts into 4 subsets (entangled or not, + type or not). Obviously, the more entangled pairs that are produced by Victor's actions affects the results that Alice and Bob see as being correlated. That would depend on the specific measurements that Alice and Bob select, and at some settings there would NOT be a difference. However, for other settings there would be significant differences in what Alice and Bob see in the way or correlations depending on what percentage were entangled versus the percentage in a product state.

In my mind, it comes back to whether Victor is changing things that Alice and Bob see. I think the results support that he is.

Joao
DrChinese said:
1. In the real DCES (entanglement swapping): Alice can make her decision either before or after Bob takes his actions. This clearly indicates that there is no causal direction to consider. In the classical version, there is causal direction and the results are NOT the same if reversed.
.
Would you agree that if you allow for instant communication between between the entangled particles then you can have a causal direction? For instance the entangled particles might act like a rubber band and whatever end you let go first collapses its new state to the other end (instantly). The EPR experiment can be modeled accurately using this algorithm. I posted example code for this a while back. I am curious where this type of model falls apart. It would be neat to learn there was some aspect of a simple causal algorithm underlying the universe.

Joao
kurt101 said:
For instance the entangled particles might act like a rubber band and whatever end you let go first collapses its new state to the other end (instantly). The EPR experiment can be modeled accurately using this algorithm. I posted example code for this a while back. I am curious where this type of model falls apart. It would be neat to learn there was some aspect of a simple causal algorithm underlying the universe.

Of course there's a model like that. It's called quantum mechanics.

Joao
Strilanc said:
Of course there's a model like that. It's called quantum mechanics.
Except that quantum mechanics is probabilistic and not deterministic.

Joao
Hi everyone! Thanks for the answers! =) that's lots of info to search upon! =) I'll try to understand better all this topics...

I have a question that maybe nobody finds relevant, if so, it's okay hehehe! Just keep the current discussion going, it's very interesting! =) and I'm sorry to bother you with this question, I'm sure they aren't well formulated and have many errors in it!

Please, can anyone tell me how the different quantum mechanics interpretations view this experiment? I mean:

Copenhagen: when there's a measurement the wave function collapses.
So the wave function should collapse when a measurement is made by Alice, Bob and so on and the delayed entanglement swapping shouldn't happen (therefore Copenhagen is wrong?)

Many worlds: the wave functions never collapses and we are just so lucky that we are in the universe where all the wave functions seens to collapse in entangled ways.

De broglie: the pilot wave is just carrying the particle, so it shouldn't interfere with future measurements or something like that...

Assembly: a really large amount of particles would behave probabilistic in a certain way, but future odds can't affect past results (or something like that...)

Buuuuuut...

If we assume that it's the conscience that collapsses the wave function, and if we wake up in a sci fi mood, we could think that the results registered by Bob, Alice and Victor doesn't really exists until someone look at then, so they could "change" to adapt to Whats is already seen...

It's a wild guess, but let's think about it...

We have three sets of recorded data, Alice, Bob and Victor, and no conscience looked into it (so they aren't really real).

One conscience looks at Bob data, at that moment, Victor and Alice's data starts to "adapt" to possible data's that allow Bob's data to be true. Another conscience looks at Victor' s data, now Alice's data also come into existence and it agrees with the Bob and Victor data.

By definition, it's impossible to make any experiment to try to prove it or not, but of all the interpretations, is this the only one that makes sense without retrocausality?

If it's not, how any other interpretation would deal with this data like "step by step", like:

See, in Copenhagen, there's a big wave function that is making the system evolve. As soon as Alice takes a measurement, that wave collapses in a certain point. After that, Bob makes a measurement and the wave function also collapses in a certain point. Now Victor can choose to entangle or not 2 photons, but since the Alice and Bob already made their measurements (and the waves already collapsed), the way Victor must act is to entangle the fotons (or not entangle), but that makes no sense because we assume that Victor has freedom to choose to entangle or not the fotons...

Thanks again! =)

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Joao said:
Copenhagen: when there's a measurement the wave function collapses.
So the wave function should collapse when a measurement is made by Alice, Bob and so on and the delayed entanglement swapping shouldn't happen (therefore Copenhagen is wrong?)

No no no. The wave function collapses when the measured is made by Alice and Bob, which affects the state held by Victor. When Victor does his measurements, he is sussing out these effects. Do the math and you'll see all the predictions come out right.

Joao
kurt101 said:
Except that quantum mechanics is probabilistic and not deterministic.

You asked for a causal model, not a deterministic one. Furthermore, many interpretations of quantum mechanics are deterministic.

Joao
Strilanc said:
No no no. The wave function collapses when the measured is made by Alice and Bob, which affects the state held by Victor. When Victor does his measurements, he is sussing out these effects. Do the math and you'll see all the predictions come out right.

Of course, this view is substantially influenced by your opinion of causal direction. If Victor measures first, we say Victor "causes" entanglement swapping so that 1 & 4 are entangled. If Victor measures AFTER, we say that Alice and Bob's measurements set the stage for Victor to observe a Bell state.

If you look at it fairly, there is a degree of tautology. I still say the question is whether Victor changes anything for the Alice/Bob correlations. I think they do, but I am not quite certain enough of the details of what percentage (and all of the details) of outcomes occur to be able to give a proof of that. I haven't seen anything that supports my position, which is always daunting.

Joao
DrChinese said:
Of course, this view is substantially influenced by your opinion of causal direction. If Victor measures first, we say Victor "causes" entanglement swapping so that 1 & 4 are entangled. If Victor measures AFTER, we say that Alice and Bob's measurements set the stage for Victor to observe a Bell state.

Yes, exactly. If you are using the Copenhagen interpretation, you have to pick some frame for the collapses to occur in. This frame orders all of the measurements, so that there is always a "correct" ordering to your explanation. This is both an upside and a downside: it trivially avoids any time shenanigans, but it also obscures the fact that re-ordering the collapses is fine because they commute with each other.

DrChinese said:
If you look at it fairly, there is a degree of tautology. I still say the question is whether Victor changes anything for the Alice/Bob correlations. I think they do, but I am not quite certain enough of the details of what percentage (and all of the details) of outcomes occur to be able to give a proof of that. I haven't seen anything that supports my position, which is always daunting.

The technical term for the "change" that Victor applies to Alice and Bob is "quantum steering". You can find many papers about it. I personally don't like to think about it that way; I just think of the measurements as being correlated and then patch on whatever time direction happened to play out in the experiment.

Joao and DrChinese
Strilanc said:
No no no. The wave function collapses when the measured is made by Alice and Bob, which affects the state held by Victor. When Victor does his measurements, he is sussing out these effects. Do the math and you'll see all the predictions come out right.

Thanks a lot kind sir! Really! =)

So... If we had a setup that we could choose freely to make Alice, Bob or Victor measures in any order we would like, and Victor could freely chooses to entangle or not The two photons in any bell state, the experiment could evolve like this according to Copenhagen interpretation:(?)

1. The laser shoots a photon.
2. The photon travels as a wave function.
3. Photon hits the bbo Crystal and collapses
4. A pair of entangled photon is made and they starts traveling as wave functions.
5. Alice measures photon 1, it collapses and it's measured as V+.
6. Photon 2 is traveling as a wave in a delayer circuit.
7. Another photon is fired from the laser, hits the bbo and we have two new entangled photons traveling as waves.
8. Bob measures photon 4, it collapses and it's a H-
9. Photon 3 is traveling in a delayer circuit and is sent to Victor, among with photon 2.
10. Now here is were it gets interesting: we have two photons traveling as wave functions that Victor is free to measure it making any bell state he would like... But if he projects it into some bell state (phi + I guess), the photon 1 and 4 should have been both V+, never V+ and H-, because they are entangled in phi + (or something like that...).

What happens right here according to Copenhagen interpretation? Does it just doesn't care and simply says "it was just a wave function that collapsed into this state...", not trying to explain how did it happened?

Thanks! =)

Strilanc said:
You asked for a causal model, not a deterministic one. Furthermore, many interpretations of quantum mechanics are deterministic.
I am having trouble understanding a meaningful distinction between causal and determinism with respect to a model. I think if something had a cause it must be deterministic and if something was deterministic it must have a cause. Can you clarify the distinction for me?

kurt101 said:
I am having trouble understanding a meaningful distinction between causal and determinism with respect to a model. I think if something had a cause it must be deterministic and if something was deterministic it must have a cause. Can you clarify the distinction for me?

I took your use of "causal" to mean the opposite of "retrocausal", i.e. only allowing forward-in-time effects.