A Forward-in-time analysis of delayed-choice entanglement swapping

[Sambuco]

Something physically changed as a result of the swap. So it couldn't have been merely a selection issue. No experimentalist has ever performed a swapping experiment and concluded they were choosing subsets that show Entanglement that are an artifact of their selection criteria. They all say the same thing: The initial state did not have any correlation between photons 1 and 4 on any basis. And therefore (after a swap) there could be no subset in which 1 and 4 have correlation resembling Entangled State statistics UNLESS the final state was different - as is predicted by QM. That final swapped state being (a la Ma):

(3) |Ψ〉1234 = |Φ−〉14 ⨂ |Φ−〉23

I wish to discuss with you this particular part of your argument, because I believe it can help us to try to understand each other. First, I'll try to summarize how I understand the situation for the the delayed-choice entanglement swapping (Ma's experiment) from a forward-in-time analysis, as in the Mjelva's paper (as @Morbert, I'll consider the case with the projection postulate, section 4.1.1 in the Mjelva's paper). At some points, my treatment will be much similar to post #21 by @Morbert. Then, I'll try to make a comparison with what you say.

At time $t_0$, two photon pairs were created, and the initial state is $\ket{\Psi(t_0)} = \ket{\psi^-}_{12}\otimes \ket{\psi^-}_{34}$. This is equation (3) in Mjelva's paper. At time $t_1$, Alice and Bob measure photons 1 and 4, respectively, projecting the state into one of four equally probable states which Mjelva's calls $\ket{\Psi(t_1)}_A$, $\ket{\Psi(t_1)}_B$, $\ket{\Psi(t_1)}_C$, $\ket{\Psi(t_1)}_D$, in his equations (5a)-(5d). Depending on the outcomes obtained by Alice and Bob, one (and only one) of these is the state of the system between $t_1$ and $t_2$. Then, Victor decides to perform a BSM, which is represented by a unitary operator that physically changes the states of photons 2&3, allowing to obtain measurement outcomes that were not possible if he performs a SSM. Given the outcomes obtained by Alice and Bob at $t_1$, the BSM at $t_2$ projected the state into a product of the state of photon 1, the state of photon 4, and the entangled state of photons 2&3. Then, in each run, 1&4 are not in an entangled state. Finally, Alice, Bob and Victor communicate to each other and compare their results, and they realized that, if they grouped the results into subsets depending on the entangled state obtained by Victor for photons 2&3, measurements on photons 1&4 appear to be Bell-correlated, as demonstrated by Mjelva's equation (7). In my opining, the previous analysis shows that the DCES experiment can be interpreted in a forward-in-time way without invoking that the swap remotely changes the state of 1&4.

However, I want to discuss all that from the opposite position, starting from something more akin to what you said. Is it possible to interpret DCES saying that, after Victor performed the swap, the quantum state of photons 1&4 is an entangled state? Well, that is not only what you say, but also what the authors say in the Ma's paper. In fact, that is why they say their experiment is a case of entanglement swapping, i.e. they entangle photons 2&3 and it remotely entangle photons 1&4, i.e. performing a swap and considering some subsets, we could say that the state of the system evolves from $\ket{\Psi(t_0<t<t_1)} = \ket{\psi^-}_{12}\otimes \ket{\psi^-}_{34}$ to $\ket{\Psi(t>t_2)} = \ket{\phi^-}_{14}\otimes \ket{\phi^-}_{23}$. In that sense, the authors said:
"If one views the quantum state as a real physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. However, there is never a paradox if the quantum state is viewed as to be no more than a “catalogue of our knowledge"".
Anyway, I think that is worth analyzing whether the previous evolution of the state of the system could be regarded as something "real", more in line with $\Psi\text{-ontic}$ interpretations. I believe that you interpreted the results in this way. Am I right?
Well, in this case, if we constrained ourselves to the textbook QM, the short answer is "No". Let me explain why I think that way trying to be a bit "rigorous". In a certain sense, (non-relativistic) QM is a set of rules that, knowing the preparation procedure of a given system at time $t_1$, allows us to calculate the probabilities of the outcomes of a measurement at $t_2$ (I assume $t_2>t_1$) by means of (i) something called "the state of the system" which unitarily evolves according to the Schrödinger equation, and (ii) the Born's rule. Because we're considering the non-relativistic version of the theory, the previous statements are true if the number of particles is conserved. This means that, in the case of the DCES, we must apply the rules of QM in two steps: first we solve for times $t_0<t<t_1$, i.e. from the creation of the two photon pairs until the measurements performed by Alice and Bob, and then for $t_1<t<t_2$, from the Alice and Bob measurements (which are considered as the preparation procedure for this stage) until the Victor measurement. After $t_1$, the system is composed of photon 2&3 only because photons 1&4 no longer exist, so that if we are unitarily evolving the state of the system, not state can be assigned to 1&4. Thus, as photons 1&4 only exist for $t_0<t<t_1$, the only state they have is non-entangled. In fact, regarding the DCES and the state of photons 1&4 after the 2&3 swap, Peres said: "(...) thus verifying that the corresponding subset of particles, if it still existed, would have an entangled state".

I want to say that the previous analysis does not disprove your interpretation. It only proves that no backward-in-time change of the state of the system is needed for explaining the measurement outcomes (and the statistics than arises out of them). Furthermore, I think that if we are to interpret the results as being due to a change of the 1&4 state, this cannot be taken as real, in an ontic sense.

For me, there are still two "intriguing" things:

1. As Mjelva's showed, forward-in-time interpretations of the delayed and non-delayed entanglement swapping experiments in terms of the states of the system are very different between them. However, as @DrChinese mentioned many times, QM predictions of the experimental outcomes are the same regardless of the time order between Alice, Bob and Victor measurements. Maybe, this "symmetry" is calling for an explanation. I don't know.

2. The Hensen's experiment is even more tricky because it is a kind of "space-like entanglement swapping", which makes the previous forward-in-time explanation of the experiment more hard to accept as they don't respect light cones, and even depend on the reference frame.

Lucas.

 

[DrChinese]

1. I'm not sure why you mentioned this paper. It's not a delayed-choiced version of entanglement swapping. Am I right? In the non-delayed case, I agree that standard QM (by standard I mean textbook QM) predicts that after the BSM measurement on 2&3, photons 1&4 will be in an entangled (non-separable) state.

2. If you are still referring to the non-delayed case, I completely agree with you.

3. I also agree with what you say here. In any case (delayed or non-delayed), the initial state of the four-photon system has no correlation between photons 1 and 4, since they are entangled with photons 2 and 3, respectively.

2. & 3. Yay!

1. I mean, you gotta believe that regardless of when the BSM occurs (delayed or not): The results are the same. I don't think there is any argument about the fact that order doesn't matter to the predictions of QM. The order might matter to the description (delayed case), and I agree that is something of the key in this thread.

But if I am wrong about the predictions being the same in both non-delayed and delayed version, let me know. I might be going a step too far.

 

[DrChinese]

At time t0, two photon pairs were created, and the initial state is |Ψ(t0)⟩=|ψ−⟩12⊗|ψ−⟩34. This is equation (3) in Mjelva's paper. At time t1, Alice and Bob measure photons 1 and 4, respectively, projecting the state into one of four equally probable states which Mjelva's calls |Ψ(t1)⟩A, |Ψ(t1)⟩B, |Ψ(t1)⟩C, |Ψ(t1)⟩D, in his equations (5a)-(5d).

OK, I objected to this characterization when @Morbert brought this up. There is no "state" corresponding to the 2 & 3 photons after the measurements on 1 & 4 other than on the basis 1 & 4 were measured on. After photon 1 is measured as (say) |L>, photon 2 is completely undefined on the H/V basis. Ditto for photon 3. The "state" of photons 2 & 3 - to the extent you can even talk about the state of 2 particles which have never interacted, and could be located anywhere in the universe at any time - could only be described by the EPR criterion of reality as being certainly in a known state on the L/R basis. So it would be one of the following:

Ψ₂₃ = ½(|L>+|R>)₂ ⊗ ½(|L>+|R>)₃
Ψ₂₃ = ¼ (|LL> + |LR> + |RL> + |RR>)

Or, if they were measured on the H/V basis originally:
Ψ₂₃ = ¼(|HH> + |HV> + |VH> + |VV>)

How can Mjelva possibly describe this otherwise, if you wish to ascribe a state at all (at Mjelva's t1) to photons 2 & 3? I reject this description. There is no Φ± or Ψ± Bell states (or other entangled states) describing photons 2 & 3 at this point, regardless of mathematical manipulation that anyone makes.

As I have said many times: Those are maximal Bell states, and their existence would violate Monogamy of Entanglement. By extension of that incorrect reasoning: all photons in existence - now and in the past - are equally in the same states and should be included mathematically.*


*(On the other hand: Because I believe the rules of QM are contextual, the predictions of QM should be analyzed by a before context and an after context.)

 

[Sambuco]

Sorry, maybe I misrepresented something and that caused confusion. To clarify, I'm not claiming that after Alice and Bob measured photons 1 and 4, photons 2 and 3 are in an entangled state. As you said, it is forbidden by monogamy of entanglement. Thus, after Alice and Bob measurements at $t_1$, but before Victor chooses a swap at $t_2$, photons 2&3 are in a separable state.

This is also what Mjelva stated in his equations (5a)-(5d). He simply represented those separable states not in the basis 1&4 were measured but in other one only for later convenience. This change of basis makes more clear how the entanglement between photons 2&3 due to the BSM will lead to his final equation (7) showing Bell-correlations between photons 1&4 in each subset.

 

[DrChinese]

1. Sorry, maybe I misrepresented something and that caused confusion. Thus, after Alice and Bob measurements at $t_1$, but before Victor chooses a swap at $t_2$, photons 2&3 are in a separable state.

2. This is also what Mjelva stated in his equations (5a)-(5d). He simply represented those separable states not in the basis 1&4 were measured but in other one only for later convenience. This change of basis makes more clear how the entanglement between photons 2&3 due to the BSM will lead to his final equation (7) showing Bell-correlations between photons 1&4 in each subset.

1. I don't think you misrepresented anything.

But there is no such thing - in my opinion - as placing into the state something for which there is no support whatsoever. There are no Bell states of photons 2 & 3 - or any other entangled states involving any other particles - that belong here.

If you wanted to, you could say that photon 2 is in a superposition of |H> and |V> after a L/R basis measurement on photon 1. That is sound. And similar for photons 3 & 4. (And by the way: the reason I reference the L/R basis here is because our ultimate goal in the Ma description is to explain photon 1 & 4 entanglement on the L/R basis after H/V measurements on photons 2 & 3.)

But to say that photons 2 & 3 are in a superposition of Bell states is false. And that is precisely what Mjelva is saying with his "preliminary" 5(a-d) equations.

To see how wrong this concept is: Suppose we measure 1 & 4 and get |LL>. We now know that 2 & 3 are certainly |RR> based on our initial state. So photon 2 must be objectively in the state on the H/V basis: ½(|H>+|V>). Similar for 3, and as you say its a Product (separable) state for the 2 combined. So:

Ψ₂₃ = ½(|H>+|V>)₂ ⊗ ½(|H>+|V>)₃

Clearly, this is not the same as any of Mjelva's states. Oh, but suppose we have other photons that, like 2 & 3, have not interacted? Say photons a, and b? Our state, per my above, becomes:

Ψ₂₃ = ¼(|H>+|V>)₂ ⊗ ½(|H>+|V>)₃ ⊗ ½(|H>+|V>)_a ⊗ ½(|H>+|V>)_b

This is a fair representation (Product state of 4 independent photons, H/V basis) by any standard. But according to Mjelva's thinking applied to this, his (5) series formulae are now expanded to 16 (or whatever) Bell states involving mixtures of 4 maximally entangled quantum particles (2, 3, a, b). What? Is this supposed to be a representation of some quantum state? Keep in mind, we are talking about particles that have yet to interact. So obviously he has jumped the gun by quite a bit. To be fair, he should only talk about what we know if we are attempting a "forward in time" explanation. And again, note that such requirement (i.e. forward in time thinking) is completely absent from any calculation based on standard QM. Ordering doesn't matter.

And yet: As I have shown in post #20: When we look at the same issues on the H/V basis for all 4 photons, there is a contradiction in outcomes between our initial state and our final state if we assume the final state is some subset of the initial state. So... there's that to cast Mjelva's evolution in doubt. It is contradicted by experiment.

 

[DrChinese]

1. On page 14 Ma describes the unitary evolution of incident photons moving through Victor's BiSA that allow him to infer Bell states from his polarization-resolution detections. I have applied this evolution to a projected state in line with Mjelva's projection-based account.

2. Assuming that by "the swap hasn't occurred yet" we mean photons 2&3 have not yet reached Victor's BiSA:

If we adopt Ma's conventions, then we describe the state as your (1) and (2), but we must be aware that Ma's convention will hide the distinction between entangled photons 1&4, and perfectly correlated outcomes of already-performed measurements on photons 1&4. As this is a delayed-choice experiment, photons 1&4 no longer exist leading up to the swap.

3. If we adopt Mjelva's projection-based account, we preserve this distinction by projecting onto one of four states after Alice's and Bob's measurements. In which case, the state is not your (1) and (2) but a projection onto one of the for terms in the relevant expansion.

1. No, you do something different. Ma takes the evolution after the swap.

2. Yes... except 1 & 4 aren't entangled after they are measured. They have absolutely no relationship whatsoever to each other. How can there be any perfect correlations yet?

3. The projections of Mjelva have no basis in reality, as I demonstrate in post #35. They are completely fictional. I challenge anyone to show me an experimental paper using these. And of course, I mean pre-swap. These are of course completely wrong - since there is no correlation whatsoever between the L/R and H/V bases pre-swap (again see my previous post), and therefore there can be no correlation post-swap. Unless a physical change occurs post swap, which it does.

 

[Morbert]

1. No, you do something different. Ma takes the evolution after the swap.

2. Yes... except 1 & 4 aren't entangled after they are measured. They have absolutely no relationship whatsoever to each other. How can there be any perfect correlations yet?

3. The projections of Mjelva have no basis in reality, as I demonstrate in post #35. They are completely fictional. I challenge anyone to show me an experimental paper using these. And of course, I mean pre-swap. These are of course completely wrong - since there is no correlation whatsoever between the L/R and H/V bases pre-swap (again see my previous post), and therefore there can be no correlation post-swap. Unless a physical change occurs post swap, which it does.

1. The evolution is before the swap. The evolution is local, acting only on 2&3, and does not induce any entanglement swapped to 1 & 4. It describes the photons moving from modes b and c, through b' and c', to b'' and c'' towards the detectors, and it is the detector events that induce a swap (upon a relevant outcome like $\Phi^-$). We can see this by first applying the plate=on evolution to Ma's (1) and (2) state, which is your (1) and (2) state, without applying Victor's detector events that happen after. \begin{eqnarray*}I_{14}\otimes U_{23}\ket{\Psi^-}_{12}\ket{\Psi^-}_{34} &=&
\frac{1}{4}(\ket{HH}_{14} - \ket{VV}_{14})\otimes i(\ket{HH}_{b''c''} - \ket{VV}_{b''c''})\\
&-&\frac{1}{4}(\ket{HH}_{14} + \ket{VV}_{14})\otimes i(\ket{HV}_{b''b''} - \ket{HV}_{c''c''})\\
&+&\frac{1}{2}\ket{HV}_{14}\otimes\ket{VH}_{b''c''}\\
&+&\frac{1}{2}\ket{VH}_{14}\otimes\ket{HV}_{b''c''}\end{eqnarray*}This evolved state shows no entanglement between 1 & 4. Entanglement is only ensured if Victor, say, selects all runs that yield $\ket{HH}_{b''c''}$ or $\ket{VV}_{b''c''}$, which is represented by the projection onto $$\frac{1}{\sqrt{2}}(\ket{HH}_{14} - \ket{VV}_{14})\otimes \ket{HH}_{b''c''}$$or$$\frac{1}{\sqrt{2}}(\ket{HH}_{14} - \ket{VV}_{14})\otimes \ket{VV}_{b''c''}$$

2. Yes, there is no correlation between 1 & 4 across all runs. The loophole explored by Mjelva and others in various papers is Victor's post-selection of runs.

3. The projections of Mjelva are standard procedure, and reproduce all predictions relevant to these experiments.

 

[Sambuco]

But there is no such thing - in my opinion - as placing into the state something for which there is no support whatsoever. There are no Bell states of photons 2 & 3 - or any other entangled states involving any other particles - that belong here.

But the introduction of the Bell states is just to make a change of basis. There is nothing physical there. The state is the same. To be more clear, I'll consider a simple case. Alice and Bob measure both H. According to the projection postulate $\ket{\Psi(t_1)}_A = \ket{H}_1 \otimes \ket{H}_4 \otimes \ket{V}_2 \otimes \ket{V}_3$. Then, I could define the entangled states $\ket{\phi^\pm}_{2,3} = \frac{1}{\sqrt{2}} (\ket{H}_2 \otimes \ket{H}_3 \pm \ket{V}_2 \otimes \ket{V}_3)$. From that, we can obtain $\ket{\phi^+}_{2,3} - \ket{\phi^-}_{2,3} = \sqrt{2} \ket{V}_2 \otimes \ket{V}_3$. Replacing in the state after Alice and Bob measurements, we obtain $\ket{\Psi(t_1)}_A = \frac{1}{\sqrt{2}} \ket{H}_1 \otimes \ket{H}_4 \otimes (\ket{\phi^+}_{23} - (\ket{\phi^-}_{23})$. The Bell states are there but it does not mean that photons 2&3 are entangled.

Clearly, this is not the same as any of Mjelva's states.

Don't forget that Mjelva considered the case where Alice measure in the $x/y$ basis, whereas Bob measure in which he called the $\pm$ basis, which is a pair of axis 45° clockwise rotated with respect to the Alice basis. That what makes his equation (5a)-(5d) more complicated, but correct anyway. It is important to be clear here: Mjelva's equations (5a)-(5d) are correct and represent the state of the system after Alice and Bob measurements (with the caveat we mentioned before that photons 1&4 no longer exist).

And again, note that such requirement (i.e. forward in time thinking) is completely absent from any calculation based on standard QM. Ordering doesn't matter.

This is a subtle point! As I said before, I agree that the order between the Alice/Bob and Victor measurements doesn't change the experimental results, but to prove that we have to (forward-in-time) evolve the initial state of the system for both kind of experiments (delayed and non-delayed one) and conclude that the QM predictions coincide. As far as I know, there is no other way to prove that the predictions are the same.

So... there's that to cast Mjelva's evolution in doubt. It is contradicted by experiment.

Why do you say that Mjelva's result contradicts the experiment? It's exactly the opposite! Mjelva's calculations predicts the Bell inequality violations of the photons 1&4 in each subset. In fact, Mjelva's analysis is the QM prediction of the experiment.

 

[DrChinese]

1. The evolution is before the swap. The evolution is local, acting only on 2&3, and does not induce any entanglement swapped to 1 & 4. It describes the photons moving from modes b and c, through b' and c', to b'' and c'' towards the detectors, and it is the detector events that induce a swap (upon a relevant outcome like $\Phi^-$). We can see this by first applying the plate=on evolution to Ma's (1) and (2) state, which is your (1) and (2) state, without applying Victor's detector events that happen after. \begin{eqnarray*}I_{14}\otimes U_{23}\ket{\Psi^-}_{12}\ket{\Psi^-}_{34} &=&
\frac{1}{4}(\ket{HH}_{14} - \ket{VV}_{14})\otimes i(\ket{HH}_{b''c''} - \ket{VV}_{b''c''})\\
&-&\frac{1}{4}(\ket{HH}_{14} + \ket{VV}_{14})\otimes i(\ket{HV}_{b''b''} - \ket{HV}_{c''c''})\\
&+&\frac{1}{2}\ket{HV}_{14}\otimes\ket{VH}_{b''c''}\\
&+&\frac{1}{2}\ket{VH}_{14}\otimes\ket{HV}_{b''c''}\end{eqnarray*}

2. This evolved state shows no entanglement between 1 & 4. Entanglement is only ensured if Victor selects all runs that yield $\ket{HH}_{b''c''}$ or $\ket{VV}_{b''c''}$, which is represented by the projection onto $$\frac{1}{\sqrt{2}}(\ket{HH}_{14} - \ket{VV}_{14})\otimes \ket{HH}_{b''c''}$$or$$\frac{1}{\sqrt{2}}(\ket{HH}_{14} - \ket{VV}_{14})\otimes \ket{VV}_{b''c''}$$

We are talking about two different points in time. I see now that where I am talking about the state after photons 1 & 4 are measured (for reasons not worth further elaborating on - just blame me): You, @Sambuco and Mjelva are clearly talking about a different point in time for the (5) series. That being either after the overlap in the beam splitter before measurement of 2 & 3; or after both overlap in the beam splitter and indistinguishable measurement of photons 2 & 3. OK, that puts us in a better spot, and what each of you are saying now makes more sense. But it skips stuff...

So trying to find the points we agree upon: I agree with Mjelva's (4) as a generic way to characterize the state after photons 1 & 4 are measured on some basis. However, we need to be talking about their measurement on the same basis rather than unbiased ones. Your equation on H/V basis tacitly acknowledges this. Because that makes it clear that in a forward in time analysis, the 2 & 3 photons are now tossed into a certain state on that same basis at t1. That is the most accurate way to describe them, his technique obscures this important fact.

We have my equation from above which is from a point in time just before yours. Hopefully you agree with this. Pretty uncontroversial for an H/V basis description using Mjelva's own (4), let's call that (4 H/V).

(4 H/V) |Ψ>₁₂₃₄= ¼(|VHHV> + |VHVH> + |HVVH> + |HVHV>)


2. You have a very different looking Product state after the interaction of the 2 & 3 photons with the beam splitter. What changes? We know it isn't photons 1 or 4, since our hypothesis is forward in time only. And it cannot be any evolution of the H and V outcomes for photons 2 or 3, because a beam splitter (or beam splitters) doesn't change polarization. And we know we need something to change in order to get the very state you have in your 2. Without a change, we are back to your very statement: "This evolved state shows no entanglement between 1 & 4."

Specifically: You have new permutations of H & V arising that are not present in my (4 H/V). These outcomes are |HHHH> and |VVVV>. Where do these come from physically? You must know that no such effect has ever been discovered after a beam splitter*. For your equation to make sense: we'd need to see |HH>₂₃ to change to |VV>₂₃, or vice versa.

So... is that what we've got as a point of contention?


*Note that other experiments reporting similar results to Ma do not use Ma's EOMs (Electro Optical Modulators) as changeable wave plates to execute a swap (or not). So the presence or absence of this particular mechanism should not be a factor to our discussion.

 

[DrChinese]

1. But the introduction of the Bell states is just to make a change of basis. There is nothing physical there. ... The Bell states are there but it does not mean that photons 2&3 are entangled.

2. It is important to be clear here: Mjelva's equations (5a)-(5d) are correct and represent the state of the system after Alice and Bob measurements (with the caveat we mentioned before that photons 1&4 no longer exist).

3. This is a subtle point! As I said before, I agree that the order between the Alice/Bob and Victor measurements doesn't change the experimental results, but to prove that we have to (forward-in-time) evolve the initial state of the system for both kind of experiments (delayed and non-delayed one) and conclude that the QM predictions coincide.

4. Why do you say that Mjelva's result contradicts the experiment? It's exactly the opposite! Mjelva's calculations predicts the Bell inequality violations of the photons 1&4 in each subset.

5. In fact, Mjelva's analysis is the QM prediction of the experiment.

1. I reject the idea that there can be any discussion of a Bell state prior to a Bell State Measurement. But maybe you aren't saying that anyway. What we can agree on is what Mjelva says about this:

"At time t=2, Vicky performs a Bell-state measurement on her pair (2,3). Assuming the projection postulate, this has the effect of projecting the state of her pair into one of the four Bell states (1). Unlike in the case of ordinary entanglement swapping, however, this does not also project the pair (1,4) into a Bell-state..."

OK, that's his assertion - worth considering - that the Bell state arises only for photons 2 & 3. And I guess it should be called a physical effect. Then presumably, a rabbit will come out of the hat and show a hidden correlation with photons 1 & 4. So let's see if that can happen. I will address this in a separate post. But keep in mind: the premise of Mjelva is as he says:

"In Section 3 I discuss the alternative view, as given by Egg (2013) and Price and Wharton (2021a), that the Bell correlations observed in the delayed-choice experiments are a consequence of selection bias, rather than a mark of genuine entanglement. In Section 4, I defend this view against Glick’s challenge, by providing an analysis of the two experiments which shows how the post-selection procedure can account for the observed correlations."

Does he mean: i) Post selection with a physical change to 2 & 3 polarization after a BSM, independent of 1 & 4? ii) Or post selection based solely on acquired new knowledge about 2 & 3, but no physical change? Hopefully my attacks are clear on either of these, as being incompatible with theory and/or experiment.


2. Well, maybe you did say this. Doesn't matter, we're all on the same page now.


3. Agreed.


4. The contradiction is actually between 2things: i) The forward in time premise requires an early measurement of photons 1 & 4 to cast photons 2 & 3 into certain states on same basis; ii) Some experimentally observed outcomes are prohibited by i). These are discussed in detail in posts #39 and #20, no need to repeat those.


5. Funny that, since it has to in the end. How he gets there doesn't work, see above.

 

[Morbert]

And it cannot be any evolution of the H and V outcomes for photons 2 or 3, because a beam splitter (or beam splitters) doesn't change polarization.

The eighth-wave plates and electro-optic modulators in Victor's BiSA can change the polarization of incident photons. E.g. Two HH photons or two VV photons will be rotated to two RR or two LL photons depending on whether they travel through mode b' or c'. Hence, two incident HH photons could result in two V detectors firing. See Ma's time-evolution rules on page 14 of his paper.

If polarization was preserved even for a successful BSM, then Victor could use the b'' and c'' detectors to infer both a separable state (HH or VV) as well as a Bell state (Φ+ or Φ-). This is impossible, as a BSM and SSM are complementary.

 

[Morbert]

PS If it was somehow possible to preserve polarization, then I think I would agree that these experiments evidence nonlocal influence, as the four subensembles sorted by Victor would map one-to-one to the four subensembles sorted by Alice and Bob. But it would also break quantum mechanics.

 

[Sambuco]

What we can agree on is what Mjelva says about this:

"At time t=2, Vicky performs a Bell-state measurement on her pair (2,3). Assuming the projection postulate, this has the effect of projecting the state of her pair into one of the four Bell states (1). Unlike in the case of ordinary entanglement swapping, however, this does not also project the pair (1,4) into a Bell-state..."

OK, that's his assertion - worth considering - that the Bell state arises only for photons 2 & 3. And I guess it should be called a physical effect. Then presumably, a rabbit will come out of the hat and show a hidden correlation with photons 1 & 4.

1. This is also a subtle point. The Mjelva's statement should be considered in the context. He said that immediately after showing that, according to the projection postulate, the state after Alice and Bob measured photons 1 and 4 is one of the four $\ket{\Psi(t_1)}_{A,B,C,D}$. Then, if we consider only one of these states and take into account the Victor measurement on photons 2&3, the resulting state for photons 1&4 is a product state. However, as any result Victor obtained is consistent with more than one of the measurement outcomes of Alice+Bob, then Victor will be able to construct a subset for each one of the 2&3 entangled states where photons 1&4 show Bell-correlations.

But keep in mind: the premise of Mjelva is as he says:

"In Section 3 I discuss the alternative view, as given by Egg (2013) and Price and Wharton (2021a), that the Bell correlations observed in the delayed-choice experiments are a consequence of selection bias, rather than a mark of genuine entanglement. In Section 4, I defend this view against Glick’s challenge, by providing an analysis of the two experiments which shows how the post-selection procedure can account for the observed correlations."

Does he mean: i) Post selection with a physical change to 2 & 3 polarization after a BSM, independent of 1 & 4? ii) Or post selection based solely on acquired new knowledge about 2 & 3, but no physical change? Hopefully my attacks are clear on either of these, as being incompatible with theory and/or experiment.

2. Neither of the two options. To get the entangled state between photons 1&4, the post-selection requires a physical change of the state of photons 2&3 as a consequence of the entanglement after the BSM, which is not independent of 1&4. Don't forget that the entangled state of photons 2&3 depends on the previously recorded results of 1&4. Let me explain. I'll consider a very simple case where everyone measure in the H/V basis. The initial state is the same $\ket{\Psi(t_0)} = \ket{\psi^-}_{12} \otimes \ket{\psi^-}_{34}$. After Alice and Bob measure photons 1&4, the state of the system is one of the following four:

$$\ket{\Psi(t_1)}_A = \ket{H}_1 \otimes \ket{H}_4 \otimes \ket{V}_2 \otimes \ket{V}_3$$
$$\ket{\Psi(t_1)}_B = \ket{H}_1 \otimes \ket{V}_4 \otimes \ket{V}_2 \otimes \ket{H}_3$$
$$\ket{\Psi(t_1)}_C = \ket{V}_1 \otimes \ket{H}_4 \otimes \ket{H}_2 \otimes \ket{V}_3$$
$$\ket{\Psi(t_1)}_D = \ket{V}_1 \otimes \ket{V}_4 \otimes \ket{H}_2 \otimes \ket{H}_3$$

Taking into account the Bell states $\ket{\psi^\pm}_{2,3} = \frac{1}{\sqrt{2}} (\ket{H}_2 \otimes \ket{V}_3 \pm \ket{V}_2 \otimes \ket{H}_3)$, and $\ket{\phi^\pm}_{2,3} = \frac{1}{\sqrt{2}} (\ket{H}_2 \otimes \ket{H}_3 \pm \ket{V}_2 \otimes \ket{V}_3)$, we can change the basis (as in post #38) and write:

$$\ket{\Psi(t_1)}_A = \frac{1}{\sqrt{2}} \ket{H}_1 \otimes \ket{H}_4 \otimes (\ket{\phi^+}_{23} - \ket{\phi^-}_{23})$$
$$\ket{\Psi(t_1)}_B = \frac{1}{\sqrt{2}} \ket{H}_1 \otimes \ket{V}_4 \otimes (\ket{\psi^+}_{23} - \ket{\psi^-}_{23})$$
$$\ket{\Psi(t_1)}_C = \frac{1}{\sqrt{2}} \ket{V}_1 \otimes \ket{H}_4 \otimes (\ket{\psi^+}_{23} + \ket{\psi^-}_{23})$$
$$\ket{\Psi(t_1)}_D = \frac{1}{\sqrt{2}} \ket{V}_1 \otimes \ket{V}_4 \otimes (\ket{\phi^+}_{23} + \ket{\phi^-}_{23})$$

As you can see there, when Victor decides to make a swap, photons 2&3 will be projected onto the state $\ket{\phi^-}_{23}$ only if the state of the system before the swap was either $\ket{\Psi(t_1)}_A$ or $\ket{\Psi(t_1)}_D$, which depends on Alice and Bob obtained HH or VV. Thus, there is a correlation between the state of 2&3 after entangled with the results of 1&4.

As a concluding remark, as you said, the entanglement of 1&4 is only possible if something physical occurs to photons 2&3 at the BSM. Then, from the Victor results, we can group photons 1&4 into subsets that violate Bell inequalities. This result is consistent with photons 1&4 entangled, even if they no longer exist. I have some hope that we'll agree. Am I right?

Well, maybe you did say this. Doesn't matter, we're all on the same page now.

You made me laugh! That was funny

The contradiction is actually between 2things: i) The forward in time premise requires an early measurement of photons 1 & 4 to cast photons 2 & 3 into certain states on same basis; ii) Some experimentally observed outcomes are prohibited by i).

3. Mmm.... no. Because the BSM changes the state of photons 2&3, so the observed outcomes in Victor measurements will be inconsistent with the state of the system after Alice and Bob measurements but before of 2&3 entanglement. I completely agree that some outcomes are prohibited if we don't considered the BSM physical effect on the state of photons 2&3.

Lucas.

 

[DrChinese]

1. This is also a subtle point. The Mjelva's statement should be considered in the context. He said that immediately after showing that, according to the projection postulate, the state after Alice and Bob measured photons 1 and 4 is one of the four $\ket{\Psi(t_1)}_{A,B,C,D}$. Then, if we consider only one of these states and take into account the Victor measurement on photons 2&3, the resulting state for photons 1&4 is a product state. However, as any result Victor obtained is consistent with more than one of the measurement outcomes of Alice+Bob, then Victor will be able to construct a subset for each one of the 2&3 entangled states where photons 1&4 show Bell-correlations.

2. Neither of the two options. To get the entangled state between photons 1&4, the post-selection requires a physical change of the state of photons 2&3 as a consequence of the entanglement after the BSM, which is not independent of 1&4. Don't forget that the entangled state of photons 2&3 depends on the previously recorded results of 1&4.

As you can see there, when Victor decides to make a swap, photons 2&3 will be projected onto the state $\ket{\phi^-}_{23}$ only if the state of the system before the swap was either $\ket{\Psi(t_1)}_A$ or $\ket{\Psi(t_1)}_D$, which depends on Alice and Bob obtained HH or VV. Thus, there is a correlation between the state of 2&3 after entangled with the results of 1&4.

As a concluding remark, as you said, the entanglement of 1&4 is only possible if something physical occurs to photons 2&3 at the BSM. Then, from the Victor results, we can group photons 1&4 into subsets that violate Bell inequalities. This result is consistent with photons 1&4 entangled, even if they no longer exist. I have some hope that we'll agree. Am I right?

3. Mmm.... no. Because the BSM changes the state of photons 2&3, so the observed outcomes in Victor measurements will be inconsistent with the state of the system after Alice and Bob measurements but before of 2&3 entanglement. I completely agree that some outcomes are prohibited if we don't considered the BSM physical effect on the state of photons 2&3.


You made me laugh! That was funny

Lucas.

1. 2. 3. I am only going to partially address these points, will come back with more tomorrow.

So let's say there is a physical effect of the BSM. I agree with most of that anyway. But that says the polarization of the 2 & 3 photons changes, but the already recorded polarizations of the 1 & 4 photons do not. See the problem? There is no known mechanism for a local change of the type you describe. It simply does not exist. A beam splitter has nothing to do with polarization.

But there is no selection going on if the 2 & 3 photons change! That's literally the assertion. Or is it? @Morbert, is that you contention as well?

4.

 

[Morbert]

But there is no selection going on if the 2 & 3 photons change! That's literally the assertion. Or is it? @Morbert, is that you contention as well?

There is still selection going on. If the BiSA is configured so that the quarter-wave plate is on, then Victor can use the detectors to select the subensemble of runs represented by the projection onto $\ket{\Phi^-}_{23}$, but cannot use the detectors to select the subensemble of runs represented by the projection onto $\ket{VV}_{23}$ or $\ket{HH}_{23}$, as the polarizations resolved by the detector do not measure the polarizations of the photons incident on the BiSA (at least when the detectors detect same polarization and different modes, or different polarizations and the same mode). This is due to the local evolution of the photons moving through the BiSA, represented by the operator $I_{14}\otimes U_{23}$ as they approach the detectors, which makes the BSM possible.

If the plate is off, the reverse is true. Victor can use the detectors to select the $\ket{VV}_{23}$ or $\ket{HH}_{23}$ runs, but not the $\ket{\Phi^-}_{23}$ runs.

 

[PeterDonis]

If the BiSA is configured so that the quarter-wave plate is on, then Victor can use the detectors to select the subensemble of runs represented by the projection onto $\ket{\Phi^-}_{23}$, but cannot use the detectors to select the subensemble of runs represented by the projection onto $\ket{VV}_{23}$ or $\ket{HH}_{23}$

If the plate is off, the reverse is true. Victor can use the detectors to select the $\ket{VV}_{23}$ or $\ket{HH}_{23}$ runs, but not the $\ket{\Phi^-}_{23}$ runs.

You're looking at this backwards. The four possible sets of results of the final polarization measurements on photons 2 & 3 are the same whether a swap is done or not. So the results can always be separated into subsets based on the same four possible combinations of results of the final polarization measurements on photons 2 & 3.

What is not the same if a swap is done vs. not done is what each of the four possible combinations of results of the final polarizations measurements on photons 2 & 3 means in terms of the states they each signal. Of course those are different if a swap is done vs. not done; that's the point. And those states are not local: they involve photons 1 & 4 as well as photons 2 & 3. That's the thing that, on any kind of realist interpretation of what the quantum state means, indicates that the experimenter choosing to do a swap vs. no swap (by turning the quarter wave plates on or off, or whatever else is done to choose swap vs. no swap in any particular experiment) is doing something real to photons 1 & 4, which are not locally present, as well as to photons 2 & 3, which are locally present.

Of course if one adopts a non-realist interpretation (such as the bare bones statistical interpretation, for example), one does not necessarily have to accept such an indication. But that just means there is a difference of opinion/personal preference regarding interpretations. It's not something that's going to be resolved here.

 

[Morbert]

You're looking at this backwards. The four possible sets of results of the final polarization measurements on photons 2 & 3 are the same whether a swap is done or not. So the results can always be separated into subsets based on the same four possible combinations of results of the final polarization measurements on photons 2 & 3.

I'm not looking at it backwards. I am distinguishing the polarizations detected by Victor's BiSA apparatus with eigenstates of an SSM like $\ket{VV}_{23}$ and $\ket{HH}_{23}$, consistent with Ma.

Victor may perform a Bell-state measurement which projects photons 2 and 3 either onto |Φ + 〉 23 or onto |Φ − 〉 23 . This would swap entanglement to photons 1 and 4. Instead of a Bell-state measurement, Victor could also decide to measure the polarization of these photons individually and project photons 2 and 3 either onto |𝐻𝐻〉 23 or onto |𝑉𝑉〉 23 [my emphasis]

Of course if one adopts a non-realist interpretation (such as the bare bones statistical interpretation, for example), one does not necessarily have to accept such an indication. But that just means there is a difference of opinion/personal preference regarding interpretations. It's not something that's going to be resolved here.

DrChinese is taking a stronger position against post-selection and pre-selection accounts.

@DrChinese is it your opinion that, if we adopt an interpretation of QM championed by people like Asher Peres - where quantum systems are understood in terms of responses to macroscopic tests - that pre-selection and post-selection fully account for entanglement-swapping experiments without the need to suppose nonlocal influence? Do you accept the formal correctness of Mjelva's paper as far as the formalism of QM goes?

 

[PeterDonis]

I am distinguishing the polarizations detected by Victor's BiSA apparatus

Polarizations of photons 2 & 3 are measured at the end of the apparatus. As I understand it, the basis in which they are measured is the same whether a swap is done or not. That means the four possible combinations of results for those measurements are the same whether a swap is done or not. So there is nothing to "distinguish" in terms of the measurement results themselves.

What you are "distinguishing" is, as I said, what the four possible combinations of results mean in terms of what states they signal. If a swap is done, they signal Bell states; if a swap is not done, they signal separable states. But that is just another way of saying that the correlations that are observed change depending on whether a swap is done. And those correlation changes also occur in the measurements of photons 1 & 4, even though photons 1 & 4 are not local to the BISA apparatus.

 

[PeterDonis]

DrChinese is taking a stronger position against post-selection and pre-selection accounts.

He is adopting an interpretation that says those are not sufficient, yes.

is it your opinion that, if we adopt an interpretation of QM championed by people like Asher Peres - where quantum systems are understood in terms of responses to macroscopic tests - that pre-selection and post-selection fully account for entanglement-swapping experiments without the need to suppose nonlocal influence?

This is a meaningless question because such interpretations do not even try to say what is going on at a microscopic level. So what these interpretations view as "fully accounting" for the results simply does not fully account for them on an interpretation like the one @DrChinese is using. In other words, one of the interpretation differences that is not going to be resolved here is what qualifies as "fully accounting" for the results.

 

[gentzen]

DrChinese is taking a stronger position against post-selection and pre-selection accounts.

So what these interpretations view as "fully accounting" for the results simply does not fully account for them on an interpretation like the one @DrChinese is using.

@Morbert I would try to avoid discussing with PeterDonis what DrChinese says. It is more productive to discuss with PeterDonis his own objections to your reasoning, and to try to answer his own questions.

It is unclear to me whether DrChinese even claims to use a consistent interpretation of QM. What he does seem to claim is to be able to disprove certain interpretations, I guess especially those interpretation which claim to be both realistic and local. Or more precisely like PeterDonis observed, DrChinese does not consider those interpretations as "fully accounting" for the results.

 

[Morbert]

Polarizations of photons 2 & 3 are measured at the end of the apparatus. As I understand it, the basis in which they are measured is the same whether a swap is done or not. That means the four possible combinations of results for those measurements are the same whether a swap is done or not. So there is nothing to "distinguish" in terms of the measurement results themselves.

What you are "distinguishing" is, as I said, what the four possible combinations of results mean in terms of what states they signal. If a swap is done, they signal Bell states; if a swap is not done, they signal separable states. But that is just another way of saying that the correlations that are observed change depending on whether a swap is done. And those correlation changes also occur in the measurements of photons 1 & 4, even though photons 1 & 4 are not local to the BISA apparatus.

The BSM and SSM eigenstates as presented by Ma pertain to the spacial modes b and c, not b" and c". When Ma writes $\ket{HH}_{23}$ this corresponds to $\ket{HH}_{bc}$ but cannot imply $\ket{HH}_{b''c''}$ or $\ket{HH}_{b''b''}$ or $\ket{HH}_{c''c''}$, when the quarter-wave plate is on.

 

[Morbert]

@PeterDonis There is a distinction between adopting an interpretation, and arguing an experimental result poses a novel challenge to an interpretation. We could, for example, argue whether or not MWI's determinism sufficiently accounts for probabilistic character of QM predictions whether or not we adopt it. @DrChinese's arguments about the challenge entanglement-swapping experiments pose for pre-selection/post-selection cannot be reduced to a subjective distaste for antirealist interpretations.

 

[PeterDonis]

The BSM and SSM eigenstates as presented by Ma pertain to the spacial modes b and c, not b" and c". When Ma writes $\ket{HH}_{23}$ this corresponds to $\ket{HH}_{bc}$ but cannot imply $\ket{HH}_{b''c''}$ or $\ket{HH}_{b''b''}$ or $\ket{HH}_{c''c''}$, when the quarter-wave plate is on.

Irrelevant. The final measurement results on photons 2 & 3 are in the H-V basis whether the quarter wave plate is on or not. What they mean (at least according to Ma's analysis) changes, but the basis does not. That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

@DrChinese is interpreting the above as showing that the experimenter choosing whether or not to do a swap has a nonlocal effect on photons 1 & 4.

You are interpreting the above as something different, something about statistics and pre and post selection and so on, which you say does not show any kind of nonlocal effect.

This is a difference of opinion about interpretation that is not going to be resolved here.

There is a distinction between adopting an interpretation, and arguing an experimental result poses a novel challenge to an interpretation.

I agree. But my point stands that the disagreement you are having with @DrChinese is not going to be resolved here. Your disagreement is basically over whether these results do indeed pose a "novel challenge" to the kind of statistical, pre selection/post selection interpretation you are arguing for. That disagreement is a disagreement over choice of interpretation that is not going to be resolved here. Choice of interpretation includes choices about what an interpretation has to explain. @DrChinese is saying that an interpretation has to explain what is going on in each individual run that accounts for these results. You are saying it doesn't; that it's enough to just point out the statistics and the pre and post selection that is being done, without having to give any account of what is happening in each individual run that produces those statistics. That disagreement is not going to be resolved here, because different QM interpretations do not even agree on whether such an account is necessary or what it must contain.

 

[Morbert]

Irrelevant. The final measurement results on photons 2 & 3 are in the H-V basis whether the quarter wave plate is on or not. What they mean (at least according to Ma's analysis) changes, but the basis does not. That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

You're not following the conversation. You said I was looking at it backwards. I said I wasn't as my terminology was consistent with Ma's. You then proceed to argue against a shadow. You are implying I am papering over the detector firings and the inferred BSM or SSM, which is of course nonsense. Please make a substantive critique of my position if you have one. I will let @DrChinese speak for himself.

 

[Sambuco]

Hi @PeterDonis!

What is not the same if a swap is done vs. not done is what each of the four possible combinations of results of the final polarizations measurements on photons 2 & 3 means in terms of the states they each signal. Of course those are different if a swap is done vs. not done; that's the point. And those states are not local: they involve photons 1 & 4 as well as photons 2 & 3. That's the thing that, on any kind of realist interpretation of what the quantum state means, indicates that the experimenter choosing to do a swap vs. no swap (by turning the quarter wave plates on or off, or whatever else is done to choose swap vs. no swap in any particular experiment) is doing something real to photons 1 & 4, which are not locally present, as well as to photons 2 & 3, which are locally present.

That exactly what the paper by Mjelva analyze. I have to say that this is not my preferred interpretation of the experimental results (I'll expand in the following paragraph) but, anyway, I believe that Mjelva's analysis of the DCES (Ma's paper) is compatible with some realistic interpretations (maybe I prefer to say that it is consistent with $\Psi\text{-ontic}$ interpretations to avoid confusion about the meaning of "realistic", but no problem) and, at the same time, it does not imply a backward-in-time change of the 1&4 state, since the forward-in-time evolution of the state of the four-photon system allows him to conclude that the Bell-correlations of photons 1&4 in each subset are due to post-selection. Anyway, this does not confront the fact that these 1&4 correlations can only be revealed when Victor chooses to perform a BSM on photons 2&3. Otherwise, there is no way we can physically project the states $\ket{\Psi(t_1)}_{A,B,C,D}$ onto entangled states for photons 1&4. To avoid confusion, I'm talking about his analysis of the delayed-choice experiment, where the 2&3 BSM is in the future light-cone of the 1&4 measurements.

Let me explain why I'm not satisfied with this "realistic" interpretation. As many said, the predictions of QM are the same irrespective of how 1&4 measurements and 2&3 BSM are time-ordered. Therefore, if we want to interpret both experiments (delayed and non-delayed) in terms of cause-and-effect, we have different explanations about which is the cause and which is the effect, even when the predictions are the same. Even more, if we consider the case where 1&4 measurements and 2&3 BSM are space-like separated (as Mjelva discuss in section 5 of his paper), these interpretations say that we have to accept that which is the cause and which is the effect depends on the reference frame. Well, maybe someone could digest that, but to me, the real problem arises when we go back to the delayed/non-delayed experiments and ask simple questions. I'll give an example. If I consider the non-delayed experiment (2&3 BSM first, 1&4 measurement later) and the 2&3 BSM changes the state of 1&4, when that occurs? At the time the 2&3 BSM was performed, photons 1&4 were located at any other position, so if we want to keep some relativistic causation, then we have to argue for something like that the change of the state of 1&4 must be sitting at the edge of the future light cone of the 2&3 measurement, waiting for photons 1&4 to enter there. Not only this kind of story seems weird enough to me, what is more important is that nothing about that is within the QM formalism. Then, at least for now, my impression is that, maybe, we have to leave aside the concept of "causation" and take "correlation" as something more fundamental.

Lucas.

 

[PeterDonis]

You are implying I am papering over the detector firings and the inferred BSM or SSM, which is of course nonsense.

Is it? Do you agree with what I said in what you quoted, as far as it goes? I know it leaves out things that you have been emphasizing. But if you do agree with it as far as it goes, it would greatly help if you would say so, since from your posts so far in this thread I don't know whether you do or not.

 

[PeterDonis]

the predictions of QM are the same irrespective of how 1&4 measurements and 2&3 BSM are time-ordered. Therefore, if we want to interpret both experiments (delayed and non-delayed) in terms of cause-and-effect, we have different explanations about which is the cause and which is the effect, even when the predictions are the same. Even more, if we consider the case where 1&4 measurements and 2&3 BSM are space-like separated (as Mjelva discuss in section 5 of his paper), these interpretations say that we have to accept that which is the cause and which is the effect depends on the reference frame.

That's correct, and it's true even for the simpler case of measurements on a pair of entangled particles, with no swaps anywhere. Whatever "cause and effect" is happening in any QM experiment involving entanglement cannot work quite the same as the usual cause and effect we are used to in the classical case. But since it can produce correlations that violate the Bell inequalities, it also can't be reduced to "well, it's just revealing something that was present in the initial conditions and gets uncovered by post-selection"--at least not if you want a realist model of how the correlations get enforced in each individual case. That's a big reason why there is no single generally accepted interpretation of QM.

 

[eloheim]

In the abstract of Mjelva's paper he says:

I will argue that a careful analysis of these experiments shows that they in fact display nothing more than ‘‘ordinary’’ spacelike entanglement, and that any purported timelike entanglement is an artefact of selection bias.

To me that sounds like he's saying you still need regular spacelike entanglement (and non-locality?) to explain the experiments. Then at the projection postulate preliminary conclusions section (4.1.3) he says (my emphasis):

I have shown how, on a projection-based account, the Bell correlations displayed in the Ma et al.- and Megidish et al.-experiments can be accounted for in terms of selection bias in the post-selected subsample.
At no point in the analysis was it necessary to posit any entanglement relation obtaining between particle 1 and particle 4. In fact, it should be clear from the analysis that, as each of the states (5) and (9) following
the Bell-state measurement can be written as the tensor product of the state of particle 1, the state of particle 4 and the state of the pair (2, 3), the particles 1 and 4 are not entangled.

So he's saying entanglement is not needed to explain 1 and 4, but what about 1&2, 3&4 and 2&3? Wouldn't the non-swapped version of the runs (in Ma's version) require spacelike entanglement to explain them at a bare minimum? Or is this beyond the point?

Also one question (at risk of sounding stupid): In Ma's experiment, in the swapped-ON runs, how will the H/V polarization readings for 1 and 4 differ between the Φ+ and Φ- subsets?

 

[Morbert]

In the abstract of Mjelva's paper he says:

To me that sounds like he's saying you still need regular spacelike entanglement (and non-locality?) to explain the experiments. Then at the projection postulate preliminary conclusions section (4.1.3) he says (my emphasis):

So he's saying entanglement is not needed to explain 1 and 4, but what about 1&2, 3&4 and 2&3? Wouldn't the non-swapped version of the runs (in Ma's version) require spacelike entanglement to explain them at a bare minimum? Or is this beyond the point?

All runs start with 1&2 entangled, and 3&4 entangled.

Also one question (at risk of sounding stupid): In Ma's experiment, in the swapped-ON runs, how will the H/V polarization readings for 1 and 4 differ between the Φ+ and Φ- subsets?

They will be correlated in both the Φ+ and Φ- subsets. If Alice and Bob measure in the +/- basis instead, they will be correlated in the Φ+ subset and anticorrelated in the Φ- subset. If Alice and Bob measure in the R/L basis, they will be anticorrelated in the Φ+ subset and correlated in the Φ- subset.

 

[Morbert]

Is it? Do you agree with what I said in what you quoted, as far as it goes? I know it leaves out things that you have been emphasizing. But if you do agree with it as far as it goes, it would greatly help if you would say so, since from your posts so far in this thread I don't know whether you do or not.

That means the four possible combinations of final measurement results are HH, HV, VH, VV. What states these results signal (or "count as", as the Ma paper puts it in the discussion on p. 5 before equation 4) changes, but the combinations do not. And because they do not, the data recording the final measurement results can be partitioned into subsets HH, HV, VH, VV regardless of whether a swap is done or not.

So we have a total data set that has the following elements for each run: whether or not a swap was done (quarter wave plate on or off), the photon 2 & 3 result combination (HH, HV, VH, or VV), and the photon 1 & 4 result combination. Then we split the data set into "swap" and "no swap" subsets, and we further split each of those into subsets based on the photon 2 & 3 result combination and what it signals.

Now focus on whatever photon 2 & 3 result combination (or set of combinations) signals the $\ket{\Phi^-}_{23}$ Bell state when a swap takes place. As I read Ma's paper, that is the subset consisting of all runs where the photon 2 & 3 result combination is HH or VV. So we now have the following:

For the subset of runs where a swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show the predicted Bell state correlations.

For the subset of runs where no swap is done and the photon 2 & 3 result combination is HH or VV, the photon 1 & 4 results show no correlations.

Victor can of course always partition runs into HH, HV, VH, VV, without regard for spatial mode resolution, and whether or not the the swap is done, but whether or not the swap is done will influence which subset a run is sorted to.

E.g. Consider photon pairs prepared in the mixture $\rho = (\ket{HH}\bra{HH} + \ket{VV}\bra{VV})/2$ incident on Victor's BiSA. If the quarter-wave plate is off, then all runs will be placed in the HH or VV subset. HV and VH will be empty. If the quarter-wave plate is on, then runs will be placed in any of the four subsets HH, VV, HV, or VH. Similarly if Victor is discarding runs that did not yield the same-polarization detection events, then when the plate is off, Victor will keep all runs, but if the plate is on, Victor will not keep all runs. Hence, Victors decision to do the swap amounts to Victor choosing one of two alternative procedures for selecting runs. This is what Mjelva means by a selection effect and what Price and Wharton mean by the Collider Loophole.

I do not know if you agree or disagree, but it is worth emphasizing that while we can label runs HH HV VH VV whether or not the swap is done, the local sorting procedure will be different, and hence the significance of the subsets will be different.

You are interpreting the above as something different, something about statistics and pre and post selection and so on, which you say does not show any kind of nonlocal effect.

This is a difference of opinion about interpretation that is not going to be resolved here.

My position is interpretation independent. My position is the Collider Loophole has explanatory power for a class of interpretations, which renders entanglement-swapping experiments no less explained than traditional EPRB experiments for these interpretations. Someone is free to adopt or reject an interpretation, but if they argue these experiments now pose an additional challenge to a class of interpretations, above standard EPRB experiments, that is an objective position that can be critiqued.

I.e. I am defending Mjelva. When he says

Though Egg’s view seems to be the most widely accepted, it has recently been criticized by Glick (2019), who argues that accepting this view renders one unable to explain the strong correlations seen in the delayed-choice experiment, leaving them as mysterious as the correlations seen in traditional Bell-type experiments appear on views that take an anti-realist stance on entanglement in general. The main objective of this paper is to answer Glick’s challenge by providing an account of the Bell correlations displayed in DCES experiments in terms of selection effects arising due to post-selection.

I am arguing he successfully met his objective.