Undergrad Quantum theory - Nature Paper 18 Sept

[stevendaryl]

Ok, if there is only one copy of the state than the experiment is no more mysterious than three polarizers experiment. When $\overline{W}$ measures the state and gets $|\overline{ok}\rangle$ the state of the system he gets is updated from $|fail\rangle$ to $|\frac{+1}{2}$ and then $W$ measuring this system obviously can get $|ok\rangle$ half of the time.
I'm not sure however what happens with $\overline{F}$ and $F$ observers and their memories.

The way that the thought experiment is described, it seems that if $\overline{W}$ gets $\overline{ok}$ and $W$ gets $ok$, then both $F$ and $\overline{F}$ are in indefinite, Schrodinger's Cat type states, a superposition of two different memory states.

 

[Strilanc]

Where does performing their two measurements require uncomputing their thoughts and measuring a single qubit. I would have thought for each of them independently they are simply measuring an alternate outcome basis for the respective labs under their control. However they themselves are left alone.

When I said "Alice and Bob" I was referring to the people being placed under superposition, not the people triggering the measurements. Sorry if that was confusing.

If you are referring to $\overline{F}$ and $F$ instead, even there is one uncomputing their thoughts? I would have thought for example that $W$ measures some strange observable $Q$ that places the $L$ lab containing $F$ into the $\{|okay\rangle,|fail\rangle\}$ basis. However I'm not sure how that corresponds to uncomputing $F$'s thoughts measuring a qubit and recomputing them. Again most likely I am missing something.

Technically speaking, you could implement the measurement described by the paper in many ways. But in these kinds of confusing paradoxical situations, it is important to be concrete about the details. The devil is literally in the details (that's a Maxwell's demon pun).

I happen to think the simplest way to implement the described measurement is to uncompute back to the state where the relevant information is in a trivial form (just one qubit), do the measurement there, then recompute. After all, you're already loading Alice and Bob into a quantum computer capable of simulating time forward while maintaining complete coherence. In that situation it's trivial to run simulated time backwards: take your forward-time circuit, invert each gate, and run them in the reverse order.

That being said, even if you use a more complicated strategy to perform the measurement it's still equivalent to uncomputing+measuring+recomputing. So I think it's fine to use an argument based on that interpretation. It's a specific case of "the measurement perturbs the system, so your previous conclusions become invalid.".

 

[DarMM]

I happen to think the simplest way to implement the described measurement is to uncompute back to the state where the relevant information is in a trivial form (just one qubit), do the measurement there, then recompute. After all, you're already loading Alice and Bob into a quantum computer capable of simulating time forward while maintaining complete coherence. In that situation it's trivial to run simulated time backwards: take your forward-time circuit, invert each gate, and run them in the reverse order.

I see now, thanks. I think this captures Bub's objection. He would say that if $F$ and $\bar{F}$ are really in a quantum computer then no "measurements" occur, i.e. $F$ doesn't obtain anything. In essence it would mean they lie behind the Heisenberg cut, no actual macroscopic events are associated with them.

 

[Strilanc]

I see now, thanks. I think this captures Bub's objection. He would say that if $F$ and $\bar{F}$ are really in a quantum computer then no "measurements" occur, i.e. $F$ doesn't obtain anything. In essence it would mean they lie behind the Heisenberg cut, no actual macroscopic events are associated with them.

If they don't "lie behind the Heisenburg cut", it's impossible to implement the measurement that is described by the paper (or rather, the system will have decohered in a way that changes the statistics of the output).

 

[DarMM]

If they don't "lie behind the Heisenburg cut", it's impossible to implement the measurement that is described by the paper (or rather, the system will have decohered in a way that changes the statistics of the output).

Exactly and thus when they do lie behind the cut he would claim you can't say such a thing as "$F$ obtained $z=+\frac{1}{2}$" and thus all such reasoning is invalid.

In other words he is saying the existence of "conclusions" is only valid in a scenario where the measurement can't be implemented.

He's not saying the measurement could be implemented even when they aren't behind the cut. He's more saying in order to have conclusions, you need to not lie behind the cut, which then prevents the measurement described for $\bar{W}$.

Although Bub's reasoning is not meant to be "interpretation neutral" where Aaranson's is to a larger degree. It's an additional objection based on a Neo-Copenhagen viewpoint, with that interpretation's specific explanation of decoherence.

 

[S.Daedalus]

OK, there's a bit I don't get, I think. So the final state is:

$|final\rangle = \frac{1}{\sqrt{3}} |\overline{h}\rangle |-\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |-\frac{1}{2}\rangle$

Expressed in the ok/fail-basis of $\overline{W}$, this is:

$|final\rangle = \frac{2}{\sqrt{6}}|\overline{fail}\rangle|-\frac{1}{2}\rangle + \frac{1}{\sqrt{6}}|\overline{fail}\rangle|\frac{1}{2}\rangle - \frac{1}{\sqrt{6}}|\overline{ok}\rangle|\frac{1}{2}\rangle$

After $\overline{W}$ measures and obtains the $\overline{ok}$-outcome, only the term $|\overline{ok}\rangle|\frac{1}{2}\rangle$ survives. If we express that again in the $\{|\overline{h}\rangle,|\overline{t}\rangle\}$-basis, we get:

$|\overline{w}=\overline{ok}\rangle=\frac{1}{\sqrt{2}}(|\overline{h}\rangle|\frac{1}{2}\rangle - |\overline{t}\rangle|\frac{1}{2}\rangle)$

But this is not a state in which we can claim that $\overline{F}$ predicts that W observes 'fail', as either outcome is possible. Consequently, if $\overline{F}$ applies quantum mechanics to themselves, they should rather reason that if $\overline{W}$ applies their measurement and observes the $\overline{ok}$-outcome, then either measurement outcome of W's measurement is possible, so no contradiction arises. Alternatively, $\overline{W}$ is wrong to believe that their inference from the measurement outcome still holds after the measurement has been performed, since that inference depends on the structure of the pre-measurement state.

The only way of making this seem reasonable, it looks to me, is if $\overline{F}$ supposes that their measurement (of the coin) 'collapses' the state to 'tails'; but that's just the same as the original Wigner's Friend-thought experiment, where if the friend were to make that assumption, they'd predict (wrongly) that a suitable experiment involving the entire lab would show no interference. So if F supposes that W observes 'fail', that just seems to me to be a misapplication of quantum mechanics in the same way as Wigner's Friend's prediction of no interference would be.

 

[PeterDonis]

He would say that if $F$ and $\bar{F}$ are really in a quantum computer then no "measurements" occur

Another way of putting this is that, if all of the interactions are reversible, then no measurement occurs; a measurement requires an irreversible interaction.

 

[msumm21]

Trying to understand some definitions in this paper:
https://www.nature.com/articles/s41467-018-05739-8

Specifically page 3, box 1: "At n:20 Wbar measures Lbar wrt a basis containing okbar"

okbar is defined in table 2 in terms of hbar and tbar which are not defined as far as I can tell. I'd guessed those were something like the heads and tails states of R, but that doesn't seem to pan out. Anyone know what okbar is?

 

[zonde]

okbar is defined in table 2 in terms of hbar and tbar which are not defined as far as I can tell.

Under Fig.2 there is description from which one can guess that $|\bar{h}\rangle$ and $|\bar{t}\rangle$ are states of the coin:
$\bar{F}$ tosses a coin and, depending on the outcome r, polarises a spin particle S in a particular direction.

I'd guessed those were something like the heads and tails states of R, but that doesn't seem to pan out.

You will have to say something more. What does not seem to pan out?

 

[atyy]

Trying to understand some definitions in this paper:
https://www.nature.com/articles/s41467-018-05739-8

Specifically page 3, box 1: "At n:20 Wbar measures Lbar wrt a basis containing okbar"

okbar is defined in table 2 in terms of hbar and tbar which are not defined as far as I can tell. I'd guessed those were something like the heads and tails states of R, but that doesn't seem to pan out. Anyone know what okbar is?

Maybe try stevendaryl's post #14 and see if that helps you out.

 

[stevendaryl]

OK, there's a bit I don't get, I think. So the final state is:

$|final\rangle = \frac{1}{\sqrt{3}} |\overline{h}\rangle |-\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |-\frac{1}{2}\rangle$

Expressed in the ok/fail-basis of $\overline{W}$, this is:

$|final\rangle = \frac{2}{\sqrt{6}}|\overline{fail}\rangle|-\frac{1}{2}\rangle + \frac{1}{\sqrt{6}}|\overline{fail}\rangle|\frac{1}{2}\rangle - \frac{1}{\sqrt{6}}|\overline{ok}\rangle|\frac{1}{2}\rangle$

After $\overline{W}$ measures and obtains the $\overline{ok}$-outcome, only the term $|\overline{ok}\rangle|\frac{1}{2}\rangle$ survives. If we express that again in the $\{|\overline{h}\rangle,|\overline{t}\rangle\}$-basis, we get:

$|\overline{w}=\overline{ok}\rangle=\frac{1}{\sqrt{2}}(|\overline{h}\rangle|\frac{1}{2}\rangle - |\overline{t}\rangle|\frac{1}{2}\rangle)$

But this is not a state in which we can claim that $\overline{F}$ predicts that W observes 'fail', as either outcome is possible. Consequently, if $\overline{F}$ applies quantum mechanics to themselves, they should rather reason that if $\overline{W}$ applies their measurement and observes the $\overline{ok}$-outcome, then either measurement outcome of W's measurement is possible, so no contradiction arises. Alternatively, $\overline{W}$ is wrong to believe that their inference from the measurement outcome still holds after the measurement has been performed, since that inference depends on the structure of the pre-measurement state.

The only way of making this seem reasonable, it looks to me, is if $\overline{F}$ supposes that their measurement (of the coin) 'collapses' the state to 'tails'; but that's just the same as the original Wigner's Friend-thought experiment, where if the friend were to make that assumption, they'd predict (wrongly) that a suitable experiment involving the entire lab would show no interference. So if F supposes that W observes 'fail', that just seems to me to be a misapplication of quantum mechanics in the same way as Wigner's Friend's prediction of no interference would be.

I think you're right. The paradox just boils down to: noncommuting operators can't all be said to have definite values at the same time.

But as I summarized in one of the earlier posts:

1. $\overline{W}$ can conclude: "If I measure $\overline{ok}$, then $F$ must measure $+1/2$.
2. $F$ can conclude: "If I measure $+1/2$, then that implies that $\overline{F}$ measured $\overline{t}$"
3. $\overline{F}$ can conclude: "If I measure $\overline{t}$, then $W$ will measure $fail$"

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

 

[msumm21]

Sorry if I'm re-stating what people have already said earlier in this thread, but isn't there a basic error in the analysis. The author assumes Fbar measures R (the "coin" heads or tails) and subsequently acts on that result, ... but later assumes the state of R was unaffected (back in the init state) when Wbar measures. That's not QM is it? QM says R is in the state pure heads OR pure tails, not the init superposition, right?

Correcting for these mistakes, the point of the paper doesn't pan out, right? E.g. the claim that OKbar implies S is spin up wouldn't hold, so the main conclusion wouldn't hold.

The explanation by stevendaryl earlier (#14) in this thread much appreciated, very clear & concise.

 

[vanhees71]

I think you're right. The paradox just boils down to: noncommuting operators can't all be said to have definite values at the same time.

But as I summarized in one of the earlier posts:

1. $\overline{W}$ can conclude: "If I measure $\overline{ok}$, then $F$ must measure $+1/2$.
2. $F$ can conclude: "If I measure $+1/2$, then that implies that $\overline{F}$ measured $\overline{t}$"
3. $\overline{F}$ can conclude: "If I measure $\overline{t}$, then $W$ will measure $fail$"

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

So to make a long story short: Much ado about nothing! Just check all such "philosophical claims" within the minimal interpretation, i.e., first through out the unobservable balast and then check what to be expected in physics experiments. I think it simply boils down to the suspicion I had after first reading the paper: The assumption of the various systems being isolated from each other but nevertheless measured by each other is simply an oxymoron. The very point of QT is that you cannot neglect the influence of measurements on microscopic systems and thus also in general you are able to prepare states such that incompatible observables have determined values (although there are exceptions, e.g., if preparing the angular momenum of a system in the state $j=0$, all three components of angular momentum (or thus any component of angular momentum) take the determined value $m=0$).

 

[DarMM]

I was thinking about this a bit more, probably doing something dumb, but considering agent $F$, if they get the result $z = +\frac{1}{2}$ they can conclude that $\bar{F}$ got $r = \bar{t}$. Fine.

Now if they think of themselves from $\bar{F}$'s reasoning and apply unitary evolution without any collapse to themselves they get that the state of their lab is:
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|+\frac{1}{2}\rangle_L + |-\frac{1}{2}\rangle_L\right)$$
which is $W$'s $|fail\rangle$ state. Thus $W$ must get $fail$.

However if they think of themselves from what they see in their own lab then either $z = -\frac{1}{2}$ or $z = +\frac{1}{2}$ results correspond to a superposition in the $\{|okay\rangle,|fail\rangle\}$ basis. Thus they would reason that $W$ could get $okay$.

So isn't there already a contradiction with just three observers?

$F$ will reach one conclusion about $W$'s result if he just considers his own experiences in his lab and another conclusion if he considers himself from $\bar{F}$'s model of him as a unitarily evolving superposition without decoherence.

 

[DarMM]

For anybody interested Renato Renner's argument has three forms. The form in the original paper from 2016 (explained in standard language by Bub here: https://arxiv.org/abs/1804.03267), the form from the nature article we have been discussing and a third form due to Luis Masanes.

It is harder to pinpoint errors of this third form in my opinion. Expositions of it are found in section 4 of this paper by Richard Healey:
https://arxiv.org/abs/1807.00421

And also this talk by Matthew Pusey (18:35):


And this lecture by Matthew Leifer (39:44):

 

[Fra]

Nice thread which i largely missed and haven't had time to engage in!

whether quantum theory can, in principle, have universal validity.The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory.

This is a good key question about the consistency of reasoning.

To summarize my opnion I think as quantum theory stands clearly isn't meant to have this universal validity. But this should be no news, is I read things this was implicit already in Bohrs views. Quantum mechanics is essentially _formulated_ with respect to a classical measurement device. Where the classical divide for example means that intercommunication in principle commute. But what happes if two different independent classical measurement devices, perform measurements on the same quantum system is a different thing. And if the two classical devices exchange quantum information then the cut is changed. So I think the contradictions that may emerge are only due to invalid inferences in the chain of reasoning, when mixing different premises in a random way.

But there is a rational incentive for asking questions that current quantum theory doesn't allow. For example how should "quantum theory" in terms of cosmological perspectives understood, if the observer is a system on earth? Asking how an observers in principle should infer and produce expectations of the process of other observers making measurements on each other, is a key way to explore this logic.

This paper to me is an argument for the need to keep working on the foundations of quantum theory to harmonize with different complexity scales, but does not contain any suggetsions. But interpretations isn't the problem, its i think that we need a revised theory. All we know is that this theory should reproduce quantum theory in the small system; dominant large observer limit. Essentially when we look at the scattering matrix. I think most agrees that talking about Scattering matrix for complex systems that are larger than the observer or even cosmologies from the perspective of Earth makes no sense, beacuse there is no way to set that experiment up. Even the gedanken experiments in this case are in my mind pathological.

/Fredrik

 

[DarMM]

If anybody wants a description of the third version of the argument.

In essence we have two observers $C, D$ and two superobservers $A, B$.
$C, D$ share a pair of spin-$\frac{1}{2}$ particles, $p_1,p_2$, in the Bell state:
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$$
They measure the spin at angles they choose associated with operators $\hat{C}_c, \hat{D}_d$.

Once the measurements are complete, the superobservers $A, B$ then apply a unitary to the $(C, p_1, D, p_2)$ system to reset everything to its original state and then measure their own spin angles $\hat{A}_a, \hat{B}_b$.

This is then repeated over and over again, so one builds up a joint probability distribution $\rho(a,b,c,d)$. The existence of a joint probability distribution then implies for the marginals:
$$|E(a,b) + E(b,c) + E(c,d) - E(a,d)| \leq 2$$

Which contradicts the normal properties of the Bell state which violates these inequalities.

Ultimately the third version of the FR theorem states that being able to reverse measurements on Bell states results in a contradiction with respect to their usual statistics, it would render their statistics classical. Also note that no one observer has knowledge of each outcome $a,b,c,d$.

In this version there are four* ways out:

1. There are systems that cannot be reversed to their initial states by a unitary time evolution, particularly certain measurements at least. Unitary evolution is not universally valid.
2. Multiple Worlds.
3. Quantum Mechanics is only about what can be measured by a single observer/from a single Boolean frame. Since nobody can experience all of $a,b,c,d$, the statistics of them together are meaningless.
4. One of the Marginals do not obey the quantum predictions and thus it is true that $|E(a,b) + E(b,c) + E(c,d) - E(a,d)| \leq 2$. This would be an experimental disagreement with QM. Some retrocausal theories might allow this.

*there are in the Nature version of Frauchiger-Renner as well, but it's not as obvious as they only mention three. The fourth is the one stevedaryl has mentioned

 

[DarMM]

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

I've a read a good few papers discussing the result now. What the result actually shows is an inconsistency with multi-agent reasoning when considering subjective collapse. Subjective collapse being that a (sealed) observer can use collapse to update their state, but it is still valid for superobservers outside of the observers' labs to use superposition.

So either you have objective collapse (as you discussed above) and superobservers should model other observers post-measurement via mixed states. Or there is no collapse and in some scenarios one is wrong to consider oneself collapsed. Or one simply rejects standard methods of reasoning between agents in QM, i.e. modal logic cannot be applied consistently and you shouldn't consider other agent's conclusions in QM, essentially because QM is about what one observer should expect, not objective reality.

The result however is not philosophy in my opinion. It does show a situation where, under the assumption QM is about objective reality in some sense, relative state formulations like Bohmian Mechanics and Many-Worlds will give different predictions to models with objective collapse. This means Bohmian Mechanics and Many-Worlds are not just interpretations of the same theory as those of objective collapse views like the minimal statistical view and Ballentine (if I understand them correctly). It means there are two quantum formalisms and we now have a scenario with a predicted difference in their results.

Objective collapse and no-collapse give different results in the Frauchiger-Renner case. Subjective collapse gives contradictory results unless you confine QM to being a single-user theory. I do think this is a significant find for this reason (currently anyway until somebody updates my probability of this with a convincing argument! )

For more on this exposition of the Frauchiger-Renner result see here:
https://arxiv.org/abs/1611.01111
https://arxiv.org/abs/1710.07212

 

[kith]

While looking for something else I just stumbled upon the following answer to Frauchiger-Renner which claims that decoherence resolves the alleged problems:
https://arxiv.org/abs/1810.07065

I don't have time to read it right now but it may be of interest for the discussion here. A quick look on the other papers of the author gives him enough initial credibility to take him serious (he has published in the field of decoherence).

 

[DarMM]

While looking for something else I just stumbled upon the following answer to Frauchiger-Renner which claims that decoherence resolves the alleged problems:
https://arxiv.org/abs/1810.07065

I don't have time to read it right now but it may be of interest for the discussion here. A quick look on the other papers of the author gives him enough initial credibility to take him serious (he has published in the field of decoherence).

Unless I'm mistaken he's saying some of the observers can't reach their conclusions because they don't know if mixtures they receive are proper or improper.

I think that's the point of agreeing on the experimental layout in advance.

 

[stevendaryl]

The result however is not philosophy in my opinion. It does show a situation where, under the assumption QM is about objective reality in some sense, relative state formulations like Bohmian Mechanics and Many-Worlds will give different predictions to models with objective collapse. This means Bohmian Mechanics and Many-Worlds are not just interpretations of the same theory as those of objective collapse views like the minimal statistical view and Ballentine (if I understand them correctly). It means there are two quantum formalisms and we now have a scenario with a predicted difference in their results.

I agree with that. People often say that Many-Worlds, Bohmian mechanics and Copenhagen are different interpretations of the same theory, and so by definition, they can't be distinguished by experiment. To me, they are slightly different theories, not different interpretations of the same theory. So they potentially could be distinguished by experiment. However, the circumstances where they might make different predictions happen to be circumstances where it is infeasible to make precise predictions (circumstances involving huge numbers of particles interacting), so in practice, they don't make different predictions, even though in principle they do.

 

[akvadrako]

so in practice, they don't make different predictions, even though in principle they do.

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work. It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

 

[Demystifier]

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work.

If someone survives thousand times in a row, one can explain it without MWI by using the anthropic argument: "If I haven't survived I woldn't be there to observe it." Do you find this argument vague?

 

[Demystifier]

It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

Why no adherent of MWI has actually performed that experiment?

 

[DarMM]

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work. It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

Related to the Pusey-Leifer theorem and other recent work in Foundations, assuming no fine tuning they (i.e. Realist interpretations like MWI, Bohmian, Transactional) should also show up in deviations from "regular" QM in the early universe, e.g. CMB or similar.

 

[atyy]

Why no adherent of MWI has actually performed that experiment?

They have. Many times. In other worlds.

 

[mfb]

Why no adherent of MWI has actually performed that experiment?

They want to stay alive in many worlds, not just one.

 

[stevendaryl]

so in practice, they don't make different predictions, even though in principle they do.

There is some famous saying along the lines of

In principle, there is no difference between 'in principle' and 'in practice'. In practice, there is.

 

[akvadrako]

If someone survives thousand times in a row, one can explain it without MWI by using the anthropic argument: "If I haven't survived I woldn't be there to observe it." Do you find this argument vague?

I would say anthropic reasoning is totally invalid for future events, assuming there is only a single world. Sure, after the fact you can use it and it wouldn't tell you much.

But if you make your predictions beforehand I think you can use bayesian reasoning. If MWI is true, I expect to survive an event with certainty, $p_\text{MW} = 1$. If it's false, it's $p_\text{1W} < 1$. So survival of an event is evidence of multiple worlds. Not much evidence, but if I'm still around in a million years it's either incredible luck (which has a very low prior) or there's a force of nature that makes it more likely than you would expect based on classical reasoning. To make it more clear, if you survive an infinite number of events, the odds that it's due to lucky quantum outcomes is 0.

Why no adherent of MWI has actually performed that experiment?

You wouldn't see evidence of others performing it. You have to perform it yourself and I would say we all are doing it right now just by living.

 

[StevieTNZ]

A link to a presentation by one of the authors, made on this thought experiment if anyone is interested:
https://www.video.ethz.ch/speakers/...oExmHKbHOT7fw62pctqqZJlz3Q9ZReWi89TiqKAO1UQzk