A A Realization of a Basic Wigner's Friend Type Experiment

[DarMM]

Again, a proper a Wigner's friend scenario assumes the decoherence can always be reversed in principle, ignoring the practically insurmountable realistic challenges. The most philosophically interesting problem (for assessing the consistency of the theory) is when we imagine a decohered human being gets unitarily reversed.

There are two levels of Wigner's friend constructions in the literature. One where the superobserver is able to perform arbitray measurements on the observer and a second where they also have full unitary control of the observer. Frauchiger-Renner and Brukner's theorem are in the first category, Masanes version of Frauchiger-Renner is in the second.

 

[kimbyd]

You're framing the question backwards. I'm not starting from the theory and asking what should happen to it at the macro scale. I'm starting from the observation that we see all sorts of quantum phenomena at the micro scale, but not at the macro scale. It's not that "QM should differ", it's that the observed phenomena do differ.

They differ only in terms of their ontological interpretation of what's occurring. The experimental predictions are absolutely identical once you're outside the quantum regime. So no, I don't reject at all that the macro scale and quantum scale are presenting fundamentally different behavior, because quantum dynamics correctly predicts what happens at all scales, without modification.

It is certainly possible that something we can't observe is occurring in the regime where quantum effects aren't measurable. But it would be stepping far outside the available evidence to try to stake a claim as to what that is.

One possible way to deal with this is to try to modify QM so that its predictions change as you go from the micro to the macro scale. But it's not the only possible way. Another obvious way is to look for a different theory that has QM as one approximation, at the micro scale, and the appropriate macro-scale theory as another approximation at the macro scale. This is one way of viewing the current search for a theory of quantum gravity.

I mean, you can modify QM. That's been the prevailing strategy in QM for a long time, and has been a primary component of most interpretations of QM.

But then it was pointed out that these modifications are unnecessary.

Then whatever interpretation of QM you are using, it isn't the MWI, which requires exactly that assumption.

Yes, MWI generally does assume unitarity. I'm not assuming MWI. I'm rejecting the assumption that additional dynamics need to be added based upon current observational evidence, though it remains plausible that the dynamics we know of today are incorrect in some manner we don't yet understand.

Rejecting the collapse assumption doesn't limit me to MWI, as there are still multiple mechanisms to go from the wavefunction dynamics to observational effects. Those other interpretations generally offer the same general picture of what's going on as MWI, but do so in different ways.

Only if you are taking "exactly unitary at all scales" as the null hypothesis, the one we should accept in the absence of evidence to the contrary. But how did that particular hypothesis, which comes from a particular theory that only has experimental validation at the micro scale, somehow get itself to be the null hypothesis?

Because it requires fewer assumptions, and predicts the same large-scale behavior.

It's very true that the realization that the assumption of wavefunction collapse was not a necessary component of the theory did not occur until decades after quantum theory first appeared, and that the interpretation of probability if you don't have collapse only had a relatively firm grounding quite recently. But the fact remains that a theory which assumes only evolution via $i\hbar{d \over dt}|\Psi(t)\rangle = H|\Psi(t_0)\rangle$ where $H$ is the appropriate Hamiltonian correctly predicts all behavior at both small and large scales, with the exception of gravity.

 

[charters]

There are two levels of Wigner's friend constructions in the literature. One where the superobserver is able to perform arbitray measurements on the observer and a second where they also have full unitary control of the observer. Frauchiger-Renner and Brukner's theorem are in the first category, Masanes version of Frauchiger-Renner is in the second.

In either case, the decoherence of the lab along the friend's measurement basis is getting reversed

 

[DarMM]

In either case, the decoherence of the lab along the friend's measurement basis is getting reversed

Sorry that wasn't to disagree, just as a point of interest.

 

[kimbyd]

Of course hence @PeterDonis 's statement that this is fine in MWI, but it doesn't resolve it in other views like Copenhagen. Thus it's not interpretation neutral.

This goes back to what I was saying earlier: it's technically possible for wavefunction collapse to occur before decoherence. And if said collapse occurs before decoherence it could, in principle, be measurable.

But if the collapse happens after decoherence, then it can't be measured and it should be disregarded. The most simplistic Copenhangen interpretation, which places the boundary of collapse far after the boundary where decoherence occurs, cannot ever possibly be tested as a result.

The Copenhagen interpretation is useful because it's simple. But that doesn't mean it's correct. And it should be expected that its usefulness will degrade whenever the precise details of wavefunction collapse (whether effective or real) are important for the behavior of a given system, as in quantum computing.

It shows that the higher observer's statistics for the lower observer, prior to measuring the lower observer, are consistent with the assumption that an outcome has occured. This is not actual collapse though. The higher observer retains all terms, they have not reduced to one term. When they observe the lower observer they then reduce using an axiom separate to the unitary dynamics.

So what distinguishes observer A from observer B that permits observer B to avoid collapse where observer A collapses? What physical property is being used to separate them?

In simple Copenhagen, the answer is simple: both A and B are fully-collapsed, so observer A can never measure quantum effects from observer B's measurement.

In MWI (and similar), the answer is that neither observer A nor observer B fully collapse, but some quantum effects are still apparent to observer A. The statement that observer A has collapsed is not intended to be a real statement of what has occurred, but instead a tool to make evaluation of the experimental result easier to interpret. And it should be a reasonable approximation as long as observer A is sufficiently complex to never directly see any quantum effects (as is the case for humans not using very specialized experimental equipment).

I'm not aware of any interpretation that would allow observer B to avoid collapse while observer A collapses, except for the outside possibility that observer B's nature allows them to experience less decoherence.

 

[charters]

Sorry that wasn't to disagree, just as a point of interest.

No worries. By the way, did you ever happen to check out the new Bub paper on Wigner' friend I replied with here a few days/maybe a week ago?

 

[DarMM]

The Copenhagen interpretation is useful because it's simple. But that doesn't mean it's correct. And it should be expected that its usefulness will degrade whenever the precise details of wavefunction collapse (whether effective or real) are important for the behavior of a given system, as in quantum computing.

Copenhagen has collapse as being epistemic, thus there are no details in this sense either effective or real.

So what distinguishes observer A from observer B that permits observer B to avoid collapse where observer A collapses? What physical property is being used to separate them?

Observer B does not avoid collapse. When they apply the theory they must use collapse. When observer A models observer B with QM the statistics they have prior to the measurement of macroscopic observables on observer B are consistent with B having an outcome. However they must use collapse when they finally observe B.

 

[DarMM]

No worries. By the way, did you ever happen to check out the new Bub paper on Wigner' friend I replied with here a few days/maybe a week ago?

Yes I've read it. Any particular aspect you are interested in. To me there are three points of discussion in it.

The consistency of NeoCopenhagen views with Frauchiger-Renner
That MWI violates both the S and C conditions of Frauchiger-Renner
That MWI is empirically wrong

That's also the order of how contentious others may find them coincidentally.

 

[charters]

Yes I've read it. Any particular aspect you are interested in.

Yes, on page 10 he says:

"Since the two Wigners measure commuting observables on separate systems, W[bar] can communicate the outcome‘ok’of her measurement to W, and her prediction that she is certain, given the outcome‘ok,’ that W will obtain ‘fail,’ without ‘collapsing’ the global entangled state. Then in a round in which W obtains the outcome ‘ok’ for his measurement and so is certain that the outcome is ‘ok,’ he is also certain that the outcome of his measurement is not ‘ok.’"

I think this is just wrong. He is letting W-bar know both her own |ok> and F-bar's |tails> at the same time, which is just a complementarity violation. Same error when he just changes the subscript from F-bar to W-bar in the subscripts in (16) to (17). If you keep W-bar and F-bar distinct in the correct way, the whole argument against MWI/representational QT falls apart (and actually instead shows the flaw in his own informational view)

 

[DarMM]

(and actually instead shows the flaw in his own informational view)

I'll have to think about the rest of your post, but regarding this part I think at best it shows Bub's defense of informational views is not correct. Richard Healey has already shown that Informational views can escape Frauchiger-Renner by rejecting intervention insensitivity.

 

[PeterDonis]

quantum dynamics correctly predicts what happens at all scales, without modification.

Only if you include collapse--call it "effective collapse" or whatever you want to allow room for interpretations like the MWI--whenever a measurement occurs. But QM does not tell you when a measurement occurs. QM does not tell you when to include collapse. It just says "do it when it makes sense to do it". That's not a dynamical prediction. It's an admission that there is no dynamical prediction, so the physicist just has to make the best of it.

Decoherence does not help here because decoherence is a continuous process, not an instantaneous change. Decoherence does not tell you "when decoherence has reached point X, include a collapse". It still says "include collapse when it makes sense to include it".

 

[PeterDonis]

a theory which assumes only evolution via $i\hbar{d \over dt}|\Psi(t)\rangle = H|\Psi(t_0)\rangle$ where $H$ is the appropriate Hamiltonian correctly predicts all behavior at both small and large scales

I strongly disagree, for the reasons I gave in my last post.

 

[charters]

I'll have to think about the rest of your post, but regarding this part I think at best it shows Bub's defense of informational views is not correct. Richard Healey has already shown that Informational views can escape Frauchiger-Renner by rejecting intervention insensitivity.

Which Healey paper is this in?

 

[DarMM]

Which Healey paper is this in?

https://arxiv.org/abs/1807.00421
Section 3

 

[DarMM]

Decoherence does not help here because decoherence is a continuous process, not an instantaneous change. Decoherence does not tell you "when decoherence has reached point X, include a collapse". It still says "include collapse when it makes sense to include it".

Precisely, in my language above it causes no inconsistencies if observer A assumes observer B included collapse at any point after B's device has decohered in A's application of quantum theory.

After decoherence A's dynamical model of B is not in contradiction with any presumed application by B of collapse, but nothing says when to apply collapse.

 

[charters]

https://arxiv.org/abs/1807.00421
Section 3

Thanks. I think Healey is correct that F&R don't show a contradiction among the 2 superobservers. But really this was never the issue for informational interpretations, and the whole move of going to 4 players is an unhelpful detour. The issue for informational interpretations is present with just Wigner and Friend, and it is that the superobserver and internal observer disagree about whether the internal (human) observer is a quantum mechanical subsystem or an observer external to quantum theory.

A new paper that explains this very nicely on pg 6-7: http://philsci-archive.pitt.edu/16238/

 

[DarMM]

Thanks. I think Healey is correct that F&R don't show a contradiction among the 2 superobservers. But really this was never the issue for informational interpretations, and the whole move of going to 4 players is an unhelpful detour. The issue for informational interpretations is present with just Wigner and Friend, and it is that the superobserver and internal observer disagree about whether the internal (human) observer is a quantum mechanical subsystem or an observer external to quantum theory.

A new paper that explains this very nicely on pg 6-7: http://philsci-archive.pitt.edu/16238/

I've read her paper before and don't agree with the analysis. The response is covered in many papers and the anaylsis is very similar to one by Deutsch as improved by Brukner's theorem that is the originator of this thread.

Wigner is measuring very different classes of observables to the friend. Thus $|0\rangle_S$ does not allow an inference of $|0\rangle_L$ with $S$ the system the observer is looking at and $L$ their lab.

This inference doesn't even hold in Spekkens toy model or epistemically restricted classical theories, so performing it in QM seems pointless to me.

 

[charters]

This inference

What is your |0>L above? When Wigner simply opens the box to ask Friend his result of the S measurement?

 

[DarMM]

What is your |0>L above? When Wigner simply opens the box to ask Friend his result of the S measurement?

The state of the friend's lab.

 

[charters]

The state of the friend's lab.

I don't understand what the validity of this inference has to do with the issue of the parties disagreeing about whether Friend is a quantum system or an external observer.

 

[DarMM]

I don't understand what the validity of this inference has to do with the issue of the parties disagreeing about whether Friend is a quantum system or an external observer.

Without the inference you don't have the disagreements in probabilities that form the core of the refutations in the rest of the article.

 

[charters]

Without the inference you don't have the disagreements in probabilities that form the core of the refutations in the rest of the article.

But only by conceding Wigner and Friend's state spaces are inequivalent, which is the underlying criticism anyway.

 

[DarMM]

But only by conceding Wigner and Friend's state spaces are inequivalent, which is the underlying criticism anyway.

I don't understand, could you explain?

 

[charters]

I don't understand, could you explain?

For Wigner |x>Lab = |x>S⊗|I see x>Friend. The inference you reject clearly holds, at least for Wigner. If he opens the box on Friend's measurement basis, he can simply go directly inspect the qubit for himself, before or after Friend reports anything verbally, and he will see what Friend saw.

For the inference to not hold, |0>S must be defined in a separate state space from the above (one where F is not a tensor factor but the external measurer).

 

[DarMM]

For Wigner |x>Lab = |x>S⊗|I see x>Friend. The inference you reject clearly holds, at least for Wigner. If he opens the box on Friend's measurement basis, he can simply go directly inspect the qubit for himself, before or after Friend reports anything verbally, and he will see what Friend saw.

Yes of course after he measures the entire state of the lab he might obtain $|0\rangle_L$ but the friend measuring and observing $|0\rangle_S$ does not imply that Wigner will with probability 1 observe $|0\rangle_L$. That's the invalid part preventing the contradictory probabilities.

The argument in the paper doesn't even hold in classical epistemically restricted theories, so why it "must" hold in QM I do not understand.

This is the reason FR and Brukner took the approach of wrapping CHSH and Hardy's paradox in Wigner's friend, because basic Wigner's friend holds no problem for these views. See Chapter 11 of Richard Healey's The Quantum Revolution in Philosophy for a full account.

 

[charters]

Yes of course after he measures the entire state of the lab he might obtain |0⟩L|0⟩L|0\rangle_L but the friend measuring and observing |0⟩S|0⟩S|0\rangle_S does not imply that Wigner will with probability 1 observe |0⟩L|0⟩L|0\rangle_L. That's the invalid part preventing the contradictory probabilities

So you are claiming if Friend gets |0>S, there is still non zero probability Wigners gets |1>L, wherein Friend will tell Wigner "I saw 1"?

Brukner & Baumamn I think agree with my view, insofar as they say Friend can't reason correctly without agreeing to use Wigner's state space: https://arxiv.org/abs/1901.11274.

 

[DarMM]

So you are claiming if Friend gets |0>S, there is still non zero probability Wigners gets |1>L, wherein Friend will tell Wigner "I saw 1"?

Brukner & Baumamn I think agree with my view, insofar as they say Friend can't reason correctly without agreeing to use Wigner's state space: https://arxiv.org/abs/1901.11274.

Yes indeed but all of this can occur in a classical epistemically restricted model with local variables, so there's nothing shocking or unacceptable about it to me.

 

[charters]

Yes indeed but all of this can occur in a classical epistemically restricted model with local variables, so there's nothing shocking or unacceptable about it to me.

It entails the conclusion that Friend who lives in Friend-world is not the same person as Friend who lives in Wigner-world. These two versions of Friend disagree about the outcome of the experiment.

 

[DarMM]

It entails the conclusion that Friend who lives in Friend-world is not the same person as Friend who lives in Wigner-world. These two versions of Friend disagree about the outcome of the experiment.

No it doesn't as the exact same mathematical structures and relations hold in Spekkens toy model without this conclusion.

 

[charters]

No it doesn't as the exact same mathematical structures and relations hold in Spekkens toy model without this conclusion.

Can you explain this or give a source then? All I see is you agreeing to the proposition that Friend can both measure 0 and still tell Wigner he saw 1. I can't understand how you could possibly explain this without having two totally disjoint versions of Friend, in a way more extreme than MWI.

 

[DarMM]

Can you explain this or give a source then? All I see is you agreeing to the proposition that Friend can both measure 0 and still tell Wigner he saw 1. I can't understand how you could possibly explain this without having two totally disjoint versions of Friend, in a way more extreme than MWI.

An explanation within Spekkens model is here:
https://www.physicsforums.com/threa...ncomplete-comments.966033/page-3#post-6152735

 

[charters]

An explanation within Spekkens model is here:
https://www.physicsforums.com/threa...ncomplete-comments.966033/page-3#post-6152735

I don't see how this is relevant. In that post, you say a state |00> is "compatible with the above use of a superposition by the superobserver" |000> + |111>. This was never in issue. The claim you agreed to here is that |00> is further compatible with |111> alone, or that is at least how I read #127.

 

[DarMM]

I don't see how this is relevant. In that post, you say a state |00> is "compatible with the above use of a superposition by the superobserver" |000> + |111>. This was never in issue. The claim you agreed to here is that |00> is further compatible with |111> alone, or that is at least how I read #127.

If you look at my post and know how measurements work in Spekkens model that is also true. If you don't know the details of measurements in Spekkens model I can go through the details here.

 

[charters]

If you look at my post and know how measurements work in Spekkens model that is also true. If you don't know the details of measurements in Spekkens model I can go through the details here.

I reread your post and the measurement subsection the wikipedia entry for Spekkens model, and I can't see how it possibly allows F to get |00> and W to get |111> (absent the solipsist/single user premise Felline discusses). So I'd appreciate the details.

 

[DarMM]

I reread your post and the measurement subsection the wikipedia entry for Spekkens model, and I can't see how it possibly allows F to get |00> and W to get |111> (absent the solipsist/single user premise Felline discusses). So I'd appreciate the details.

No worries I'll try to put it up later today.

 

[DarMM]

I drop normalization here. I think I got confused at one point, so I will start again.

So first do you agree there is no problem with Wigner's measurements in the $\{|000\rangle,|111\rangle\}$ basis and the friend obtaining outcomes like $|00\rangle$?

This is no more a problem than you would have with two states in statistical mechanics being used at two different levels. The statistics match, both obtaining each outcome 50% of the time. One need only reason that each time the friend gets $|00\rangle$ Wigner will get $|000\rangle$ and similarly for $|11\rangle$. Wigners "uncollapsed" probability reflects only his ignorance of what has occured.

It is in fact measurements along other bases like $\{|000\rangle + |111\rangle, |000\rangle - |111\rangle\}$ demonstrating inteference that are the problem.

 

[charters]

One need only reason that each time the friend gets |00⟩|00⟩|00\rangle Wigner will get |000⟩|000⟩|000\rangle and similarly for |11⟩|11⟩|11\rangle. Wigners "uncollapsed" probability reflects only his ignorance of what has occured.

Yes I agree with this of course, but this is not what you were suggesting before. You were saying in a run when F gets |00>, W can get |111> and furthermore that this does not imply a single user/solipsism interpretation. This was what you suggested to undermine Felline's argument. So, to be clear, 1) are you no longer making this claim and 2) if not, where is your disagreement with Felline?

I will also mention I spent some time with Spekkens' original paper yesterday, and I would caution against drawing any conclusions about a QBist or Bub type view based on what works in Spekkens toy model. The latter handles Wigner's Friend in the same manner as a hidden variables approach, and it is still an ontological model at heart. The defective interpretations are these fully non-ontological, informational ones.

 

[DarMM]

Yes I agree with this of course, but this is not what you were suggesting before. You were saying in a run when F gets |00>, W can get |111> and furthermore that this does not imply a single user/solipsism interpretation. This was what you suggested to undermine Felline's argument. So, to be clear, 1) are you no longer making this claim and 2) if not, where is your disagreement with Felline?

As I said I got confused about what we were discussing. I'm aware of how Spekkens model differs.

So as that we can focus the discussion and so that I am not discussing the wrong thing, what to you is the point Felline makes that refutes these views?

 

[charters]

As I said I got confused about what we were discussing. I'm aware of how Spekkens model differs.

So as that we can focus the discussion and so that I am not discussing the wrong thing, what to you is the point Felline makes that refutes these views?

These views being Bub's type of view?

 

[DarMM]

These views being Bub's type of view?

Primarily, although if you wish to include QBism that is fine as well.

 

[charters]

Primarily, although if you wish to include QBism that is fine as well.

The problem is F and W don't agree whether F gets entangled with the qubit or causes a collapse. In the former case, the state after F measures the qubit is (4) on pg 7 of Felline. In the latter the state is either (5) or (6). These behave differently "at the second beamsplitter" and affect W's measurement on the +/- or "ok/fail" basis. Observers who share a reality can't disagree about this.

But I stress this is only a provisional problem, not a knockout inconsistency in QT that makes it un-usable. It can be cured in various ways. At least some QBists pay the price of accepting QT as a single user theory, and adopting a general worldview along these lines. Spekkens, Bohmians, TSVF go to hidden variables. MWI and GRW have their obvious answers. But the pied piper has to be paid in some way. The neo-Copenhagen/informational folks seem to deny the existence of price they pay (single user) so I am reluctant to credit them with having a tenable position by imputing one of the acceptable cures.

 

[DarMM]

The problem is F and W don't agree whether F gets entangled with the qubit or causes a collapse. In the former case, the state after F measures the qubit is (4) on pg 7 of Felline. In the latter the state is either (5) or (6). These behave differently "at the second beamsplitter" and affect W's measurement on the +/- or "ok/fail" basis. Observers who share a reality can't disagree about this.

Okay let us stick to Spekkens model for the moment. It can be seen in that model that Wigner uses a state like $|000\rangle + |111\rangle$ but this is not in conflict with the $|00\rangle$ of the friend. I agree with Baumann in the paper you linked with above that the friend would be wrong to conclude that the state of the entire lab is $|000\rangle$.

Now how does the use of $|000\rangle + |111\rangle$ by Wigner and $|00\rangle$ by the friend imply solpsism of some form?

 

[charters]

Now how does the use of |000⟩+|111⟩|000⟩+|111⟩|000\rangle + |111\rangle by Wigner and |00⟩|00⟩|00\rangle by the friend imply solpsism of some form?

It doesn't. The problem is when Wigner measures on the +/- basis. The state after F measures, but before the path recombination is either

W says: |00>+|11> ⊗|ready to measure >

or

F says: |00>⊗|ready to measure >

After (attempted) recombination, these become:

W says: |0+1>⊗|F's brain erased>⊗|+>

or

F says: |00+>+|00->

W says he never gets |->, F says W does. F rejects the premise that (properly) wiping his brain restores the original state of the qubit, W assumes it does. If both these people are correct, they don't share a reality.

 

[DarMM]

Sorry perhaps I'm missing something. Wigner and the Friend have the same number of qubits there. Wigner should have three (system, device, lab) and the friend two (system, device).

 

[charters]

Sorry perhaps I'm missing something. Wigner and the Friend have the same number of qubits there. Wigner should have three (system, device, lab) and the friend two (system, device).

The tension arises when Friend makes a prediction about what Wigner will measure. Are you claiming this is impossible?

 

[DarMM]

The tension arises when Friend makes a prediction about what Wigner will measure. Are you claiming this is impossible?

For the friend to make predictions about what Wigner will measure? No, but what is the tension? He would reason his own experiences permit the use of $|00\rangle$ in future predictions about the system and the device. However he would reason the superposed state is the correct one for Wigner to use rather than $|000\rangle$. Neo-Copenhagenists such as Richard Healey and others agree that the superposed state is correct for measurements on the entire lab that Wigner is capable of. How is this in tension with the $|00\rangle$ for the device and system?

 

[charters]

For the friend to make predictions about what Wigner will measure? No, but what is the tension? He would reason his own experiences permit the use of $|00\rangle$ in future predictions about the system and the device. However he would reason the superposed state is the correct one for Wigner to use rather than $|000\rangle$. Neo-Copenhagenists such as Richard Healey and others agree that the superposed state is correct for measurements on the entire lab that Wigner is capable of. How is this in tension with the $|00\rangle$ for the device and system?

If the device-system is in |00>, it does not behave the same under recombination as |00>+|11>. Friend can't have it both ways. Either he thinks the state collapsed to |00> in which case he predicts no interference effects from the |11> term under recombination, or he thinks the device/system got entangled, in which case he does predict interference effects. Friend can even pass a note to Wigner with this prediction on it as it does not depend on whether Friend saw 0 or 1.

Or, if Friend's state is only valid up to Wigner's choice to do a recombination experiment, at which point Friend has to switch to using Wigner's state (this being one of Baumann & Brukner's ideas to resolve the tension), then Friend is admitting they need MWI or HV type reasoning, at least in some cases/for some predictions. At this point, they might as well just apply this full time, since it will work in all cases.

 

[DarMM]

If the device-system is in |00>, it does not behave the same under recombination as |00>+|11>

You're dropping a system here which is crucial. The friend is using $|00\rangle$ (note two systems) and Wigner is using $|000\rangle + |111\rangle$ (note three systems). The question concerns what is the conflict between the $|00\rangle$ used by the friend and the $|000\rangle + |111\rangle$ used by Wigner.

Wigner does not use $|00\rangle + |11\rangle$

 

[charters]

You're dropping a system here which is crucial. The friend is using $|00\rangle$ (note two systems) and Wigner is using $|000\rangle + |111\rangle$ (note three systems). The question concerns what is the conflict between the $|00\rangle$ used by the friend and the $|000\rangle + |111\rangle$ used by Wigner.

Wigner does not use $|00\rangle + |11\rangle$

This notational difference doesn't matter. The physical experiment is equivalent to Wigner sending Friend's entire lab through an interferometer. The interferometer has 2 exit ports labelled |+> and |->. The question to both parties is simply the statistics for when the lab arrives at each exit. W says it is 100% at |+> when he does a recombination. F says it will be 50/50, if he genuinely believes his measurement collapsed the state. So either someone discovers he is wrong, or they must live in disjoint realities. Friend is wrong = many worlds/hidden variables. Wigner is wrong = GRW. Disjoint realities = Copenhagen/QBism

 

[DarMM]

This notational difference doesn't matter...F says it will be 50/50, if he genuinely believes his measurement collapsed the state

It does, because it is central to how QBism and Neo-Copenhagenism resolve this point. Why would the friend using the $|00\rangle$ state after his measurement believe the outcome of such an interferometry experiment on the entire lab to have 50:50 odds? To obtain these odds for the entire lab he'd have to ascribe it the state $|000\rangle$, but why would he do this on the basis of the $|00\rangle$ state for the device and system alone? He didn't observe the lab down to the atomic level.