I Does Time-Symmetry Imply Retrocausality? How does the Quantum World Say “Maybe”?

[DrChinese]

You're misinterpreting these states as initial states. These states as initial states cannot lead to entanglement swapping however it is interpreted. But these states are not initial states.

Who cares if they are initial state or not? Your objection is completely arbitrary. Whether Mjelva's 4 states occur as written at T(0) or T(1) should not matter. He specifically says these intermediate states are certain: "On any given run of the experiment, the total system will be in one of the these [4] possible states."

Well, is he right or wrong?

What you must really conclude is that there is NO such intermediate state (and Mjelva is in error). That would be the usual orthodox application of QM to this situation. A la the Peres quote about unperformed experiments. And did you forget the entire Bell line of thinking regarding EPR?

Any other viewpoint falls to experimental disproof, as you are starting to realize (by claiming it is not an initial state, and therefore something different).

 

[DrChinese]

I am saying that, in Megedish's experiment, the rotation of indistinguishable particles (interference terms) vs the rotation of distinguishable particles (no interference terms) plays the same role as rotation vs no rotation in Ma's experiment. It breaks any correspondence between the directly-recorded polarization signatures in BSM and no-BSM runs.

Read it again. Nothing like that happens in Megidish. I quoted the relevant text. How about you quote something from the paper that says otherwise.

"One can also choose to introduce distinguishability between the two projected photons. ... We
observed this when we introduced a sufficient temporal delay between the two projected photons (see Fig. 3c)."

@Morbert, there's nothing here about rotation.

 

[DrChinese]

1. It should be pretty clear what I mean by "Challenging that consensus". If you didn't intent to mention Bohmian mechanics, then that is OK for me, and it was just a misunderstanding/miscommunication.


2. Postselection in this context means that you only keep 1 out of 4 results.

1. Apologies, I didn't intend to imply that Bohmian mechanics fails due to a Mjelva-like flaw. I am not strong enough in my understanding how BM explains DCES to comment. I would definitely like to learn more though.

2. No, this is part of the original hypothesis. Note that 2 of the 4 Bell states can't even be discriminated using current technology (and perhaps never will).

Placing results in buckets is scientifically acceptable in all fields, and in no way invalidates the results. The question is akin to a medical study on British women ages 18-30 with blue eyes vs brown eyes. As long as I identify an independent variable in my hypothesis, I don't need to look at subjects that don't meet my profile.

 

[gentzen]

2. Postselection in this context means that you only keep 1 out of 4 results.

2. No, this is part of the original hypothesis. Note that 2 of the 4 Bell states can't even be discriminated using current technology (and perhaps never will).

You mean "yes"? The protocol for quantum teleportation would require you to apply 1 of 4 different unitary transformations (one of them can be the identity), depending on the 4 different classical results of a BSM. If you apply one of these 4 unitary transformation, but independent of the classical result, then you are only lucky in 1 out of 4 runs, and have to discard the 3 out of 4 runs where you were unlucky.

Nothing wrong with that. I don't worry about a collider loophole here. I just point out this fact, that you have now a postselection based poor-man's quantum teleportation, instead of a full-blown reliable quantum teleportation. This mostly becomes critical when you start to emphasize "either before or after the measurements of Alice and Bob", because this "postselection based poor-man's" part deflates its importance.

 

[Morbert]

Who cares if they are initial state or not?

If they are initial states, then you do not get entanglement swapping. If they are not initial states, you get entanglement swapping.

I have showed you the maths over and over and over and over.

 

[Morbert]

Read it again. Nothing like that happens in Megidish. I quoted the relevant text. How about you quote something from the paper that says otherwise.

"One can also choose to introduce distinguishability between the two projected photons. ... We
observed this when we introduced a sufficient temporal delay between the two projected photons (see Fig. 3c)."

@Morbert, there's nothing here about rotation.

"After passing through the PBS, the photons are rotated by HWPs to the |p/m〉 = 1√2 (|h〉 ± |v〉) polariza-
tion basis. For reasons of complementarity, we also define the circular polarization basis |r〉 = 1√2 (|h〉 + i|v〉) and |l〉 = 1√2 (i|h〉 + |v〉). When the polarizations of the middle photons are correlated (hh or vv) they are projected onto a |φ+〉τ,τ a,b state. [...] One can also choose to introduce distinguishability between the two projected photons. In this case, the phase between the two terms of the |φ〉 projected state is undefined, resulting in a mixture of |φ+〉 and |φ−〉 in the projected state, and the first and last photons do not become quantum entangled but classically correlated" -- Megidish

 

[DrChinese]

"After passing through the PBS, the photons are rotated by HWPs to the |p/m〉 = 1√2 (|h〉 ± |v〉) polariza-
tion basis. For reasons of complementarity, we also define the circular polarization basis |r〉 = 1√2 (|h〉 + i|v〉) and |l〉 = 1√2 (i|h〉 + |v〉). When the polarizations of the middle photons are correlated (hh or vv) they are projected onto a |φ+〉τ,τ a,b state. [...] One can also choose to introduce distinguishability between the two projected photons. In this case, the phase between the two terms of the |φ〉 projected state is undefined, resulting in a mixture of |φ+〉 and |φ−〉 in the projected state, and the first and last photons do not become quantum entangled but classically correlated" -- Megidish

And again I point out: This is done for both BSM and SSM. No difference whatsoever. You stopped reading too soon.

The rotations are carried out to generate a full QST as I have previously explained. The QST settings are changed during the full QST. But it is performed identically in all cases using the angle pairs in Table I. This is for both the main experiment (all BSMs) and the secondary experiment (BSM and SSM). No rotations occur differently between 3a, 3b, and 3c.

There... is... no... difference. Please study the paper more closely until this point is clarified. I keep quoting the same sentences about the BSM vs. SSM testing: temporal delay (and nothing else!) creates distinguishability, which eliminates swapping, and leads to Product State statistics.

 

[DrChinese]

If they are initial states, then you do not get entanglement swapping. If they are not initial states, you get entanglement swapping.

I have showed you the maths over and over and over and over.

There is no such thing in any entanglement experiment anywhere, and no derivation as you claim other than what you make up. The Bell state of an entangled stream is usually presented as HV> + VH> or similar. Once Alice measures H>, the other photon is NOT V> as Mjelva claims (and apparently you do too). Period. At least, not until you measure it on the H/V basis.

And in fact just to create a single entangled stream using PDC, you don't start with an "initial" entangled stream at all. There is substantial and multiple state conversions occurring prior to that point. So what anyone calls "initial" is purely arbitrary.

 

[DrChinese]

... I just point out this fact, that you have now a postselection based poor-man's quantum teleportation, instead of a full-blown reliable quantum teleportation. This mostly becomes critical when you start to emphasize "either before or after the measurements of Alice and Bob", because this "postselection based poor-man's" part deflates its importance.

Agreed, this is not a teleportation protocol. Because this is not teleportation, it is swapping. There are plenty of early swapping experiments* where a single Bell state is discriminated, just 1 of the 4.

All good science!


*Such as by those experimental teams that many here seem to dismiss so easily.

 

[Morbert]

There... is... no... difference.

I am saying that, in Megedish's experiment, the rotation of indistinguishable particles (interference terms) vs the rotation of distinguishable particles (no interference terms) plays the same role as rotation vs no rotation in Ma's experiment. It breaks any correspondence between the directly-recorded polarization signatures in BSM and no-BSM runs.

There is absolutely a difference between the rotation of distinguishable vs rotation of indistinguishable particles. You cannot associate a polarization signature during a run with rotated distinguishable particles with the same polarization signature during a run with rotated indistinguishable particles.

 

[Morbert]

There is no such thing in any entanglement experiment anywhere, and no derivation as you claim other than what you make up.

I did not make anything up. I applied basic quantum mechanics to compute probabilities for possible sequences of measurement outcomes and commented on their correlations, consistent with those reported by Ma etc. There's nothing else to it.

 

[Morbert]

@DrChinese As I have derailed this thread enough, I will start a new thread in the next couple of days to continue the discussion (unless you want to do so first)

 

[Sambuco]

Experimental contradiction of Mjelva: It is an indisputable experimental fact that NONE of these 4 states - and no MIXTURE of these 4 states - can ever lead to an entanglement swap.

There is a certain confusion between the prediction of the experimental results and its interpretation in terms of entanglement swapping. Let me explain that. On the one hand, Mjelva predicts exactly the same results experimentally obtained in Ma's paper. This is demonstrated mathematically in his paper. I carefully studied it, and there is no error along his calculations.

However, there is an important issue regarding the interpretation of these results in terms of entanglement. Even when the measurement outcomes predicted by Mjelva are exactly the same as those observed experimentally by Ma et al., since Mjelva's calculations are always forward-in-time (as textbook Schrödinger equation), Alice and Bob's particles are never entangled, in the sense that they do not have a non-separable quantum state, even when Bell correlations are predicted!

That's why I said in post #36 that entanglement in entanglement swapping experiments is not an interpretation-independent fact about Alice and Bob's particles. If DCES is analyzed using a
$\Psi$-ontic interpretation, which consideres a single, forward-in-time evolving wave function, the quantum state of Alice and Bob's particles is always separable, so there is no entanglement, and obviously, no swapping, even when the measurements results are the same! The entanglement swapping only arises if the results are analyzed from a perspective, such as Victor's one, that considers a quantum state that reflects the information available to him after the BSM.

Summarizing, there is nothing wrong with the fact that Mjelva's calculatins predict the measurement results reported by Ma et al., and at the same time, there is no entanglement (as non-separable quantum state) between Alice and Bob's particles.

Lucas.

Edit: I just corrected a typo.

 

[PeterDonis]

There is a certain confusion between the prediction of the experimental results and its interpretation in terms of entanglement swapping.

This illustrates an issue that is common in this subforum: there is no way to resolve disputes about interpretations.

The experimental facts don't seem to be in dispute here. The dispute seems to be about how to interpret them: things like whether the term "entanglement swapping" is an apt term to describe what's happening.

That is a matter that can't be resolved here. Ultimately it comes down to personal preference. So discussions like this at some point just have to stop, with everyone having stated their position as best they can, and any remaining disagreements simply unresolvable.

This thread is probably getting close to that point. There is nothing here that hasn't been said in multiple previous threads on these types of experiments.

 

[Sambuco]

The experimental facts don't seem to be in dispute here. The dispute seems to be about how to interpret them: things like whether the term "entanglement swapping" is an apt term to describe what's happening.

That is a matter that can't be resolved here. Ultimately it comes down to personal preference.

On the one hand, I completely agree with you in that certain things related to the interpretation of entanglement swapping experiments are, well, interpretation-dependent. As I said in post #73, even the notion of "entanglement" depends on one's preferred interpretation.

On the other hand, the fact that $\Psi$-ontic interpretations, such as many-worlds or Bohmian mechanics are able to predict the experimental results reported in Ma's paper by a forward-in-time evolution of the four-particle quantum state from preparation up to measurement (as in Mjelva's calculations) is not something that can be subject to interpretation. It is a mathematical fact.

All this aside, perhaps we can focus again on the OP about the relationship between time symmetry and retrocausality, given that @MrRobotoToo shared a reference in post #55, which seems useful for that purpose. I others agree, we can continue the discussion about (delayed-choice) entanglement swapping in another thread.

Lucas.

 

[PeterDonis]

As I said in post #73, even the notion of "entanglement" depends on one's preferred interpretation.

And as I said in post #74, that's not true for the standard QM definition of entanglement.

the fact that $\Psi$-ontic interpretations, such as many-worlds or Bohmian mechanics are able to predict the experimental results reported in Ma's paper by a forward-in-time evolution of the four-particle quantum state from preparation up to measurement (as in Mjelva's calculations) is not something that can be subject to interpretation. It is a mathematical fact.

Yes, mathematical facts are not matters of interpretation. But what a particular mathematical fact means physically can be.

 

[Sambuco]

And as I said in post #74, that's not true for the standard QM definition of entanglement.

Just to be clear, given a quantum state (I'm assuming only two particles for simplicity), there is entanglement if it cannot be decomposed in a product state. I think we all agree on that. The "problem" arises when different quantum states are considered when analyzing an experiment from different interpretations. For example, in the DCES, a $\Psi$-ontic interpretation (MWI, Bohmian mechanics) shows no entanglement between Alice and Bob particles, since the quantum state is separable at any time during the experiment. However, if we take relational QM as an example of a $\Psi$-epistemic interpretations, it says that the presence of entanglement between Alice and Bob's particles depend on the observer: For Alice/Bob, there is no entanglement according to the quantum state they assign to their particles, while there is entanglement for the quantum state Victor defines according to the information he has access to.

Lucas.

 

[Sambuco]

What you must really conclude is that there is NO such intermediate state (and Mjelva is in error). That would be the usual orthodox application of QM to this situation.

There is no error. These "intermediate states" arise when the four-particle state is updated based on the results of Alice and Bob's measurements. We discussed this issue in the other thread and I even provided a reference to Zwiebach's textbook showing that Mjelva's analysis follows from the textbook formulation.

What you must really conclude is that there is NO such intermediate state (and Mjelva is in error). That would be the usual orthodox application of QM to this situation. A la the Peres quote about unperformed experiments.

Again, these intermediate states arises because a measurement was perfomed, as Peres said! Since particles 1&2 and 3&4 are initially entangled, when Alice measures particle 1 and Bob measures particle 4, the state of particles 2&3 is remotely updated according to the collapse postulate applied to entangled states, as explained in Zweibach's book.

Lucas.

 

[PeterDonis]

Just to be clear, given a quantum state (I'm assuming only two particles for simplicity), there is entanglement if it cannot be decomposed in a product state.

Not quite. The standard definition of an entangled state is a state that cannot be expressed as a product of states of subsystems.

For example, in the DCES, a $\Psi$-ontic interpretation (MWI, Bohmian mechanics) shows no entanglement between Alice and Bob particles, since the quantum state is separable at any time during the experiment.

Huh?

That's not at all true for the MWI: in the MWI, in fact, the state becomes more and more entangled with each measurement, since measurements in the MWI just entangle the measuring device with the measured system.

In Bohmian mechanics, the wave function is not the complete state of the system anyway--the complete state includes the unobservable particle positions. So entanglement in Bohmian mechanics, in terms of a property of the wave function, doesn't have quite the same meaning.

if we take relational QM as an example of a $\Psi$-epistemic interpretations, it says that the presence of entanglement between Alice and Bob's particles depend on the observer: For Alice/Bob, there is no entanglement according to the quantum state they assign to their particles, while there is entanglement for the quantum state Victor defines according to the information he has access to.

Yes, but in such an interpretation, entanglement isn't a physical property of the system to begin with, so again, it doesn't have quite the same meaning.

 

[bhobba]

The way that I've heard it explained is that to explain phenomena like quantum entanglement you need to sacrifice at least one of three things: causality, locality, or "realism" (although you could sacrifice more than one).

You know, I think it's because my background is in math, not physics, but what the math requires needs no further explanation.

Entanglement is a simple consequence of the principle of superposition, which itself follows from a Hilbert space being a vector space.

Here is the math. Suppose we have two systems that can be in state |a> or state |b>. If system 1 is in state |a> and system 2 is in state |b>, we write that as |a>|b>. Conversely, if system 1 is in state |b> and system 2 is in state |a>, that is written as |b>|a>. Nothing weird so far. But let us apply the principle of superposition. A possible state is 1/√2 |a>|b> + 1/√2 |b>|a>. Neither system is in state |a> or |b>. It is now a single system where each system has lost its individuality. It is easy to construct an observable that, when applied to this new system, breaks the entanglement, and one gets separate systems again, one in state |a> and the other in state |b>. It's just math - no interpretation required.

Bell's Theorem states that when entangled, we can still consider it as two separate systems using an interpretation, eg Bohmian Mechanics (going beyond the math and trying to understand if there is anything deeper). Then it can still be considered two separate systems, but there is a cost associated with it. We need to abandon locality.

I take the math at face value and don't look for a deeper meaning. Still, each to their own, and Bell's Theorem is interesting. Except not to Feynman:


I think it's fair to say that he had a complicated relationship with Bell.

https://pubs.aip.org/aapt/ajp/article/84/7/493/1040313/RICHARD-FEYNMAN-AND-BELL-S-THEOREM

Thanks
Bill

 

[Sambuco]

That's not at all true for the MWI: in the MWI, in fact, the state becomes more and more entangled with each measurement, since measurements in the MWI just entangle the measuring device with the measured system.

Right, but to look for some kind of entanglement between Alice and Bob's particles, one needs to consider branching due to decoherence and assume a sort of "branch-relative notion of reality", using the term as in the Egg's paper. In that sense, no correlation can be observed between Alice and Bob's particles, unless Victor performs the BSM and four different subensembles are formed due to post-selection. Since post-selection is not a physical process, in an interpretation with only forward-in-time state evolution, the resulting correlation does not modify the past quantum state of Alice and Bob's particles. Of course, this situation is much drastic in the case of Megidish's experiment, where Alice and Bob's particles never coexist, so no entanglement relation between these particles could be "real" if it's not even possible to write a quantum state that includes both particles at the same time.

In Bohmian mechanics, the wave function is not the complete state of the system anyway--the complete state includes the unobservable particle positions. So entanglement in Bohmian mechanics, in terms of a property of the wave function, doesn't have quite the same meaning.

I completely agree. However, I was only analyzing whether entanglement exists between Alice and Bob's particles from the perspective of different interpretations, which is why I focused solely on the wavefunction.

Yes, but in such an interpretation, entanglement isn't a physical property of the system to begin with, so again, it doesn't have quite the same meaning.

That's exactly my point!
What I was trying to convey is that whether Alice and Bob's particles were "really" entangled depends on the interpretation we use to analyze the DCES experiment. As you said, even the meaning we give to the phrase "Alice and Bob's particles were entangled" also depends on the interpretation.

In other words, on a purely forward-in-time interpretation, as is the case with most $\Psi$-ontic ones, there is no entanglement between Alice and Bob's particles in DCES. On the other hand, there is entanglement in some $\Psi$-epistemic interpretations, such as RQM. These two perspectives are not contradictory because, as you said, each interpretation gives a different meaning to entanglement.

Lucas.

 

[DrChinese]

You cannot associate a polarization signature during a run with rotated distinguishable particles with the same polarization signature during a run with rotated indistinguishable particles.

Again, I have provided multiple authoritative citations saying precisely the opposite. See Megidish figure 3 where indistinguishable vs distinguishable are associated and compared, and presented as an important result. Are you seriously suggesting their conclusion is in error and should be retracted? A conclusion which agrees with other experimental teams and with quantum theory?

Meanwhile, your only reference is… still … yourself. Perhaps you can find a quote from an experimentalist who agrees with you?

And a reminder: in Megidish, the distinguishable photons don’t interfere because: they don’t physically overlap due to one being deliberately delayed. It obviously has nothing to do with earlier processing (which is the same in all cases), and definitely nothing to do with rotations which act identically on all photons.

 

[DrChinese]

1. ... and I even provided a reference to Zwiebach's textbook showing that Mjelva's analysis follows from the textbook formulation.

2. Again, these intermediate states arises because a measurement was perfomed, as Peres said! Since particles 1&2 and 3&4 are initially entangled, when Alice measures particle 1 and Bob measures particle 4, the state of particles 2&3 is remotely updated according to the collapse postulate applied to entangled states, as explained in Zweibach's book.

1. Sorry, Zwiebach's writing notwithstanding, I reject this as a suitable reference. You must present something better. There should be plenty of suitable authors that have claimed the same if it is textbook QM.

2. An unperformed measurement on particle 2 is... an unperformed measurement on particle 2! Per Peres: There are no results yet for photon 2. It is absolutely not in an intermediate state due to Alice's measurement.

Were what you claim true, then imagine this: Alice measures photon 1 as V>, meaning (per you) photon 2 is now H>. So placing an H> filter in the path of photon 2 should then be a redundant measurement, having no effect. Can photon 2 still be used for swapping?

That's a rhetorical question, because it obviously cannot. That contradicts your assertion that it was ever in the state H>.

 

[Sambuco]

1. Sorry, Zwiebach's writing notwithstanding, I reject this as a suitable reference. You must present something better. There should be plenty of suitable authors that have claimed the same if it is textbook QM.

You're very confused. First of all, I don't need to provide any additional reference to explain something as basic as how to apply the collapse postulate on entangled states when measuring one of the subsystems. Anyway, I was reading McIntyre's textbook the other day, and (of course) he applies the collapse postulate to entangled states in the same way as Zweibach (there is only one way!), so I share with you the following excerpt from section 16.2.3 on Quantum teleportation:

As you can see, if you takes into account that Alice measures the state $\ket{\beta_{00}}_{AC}$, and apply the collapse postulate (according to the formula presented in Zweibach textbook) to the state $\ket{\psi}_{ABC}$ in eq. (16.52) , you obtain the state $\ket{\psi}_B$ in eq. (16.53).

Now, I provided you with not one, but two references from quantum mechanics textbook that show how the collapse postulate should be applied to entangled states when a measurement is performed on one of the subsystems. If you're really interested in learning about this topic, read these references or find another one you like, but please stop denying basic postulates of (textbook) formulation of quantum mechanics.

2. An unperformed measurement on particle 2 is... an unperformed measurement on particle 2! Per Peres: There are no results yet for photon 2. It is absolutely not in an intermediate state due to Alice's measurement.

I already addressed this minsunderstaing of yours in the other thread. You're also confused about what means to apply the collapse postulate to entangled states. The fact that the quantum state of particle 2 changes after measurement on particle 1 doesn't mean that particle 2 has been measured and a definite result was obtained. It's simply a state change that allows us to accurately predict the probability of obtaining certain measurement outcomes if particle 2 is measured.

We can't continue arguing about interpretation until you understand these basic concepts. I believe this misunderstading is the reason why you don't fully accept that a forward-in-time formulation can predict experimental results in entanglement swapping experiments.

Lucas.

 

[PeterDonis]

It's simply a state change

It's a state change in the math. Whether or not it's a state change of the actual, physical system is interpretation dependent.

 

[DrChinese]

1. First of all, I don't need to provide any additional reference to explain something as basic as how to apply the collapse postulate on entangled states when measuring one of the subsystems. Anyway, I was reading McIntyre's textbook the other day...

2. The fact that the quantum state of particle 2 changes after measurement on particle 1 doesn't mean that particle 2 has been measured and a definite result was obtained. It's simply a state change that allows us to accurately predict the probability of obtaining certain measurement outcomes if particle 2 is measured.

1. Still makes no sense in our context. There is no such thing as saying a system of unentangled particles (photons 2 & 3) being in a Bell state prior to a BSM or swap or similar. Mjelva makes this specific error too.

2. Alice's measurement can be said to drive a state change for photon 2, I quite agree. It's just not a state change to a specific polarization eigenstate. As I keep saying, that hypothesis is experimentally falsified*.

Oh, and your description makes it action** at a distance. The remote change of state of photon 2 - by your own description - is dependent on Alice's distant choice of measurement basis. They call that steering.


*I'll provide that in a separate post.
** As @PeterDonis says, that designation is interpretation dependent; but I trying to use your narrative.

 

[PeterDonis]

You're very confused.

I don't think so. I don't think anyone here is confused about the math. The dispute is about what the math means, physically. Basically, you and the references you give are saying that, because we can write the state $\ket{\psi_{ABC}}$ mathematically in a basis of Bell states, that has a physical meaning. @DrChinese and other references he's given do not accept that claim. And since everyone agrees about the actual experimental predictions, there's no way to resolve such a dispute. It's a matter of personal choice of interpretation.

 

[Sambuco]

It's a state change in the math. Whether or not it's a state change of the actual, physical system is interpretation dependent.

So what? I think you're missing the point. In post #84, I don't say anything about the interpretation of these matematical operations, that is, how they correlated with physical properties of the system. What I explained is how to apply the collapse postulate after the measurement of a subsytem of an entangled system.

Lucas.

 

[DrChinese]

In our ongoing example of a 4 photon entanglement swap (BSM on photons 2 & 3), per experiments like Kaltenbaek et al, it has been claimed by Mjelva and others that photons 2 & 3 end up in definite polarization states after an H/V basis measurement on photons 1 & 4. That hypothetical intermediate evolution is critical to their forward-in-time-only analysis. What if that were true?

We could actually test that hypothesis by performing a redundant polarization measurement on photons 2 & 3. We simply add a few components to the setup to accomplish that.

a) Add a polarizing beam splitter (PBS) in the path of photons 2 & 3 (call them PBS2 & PBS3). If photon 1(photon 4) comes out H>, then photon 2(photon 3) comes out the V> port of the PBS2(PBS3). Vice versa if photon 1(photon 4) comes out V>.

b) Route the PBS output ports for H> to the Bell State Measurement (BSM1) setup. If both the 1 & 4 photons are V>, then the PBS did nothing as 2 & 3 proceed to have a BSM performed.

c) Route the PBS output ports for V> to a new additional and identical Bell State Measurement (BSM2) setup. If both the 1 & 4 photons are H>, then the PBS did nothing as 2 & 3 proceed to have a BSM performed at BSM2.

d) Regardless of which BSM setup photons 2 & 3 are sent to, they are designed such that they are otherwise indistinguishable upon detection. A swap is possible via the BSMs.

Will there be BSM stats or SSM stats? Experiment should show SSM stats. That's because photons 2 and 3 were not either H> or V> polarized before going through PBS2 or PBS3. If they had been, as hypothesized, they should be eligible for swapping and you would get BSM stats. If that didn't happen, it must be because they weren't in the hypothesis intermediate state.

So why am I sure of the predicted result? Because you can easily produce photon pairs in the HV> or VH> states at will, but they cannot be used for swapping. Every swapping experimentalist knows this. And in fact even a proper random mixture of HV> or VH> states can be produced. Every swapping experimentalist knows this too - because they could substantially increase entangled pair production were that possible. Instead they must implement a complex set of geometric settings to achieve entanglement production under either Type I or Type II PDC.

 

[Sambuco]

Basically, you and the references you give are saying that, because we can write the state $\ket{\psi_{ABC}}$ mathematically in a basis of Bell states, that has a physical meaning.

No! I'm not saying that. In fact, I don't believe that these operations have a physical meaning in the sense of action-at-a-distance or something like that. In fact, I prefer information-based interpretations, which deny this "realist" interpretation of the collapse postulate.

Furthermore, the references I provide don't say anything about how to physically interpret these operations, they just explain how they work.

I don't think so. I don't think anyone here is confused about the math.

If that's the case, I have no problem, and our differing opinions are due to the different interpretations proposed. However, @DrChinese doesn't say he prefers one interpretation over another; what he's saying is that interpretations that assume a forward-in-time evolution of the quantum state are unable to reproduce the experimental results obtained in delayed-choice entanglement swapping. When I ask him why, he argues that there's an error in the way the collapse postulate is applied. What he says is erroneous and does not depend on the interpretation.

Lucas.