A Realization of a Basic Wigner's Friend Type Experiment

[DarMM]

E.g. if the particle is prepared in the state
$$\frac{1}{\sqrt{2}}\left(|0\rangle + |1\rangle\right)$$
as is usually the case, then the probabilities will all be 0.25, but the decoherence functional will (I think) report interference. E.g. $\mathcal{D}( \left[ 0\right]\otimes\left[W_{+}\right] , \left[ 1\right]\otimes\left[W_{+}\right]) = 0.25$ If, however, the particle is prepared in a state $|0\rangle$, then the interference all goes away and the family becomes consistent (with a probability of 0.5 for two and 0 for the others)

To check my reasoning I got that they don't have interference because the chain kets are proportional to $|0,+\rangle$ and $|1,+\rangle$ respectively in the Wigner-Friend product space, which are orthogonal. Not confident in by reasoning though, these encapsulated histories don't have much literature behind them at the moment.

 

[vanhees71]

Then I don't understand, where the problem is. I thought Wigner's friend is about an apparent contradiction, which however is resolved when the proper notion of states:

https://en.wikipedia.org/wiki/Wigner's_friend

Of course, what's wrong is the collapse postulate!

 

[Morbert]

To check my reasoning I got that they don't have interference because the chain kets are proportional to $|0,+\rangle$ and $|1,+\rangle$ respectively in the Wigner-Friend product space, which are orthogonal. Not confident in by reasoning though, these encapsulated histories don't have much literature behind them at the moment.

Ah ok. Would you also need to include $|0,-\rangle$ and $|1,-\rangle$ for completeness? ([edit]-actually nvm that's not the problem, I have to think about it). I just used $|+\rangle$ and $|-\rangle$ which might not have been kosher. And yeah they're super weird to work with. A lot of intuition disappears.

 

[DarMM]

Ah ok. Would you also need to include $|0,-\rangle$ and $|1,-\rangle$ for completeness? ([edit]-actually nvm that's not the problem, I have to think about it). I just used $|+\rangle$ and $|-\rangle$ which might not have been kosher. And yeah they're super weird to work with. A lot of intuition disappears.

Yeah I missed them in my original post, but have them in #202 because I think they are also orthogonal. I'm not sure though.

 

[DarMM]

Then I don't understand, where the problem is. I thought Wigner's friend is about an apparent contradiction, which however is resolved when the proper notion of states:

What's the resolution though? What do you mean by the "proper notion of states" and how does it resolve the issue?

Wigner's friend has several resolutions but they are interpretational dependent. Can you state explicitly what your resolution is?

 

[DarMM]

Of course, what's wrong is the collapse postulate!

This is wrong in my opinion. Despite the problems with physical collapse in other cases, it offers a clear resolution to Wigner's friend. So it's not what's wrong in this case.

It's hard (but not impossible) to come up with a solution that avoids collapse without being Bohmian Mechanics or Many Worlds. That's why I'm interested to hear your resolution.

 

[vanhees71]

Of course I refer to the minimal interpretation. There's no contradiction between the probabilities you get from either using the pure state including Wigner's friend's pointer states and the reduced density matrices that describe the spin alone.

Of course, choosing subensembles according to Wigner's friend measurement outcomes changes the statistics due to entanglement. It's the same thing we discuss again and again concerning measurements on photon-Bell states, including "teleportation", "entanglement swapping", "delayed choice", and all that.

In short: Everywhere, where the collapse interpreters say "the state is collapsed" you have to concretely state what's measured: The "collapse" usually is just the selection of a subensemble depending on a measurement. In the minimal interpretation all these issues resolve in looking at the right ensembles and subensembles prepared and measured in the concrete experiments.

In the above example you say

Wigner has prepared his system in the state
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|0 \rangle +|1 \rangle).$$
At the same time you say, Wigner's friend has prepared the system in the state
$$|\Psi \rangle =\frac{1}{\sqrt{2}} (|0 \rangle \otimes |0 \rangle + |1 \rangle \otimes |1 \rangle).$$
That's a contradiction in adjecto, because if the latter preparation procedure is done, for Wigner's system the state is the reduce density matrix, tracing out the friend's pointer state, i.e.,
$$\hat{\rho}_W=\frac{1}{2} \hat{1}.$$
As long as W measured only the observable given by the corresponding basis, i.e., the observable described by $$\hat{O}=|1 \rangle \langle 1|,$$
of course both descriptions are compatible, because both predict for W's outcome of a measurement of $O$ that he gets with 50% probability 0 and with 50% probability 1.

However, both states are of course not the same, and W could figure out that his system was not prepared in the pure state but in the mixture, if F had in fact prepared the system in the state $|\Psi \rangle$.

The point is that F cannot prepare the system+pointer state without disturbing the system itself. According to QT she cannot be a godlike creature that can determine the state of the system + pointer without disturbing the system.

I'm not so sure, where the resolution of this Frauchiger et al example really is, because I find their paper very confusing, but I'm pretty sure that there cannot be insconsistencies of the QT formalism within the minimal interpretation. I'm pretty inclined to believe in the argument by Aaronson. At least this was my first suspicion when reading the Frauchiger paper, but not being able to point my finger on the specific point of the argument without taking a lot of efford to translate the writing into math ;-)):

But I reject an assumption that Frauchiger and Renner never formalize. That assumption is, basically: “it makes sense to chain together statements that involve superposed agents measuring each other’s brains in different incompatible bases, as if the statements still referred to a world where these measurements weren’t being done.” I say: in QM, even statements that look “certain” in isolation might really mean something like “if measurement X is performed, then Y will certainly be a property of the outcome.” The trouble arises when we have multiple such statements, involving different measurements X1, X2, …, and (let’s say) performing X1 destroys the original situation in which we were talking about performing X2.

https://www.scottaaronson.com/blog/?m=201809

He rightfully quotes Peres with his famous dictum: "Unperformed measurements have no results."

 

[DarMM]

Wigner has prepared his system in the state
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|0 \rangle +|1 \rangle).$$
At the same time you say, Wigner's friend has prepared the system in the state
$$|\Psi \rangle =\frac{1}{\sqrt{2}} (|0 \rangle \otimes |0 \rangle + |1 \rangle \otimes |1 \rangle).$$
That's a contradiction in adjecto, because if the latter preparation procedure is done, for Wigner's system the state is the reduce density matrix, tracing out the friend's pointer state, i.e.,
$$\hat{\rho}_W=\frac{1}{2} \hat{1}.$$
As long as W measured only the observable given by the corresponding basis, i.e., the observable described by $$\hat{O}=|1 \rangle \langle 1|,$$
of course both descriptions are compatible, because both predict for W's outcome of a measurement of $O$ that he gets with 50% probability 0 and with 50% probability 1.

To be clear on two things:

1. The friend is the person in the lab measuring the system. Wigner is the one outside.
2. I'm only talking about the basic Wigner's friend, not Frauchiger-Renner which is a more advanced version

What you discuss above is fine if Wigner measures the friends device or the system itself, but not if he measures the friend's entire lab. There's no contradiction in the case you've discussed for the reasons you've mentioned, but it doesn't resolve the case of measuring the entire lab state which is what the paradox is about.

The whole point is that Wigner has access to observables for the whole lab that are complimentary to the fact that the friend performed a measurement. That's the case you have to deal with.

 

[DarMM]

Wigner has prepared his system in the state
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|0 \rangle +|1 \rangle).$$
At the same time you say, Wigner's friend has prepared the system in the state
$$|\Psi \rangle =\frac{1}{\sqrt{2}} (|0 \rangle \otimes |0 \rangle + |1 \rangle \otimes |1 \rangle).$$
That's a contradiction in adjecto

I only realized this now. This isn't a contradiction because you have the scenario confused.

The friend prepares the state in:
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|0 \rangle +|1 \rangle).$$

To Wigner outside this corresponds to the initial state:
$$\frac{1}{\sqrt{2}}\left(|\uparrow\rangle + |\downarrow\rangle\right)\otimes|D_{0}\rangle\otimes |L_{0}\rangle$$

Thus tracing gives you the superposed state. This is the preparation and there is no contradiction here.

The difficulty comes after the measurement as I discussed above in #201

 

[vanhees71]

To be clear on two things:

1. The friend is the person in the lab measuring the system. Wigner is the one outside.
2. I'm only talking about the basic Wigner's friend, not Frauchiger-Renner which is a more advanced version

What you discuss above is fine if Wigner measures the friends device or the system itself, but not if he measures the friend's entire lab. There's no contradiction in the case you've discussed for the reasons you've mentioned, but it doesn't resolve the case of measuring the entire lab state which is what the paradox is about.

The whole point is that Wigner has access to observables for the whole lab that are complimentary to the fact that the friend performed a measurement. That's the case you have to deal with.

What do you mean by "entire lab state". Then also the rules of QM apply. I don't see the paradox (at least not within the minimal statistical interpretation). As explained in the Wikipedia version, the two-spin state (let's call them Alice and Bob, i.e., A is measuring the spin in the lab and B entangles it with another spin ("pointer")) is all the fuss is about, and that I've discussed above.

It's simply wrong to say, when in this case you have
$$|\Psi \rangle =\frac{1}{\sqrt{2}}(\alpha |0 \rangle_A \otimes |0 \rangle_B + \beta |0 \rangle_A \otimes |0 \rangle_B),$$
then A's spin is described by the pure state
$$|\psi \rangle = \frac{1}{\sqrt{2}} (\alpha |0 \rangle_A + \beta | 0 \rangle_A),$$
but it's in a mixed state you get from taking the partial trace over B from $$\hat{\rho} = |\Psi \rangle \langle \Psi|$$.

 

[DarMM]

What you're describing there is not related to the paradox. I'm not saying that when the two particle system is in a pure state a one particle subsystem is in a pure state.

That is obviously wrong, but I'm not saying it nor does it really relate to the paradox.

Let me put it this way, most of the people working in Foundations are not complete idiots. The problem is not due to thinking a traced system gives a pure state as that point is obvious and clearly resolved.

 

[vanhees71]

Ok, then where can I find a clear definition of the paradox related to "Wigner's friend".

I'm also not claiming that people working in Foundations are complete idiots. Physicists usually are not... ;-))

 

[DarMM]

Ok, then where can I find a clear definition of the paradox related to "Wigner's friend".

I'm also not claiming that people working in Foundations are complete idiots. Physicists usually are not... ;-))

Don't worry I know you're not, it's just to summarise that the paradox is not so simple. There's a good description of the paradox in this paper section B:
https://arxiv.org/abs/1804.00749

 

[vanhees71]

Ehm, is this journal "entropy" ok? I was a bit wondering recently (not related with the article you quote here, which I don't know yet).

 

[DarMM]

Ehm, is this journal "entropy" ok? I was a bit wondering recently (not related with the article you quote here, which I don't know yet).

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.

 

[PeterDonis]

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]

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]

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]

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]

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]

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 occurred for the macroscopic degrees of freedom, but not the lab's microscopic dofs.

 

[vanhees71]

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]

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]

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.

 

[akvadrako]

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]

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]

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]

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.