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

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Superobservers shouldn't be allowed to be outside the rules of QT
I don't think anyone claims they are. But making the measurement I described would require that the superobserver can maintain quantum coherence over an entire human brain. That doesn't seem practically possible, and depending on what (if any) more fundamental theory we end up finding that underlies QFT in its current form, it might end up not even being possible in principle.
 

DarMM

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I don't think anyone claims they are. But making the measurement I described would require that the superobserver can maintain quantum coherence over an entire human brain. That doesn't seem practically possible, and depending on what (if any) more fundamental theory we end up finding that underlies QFT in its current form, it might end up not even being possible in principle.
Omnes gives calculations in Chapter 7 of his book I mentioned that make it seem pretty implausible that it could be done, even in non-relativistic QM.

I could be wrong about this, but I thought Wigner's friend is the most "stark" when applied to human beings, but that the paradox is still there even with automated measuring devices. It seems to be more a paradox about macroscopic facts. Of course historically Wigner's original paper was concerned with consciousness.
 

vanhees71

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I'm not sure. I have been skeptical of it myself at times. Several good people publish in it and I've never seen "crank" material, but some papers are not far above lecture notes, i.e. they're not wrong but they seemed basically just a nice way to present something already known.

I just link that paper because Brukner is a good researcher and his explanation is correct and succinct.
Well, this paper seems to be good too. It's also nothing wrong with journals providing different approaches to explain well-known textbook material. One of my favorites of this kind is the American Journal of Physics.

Concerning Brukner's paper, I think I've found, where the Wigner's-friend-argument deviates from standard QT, namely in Eq. (2). He claims that when F measures her spin and gets a definite answer, then W describing the F's spin, his pointer spin associates simply with the knowledge that F has a definite outcome from the measurement is the product state ##|\Psi \rangle \otimes |\text{"I have a definite outcome"} \rangle_M##, which is just an additional unrelated and uncorrelated observable living in yet another extension of the spin+pointer Hilbert space, but according to standard QT that's not the case. Knowing that F has a definite outcome having measured her spin, but W not knowing which outcome she found, would be the corresponding "decohered" state, i.e., in the case of the paper
$$\hat{\rho}=\frac{1}{2} (|z_+,F_{z_+} \rangle \langle z_+,F_{z_+}| + |z_-,F_{z_-} \rangle \langle z_-,F_{z_-}|).$$
Then, there's of course no contradiction or paradox whatsoever.
 

DarMM

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That's if you measure the macroscopic degrees of freedom alone and is certainly the resolution in that case.

What about if Wigner measures the entire lab and thus will not have decoherence to generate the mixed state.
 

vanhees71

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If Wigner measures the entire lab he has to use some device to do that. This device/measurement apparatus has to ensure the decoherence to store the result of its measurement. Bohr was right with this statement, though wrong in claiming you'd need a "cut" between classical and quantum dynamics. If there's anything efficient in nature than its decoherence, and it can be understood from quantum dynamics. This Bohr couldn't know in 1927/28, when he gave his (in?)famous Como Lecture.
 

DarMM

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If Wigner measures the entire lab he has to use some device to do that. This device/measurement apparatus has to ensure the decoherence to store the result of its measurement.
True, but that still doesn't resolve the issue. That's just decoherence needed to record the measurement, but Wigner recording an outcome was never an issue. The decoherence I'm referring to is that which has taken place within the lab.

The point is that the entire lab is in a superposed state and thus Wigner can measure the interference terms using an appropriate observable. Decoherence has already occured for the macroscopic degrees of freedom, but not the lab's microscopic dofs.
 

vanhees71

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For the measurement within the lab the same argument applies. If F makes a measurement with a definite outcome, she has to couple her spin to an apparatus being able to do the that measurement. So W has to take into account that measurement apparatus too. For sure it's not sufficient to discuss this situation with the two spins alone, if you don't want to use the FAPP argument, I used above, but describe measurements, be it by W or F, by taking into account only the single spin in the lab or the two spins by F and W, is not sufficient.

The point is that this paradox only occurs when you falsely assume you could describe a measurement as if nothing would happen to the measured system. That's approximately true for many "classical" measurements on macroscopic systems, where the influence of the measurement apparatus on the measured macroscopic, relevant degrees of freedom can be made negligibly small. That's not the case for single particles or other "quantum" measurements.
 

DarMM

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For the measurement within the lab the same argument applies. If F makes a measurement with a definite outcome, she has to couple her spin to an apparatus being able to do the that measurement. So W has to take into account that measurement apparatus too.
There was never any question about whether the lab device undergoes decoherence. As I said above it clearly does. And W includes the device in his account. Also the paradox isn't avoided by a realistic treatment of the device. Let me just focus on the core of the paradox.

Do you think W, who is completely isolated from the lab, is justified to model the time evolution of the entire lab (not some macroscopic subsystem) with a unitary evolution?
 

vanhees71

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As I repeatedly said, the contradiction is already in the very assumption: W cannot be completely isolated from the lab, if he wants to gain information what's inside the lab. To understand, how a measurement outcome, including sufficient stable "storage" implies that you have to treat the measurement device as a macroscopic subsystem to have decoherence and irreversibility of the measurement result. On this account Bohr was right, I only don't think that for this argument you need to envoke a "quantum-classical cut". The dynamics is completely quantum. It's only impossible to follow the microscopic details of macroscopic systems, and that's why the relevant macroscopic degrees of freedom always couple to some "bath" of very many microscopic degrees of freedom (or an "environment") and the situation has to be treated as an open quantum system.
 
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You are denying an assumption, but that assumption is reasonable if you consider a future quantum computer which can simulate observers. Such a computer must be effectively isolated from the outside, yet also be measurable along any specific basis.

Some people do suggest such a large quantum computer is impossible but it’s a rather strong claim to state with any certainty.
 

vanhees71

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Of course for the quantum computer to operate you have to isolate it sufficiently from "the environment", which is evil due to decoherence. But that's fine, though technically a hard challenge. Of course, if you finally want to read out the result you have to couple it to "the environment" somehow to do so. I guess, as soon as you read out the result, the entangled state of the computer is destroyed, but that's ok since you just read out the result and stored it, the quantum computer did its job as wanted.

In other words, as soon as I want to know the outcome of the calculation, I have to measure some appropriate observable, and thus I have to couple some measurement device (here used as the "read-out" device) to the quantum computer.

Isn't this argument also behind the idea of quantum cryptography? Usually the argument is: Using entanglement makes it from fundamentals principle impossible to interfere with the entangled system without destroying the entanglement, and this also destroys the message, i.e., the Alice and Bob immediately realize that Eve is watching their conversation.

Given the amazing speed with which quantum optics (in the extended AMO sense) develops today, I'm not so pessimistic that in the near future there are really big quantum computers available.
 

DarMM

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As I repeatedly said, the contradiction is already in the very assumption: W cannot be completely isolated from the lab, if he wants to gain information what's inside the lab
Nothing in the set up assumes he remains isolated when he makes the measurement.
 

DarMM

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I think the issue in Wigner's friend is a contradiction between macroscopic outcomes, presumed unitary reversibility and certain quantum correlations such as those in CHSH set up or the GHZ state etc

Assume super-quantum correlations as an approximation. Two observers ##A## and ##B## and two observables ##X## and ##Z## with dichotomic outcomes (##0## and ##1##)

We have the correlation conditions:
##X_A####Z_A##
##X_B####=####=##
##Z_B####=####\neq##

Meaning if ##A## measures ##X## and ##B## measures ##X## the results will be equal.

Assume ##A## and ##B## measure ##X## and ##X## respectively and both obtain the outcome ##0##. Then two superobservers ##W## and ##Y## reverses their measurements via some unitary and measure ##Z_{W}## and ##Z_{Y}## respectively obtaining outcomes ##1## and ##0##.

I'll label all four measurements as ##X_{A}, X_{B}, Z_{W}, Z_{Y}##. There exist reference frames where ##X_{B}## and ##Z_{W}## coexist before the reversal and similarly for ##X_{A}## and ##Z_{Y}##.

However if you look at the correlation matrix above the ##X_{B}## and ##Z_{W}## pair break the correlations, they got ##X_{B} = 0## and ##Z_{W} = 1##.

Thus assuming actual objective outcomes to the experiments and reversals leads to a contradiction for certain entangled states.

In essence superobervers and definite outcomes allow outcomes for all observables involved in a Bell-type proof to take a value, thus there is a common sample space and so at least one marginal must be classical and not match the quantum predictions.

You get a different Wigner's friend set up depending on what type of entangled state you choose to "wrap" the superobservers around, e.g. Hardy, GHZ, CHSH etc.

Of course there are a few ways out of this, but that's the basic contradiction.

I'm not aware of a difficulty or contradiction (for any interpretation) in the most basic Wigner's friend scenario since there we do not have entanglement and thus no statistics in direct contradiction with outcomes.
 

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